This paper addresses the job shop scheduling problem including time lag constraints. This is an extension of the job shop scheduling problem with many applications in real production environments, where extra delays can be introduced between successive operations of the same job. It belongs to a category of problems known as NP-hard problem due to large solution space. Biogeography-based optimization is an evolutionary algorithm which is inspired by the migration of species between habitats, recently proposed by Simon in 2008 (...) to optimize hard combinatorial optimization problems. We propose a hybrid biogeography-based optimization algorithm for solving the job shop scheduling problem with additional time lag constraints with minimization of total completion time. In the proposed HBBO, the effective greedy constructive heuristic is adapted to generate the initial population of habitat. Moreover, a local search metaheuristic is investigated in the mutation step in order to ameliorate the solution quality and enhance the diversity of the population. To assess the performance of HBBO, a series of experiments on well-known benchmark instances for job shop scheduling problem with time lag constraints is performed. (shrink)

Merging logic and mathematics in deductive inference-an innovative, cutting-edge approach. Optimization methods for logical inference? Absolutely, say Vijay Chandru and John Hooker, two major contributors to this rapidly expanding field. And even though "solving logical inference problems with optimization methods may seem a bit like eating sauerkraut with chopsticks... it is the mathematical structure of a problem that determines whether an optimization model can help solve it, not the context in which the problem occurs." Presenting powerful, proven (...) optimization techniques for logic inference problems, Chandru and Hooker show how optimization models can be used not only to solve problems in artificial intelligence and mathematical programming, but also have tremendous application in complex systems in general. They survey most of the recent research from the past decade in logic/optimization interfaces, incorporate some of their own results, and emphasize the types of logic most receptive to optimization methods-propositional logic, first order predicate logic, probabilistic and related logics, logics that combine evidence such as Dempster-Shafer theory, rule systems with confidence factors, and constraint logic programming systems. Requiring no background in logic and clearly explaining all topics from the ground up, Optimization Methods for Logical Inference is an invaluable guide for scientists and students in diverse fields, including operations research, computer science, artificial intelligence, decision support systems, and engineering. (shrink)

The high traffic density of railway line causes ballasted track to be extremely busy, and thus it is particularly important to improve the efficiency during railway maintenance. The changing law of dynamic characteristics of ballast bed during operation for the dynamic track stabilizer is conducive to optimize simulation analysis of the vehicle-track system, so as to provide an optimized choice of operating parameters for promoting the pertinence and efficiency of dynamic track stabilizer. This paper presents the acceleration response of (...) vehicle-track-subgrade system during operation of a WD-320 dynamic track stabilizer and proposes the range of effective operating parameters. Then, the influence of operating parameters on the dynamic characteristics of the ballast bed is discussed for searching the optimal operating parameters under the single factor influence. Finally, the change laws including the support stiffness, damping, lateral resistance, and subsidence for the ballast bed are studied, and a parameterized model for dynamic characteristics of the ballast bed which can optimize the selection for operating parameters is constructed, rendering an effective reference variable for improving the simulation accuracy of the vehicle-track coupling system. (shrink)

Mental representations have continuous as well as discrete, combinatorial properties. For example, while predominantly discrete, phonological representations also vary continuously; this is reflected by gradient effects in instrumental studies of speech production. Can an integrated theoretical framework address both aspects of structure? The framework we introduce here, Gradient Symbol Processing, characterizes the emergence of grammatical macrostructure from the Parallel Distributed Processing microstructure (McClelland, Rumelhart, & The PDP Research Group, 1986) of language processing. The mental representations that emerge, Distributed Symbol Systems, (...) have both combinatorial and gradient structure. They are processed through Subsymbolic Optimization–Quantization, in which an optimization process favoring representations that satisfy well-formedness constraints operates in parallel with a distributed quantization process favoring discrete symbolic structures. We apply a particular instantiation of this framework, λ-Diffusion Theory, to phonological production. Simulations of the resulting model suggest that Gradient Symbol Processing offers a way to unify accounts of grammatical competence with both discrete and continuous patterns in language performance. (shrink)

A pioneering look at the fundamental role of logic in optimizationand constraint satisfaction While recent efforts to combine optimization and constraintsatisfaction have received considerable attention, little has beensaid about using logic in optimization as the key to unifying thetwo fields. Logic-Based Methods for Optimization develops for thefirst time a comprehensive conceptual framework for integratingoptimization and constraint satisfaction, then goes a step furtherand shows how extending logical inference to optimization allowsfor more powerful as well as flexible modeling (...) and solutiontechniques. Designed to be easily accessible to industryprofessionals and academics in both operations research andartificial intelligence, the book provides a wealth of examples aswell as elegant techniques and modeling frameworks ready forimplementation. Timely, original, and thought-provoking,Logic-Based Methods for Optimization: * Demonstrates the advantages of combining the techniques inproblem solving * Offers tutorials in constraint satisfaction/constraintprogramming and logical inference * Clearly explains such concepts as relaxation, cutting planes,nonserial dynamic programming, and Bender's decomposition * Reviews the necessary technologies for software developersseeking to combine the two techniques * Features extensive references to important computationalstudies * And much more. (shrink)

For companies involved in the supply chain, proper warehousing management is crucial. Warehouse layout arrangement and operation play a critical role in a company’s ability to maintain and improve its competitiveness. Reducing costs and increasing efficiency are two of the most crucial warehousing goals. Deciding on the best warehouse layout is a remarkable optimization problem. This paper uses an optimization method to set bin allocations within an automated warehouse with particular characteristics. The warehouse’s initial layout and the (...) automated platforms limit the search and define the time required to move goods within the warehouse. With the help of historical data and the definition of the time needed to move goods, a mathematical model of warehouse operation was created. An optimization procedure based on the well-known Variable Neighbourhood Search algorithm is defined and applied to the problem. Experimental results demonstrate increments in the efficiency of warehousing operations. (shrink)

Dry port construction can reduce the cost of container transportation, and its location is the focus of existing research. Considering dry port capacity limitations and scale advantages, this study calculates the costs associated with dry port construction and operations, transportation, time, and the environment and constructs a joint optimization model of the dry port location and transportation scheme to minimize the total cost. Taking 35 prefecture-level cities in Northeast China as the source of container goods and Dalian port as (...) the destination, this study conducts an empirical analysis using the Gurobi 9.0.2 optimizer of the AMPL software to solve the problem and takes the minimum total cost as the goal to select the best dry port and container transshipment scheme. The research draws the following conclusions. Seven dry ports also need to be built in the road-rail mode, which shares 82.76% of the container transshipment volume, to reduce the total transportation cost by approximately 21.67%. Although multimodal transport through dry ports increases the time cost slightly, it can significantly reduce the economic and environmental costs of container transportation. (shrink)

This article presents a simple derivation of optimization models for reaction networks leading to a generalized form of the mass-action law, and compares the formal structure of Minimum Information Divergence, Quadratic Programming and Kirchhoff type network models. These optimization models are used in related articles to develop and illustrate the operation of ontology alignment algorithms and to discuss closely connected issues concerning the epistemological and statistical significance of sharp or precise hypotheses in empirical science.

Based on the Internet of Things technology, this paper proposes building a cross-border e-commerce logistics supervision system and determines the evaluation index system from the overall framework design of the system, supply chain supervision process optimization, risk supervision optimization, and system order degree optimization. First of all, the framework adopts the national certification center to supervise the logistics service platform and logistics service platform to supervise the logistics participants of the secondary supervision system. Then, functions such as (...) swarm intelligence contract, legal anonymous identity authentication, intelligent transaction matching, abnormal data analysis and detection, privacy protection, and traceability are realized under the framework of the supervision system. Then, the security analysis and transaction supervision component software are used to verify the security, control, and operating efficiency of the transaction supervision framework. Finally, in a real crowd sourcing logistics enterprise platform to run on the software component, the actual measurement, the measured results show that the proposed cross-border supervision system is safe and controllable, and electronic business logistics protects users and data privacy, prevents forgery and fraud, and realizes the user behavior and user data in addition to auditability and traceability. (shrink)

Wheels are the key components of a train, and the shape of the wheel flange should be maintained to ensure the security of train operations. As a method to maintain the shape at the cost of the diameter size, reprofiling has significant impacts on the lifecycle of a train. A wheel model is built in this paper based on the analysis of the wheel wear features and datasets from Taiyuan locomotives. With the decision variables T i, T i ′, which (...) describe the reprofiling strategy, we formulate a multiobjective optimization problem simultaneously minimizing the reprofiling numbers and maximizing the serving years. To find the solutions of the multiobjective model, the NSGA-II is extended with an alteration of the crowding distance calculation and genetic operators. The improved NSGA-II performs better than other approaches. Meanwhile, outstanding solutions with longer servicing years and less reprofiling are listed in this paper. Our study reveals the relationship between the diameter, flange thickness, and their individual attrition rates and proposes a wear model, multiobjective model, and improved NSGA-II. Compared with existing reprofiling strategies, the strategy recommended in our work can significantly increase the lifecycle of the wheel coupled with a low repair frequency. (shrink)

GIS is important equipment in the substation system in a complex microgrid network. Due to the long-term service in harsh operation environments, the electrical performance of GIS equipment will be seriously affected. Therefore, the regular maintenance of GIS equipment in the substation system is a routine task so as to ensure the normal operation of the microgrid networks. The traditional method relies on manual labor, where not only with the low operation efficiency but also regarding some maintenance, (...) labors cannot reach the inside of the GIS equipment, which seriously restricted the completion of GIS equipment maintenance operation. Based on the above analysis, a basic configuration of a GIS equipment maintenance robot with smart structure, convenient control, and stable motion characteristic has been proposed in this paper. Through the optimization design of the chassis adsorption system, the GIS inspection robot can achieve hanging and vertical adsorption inside the GIS equipment and some special motion status. In this way, the entire GIS equipment can be inspected without blind spots. Through establishing the mechanical model of the GIS inspection robot under the hanging and vertical motion state, the robustness and stability of the GIS inspection robot in the special status have been analyzed, and the corresponding GIS inspection robot robust stability motion control method has also been proposed. Finally, through the integrated design of mechanical system and hardware and software control system, the GIS inspection robot physical prototype system has been developed and the maintenance operation experiment has been carried out in Hunan Electric Power Company Maintenance Company through simulating the internal GIS equipment. The physical prototype can realize the basic movement and special movement in internal GIS equipment without any blind spots and complete the inspection task of GIS equipment operation; the movement of GIS robot is dexterous and stable in the whole operation process, which has strong robust stability. The research of GIS inspection robot in the complex microgrid networks has important theoretical significance and practical application value for the intelligent operation and maintenance management of substation system in complex microgrid networks. (shrink)

In the chemical production process, the temperature of the continuous reactor has nonlinear characteristics such as large inertia. An improved autodisturbance control method is proposed. By improving the tracking differentiator with adjustable parameters, the expanded state observer and the control structure obtained an improved automatic disturbance rejection control model and realized the optimal control of the nonlinear and large-delay systems. On the process control training system, the experiment of the continuous system process flow is compared with the anti-interference of the (...) Smith predictive compensation system, which uses an optimal set of data. The reactor temperature fluctuates, but the self-resistance is improved. The optimal overshoot of the disturbance is close to 0. Compared with the original antidisturbance controller, the antidisturbance time is not affected by the number of iterations, which reduces the high requirements on the accuracy of the parameters. Therefore, the improved automatic disturbance rejection control improves the operation and enhances the ability to resist external disturbance that changes the controlled object. (shrink)

Application of the reliability of repairable systems on solving problems from constructing production systems takes an important place in the process of finding the optimal solution among the suggested system choices. The basic hypothesis when using the reliability of the repairable systems is that every machine is representing a component, a fact that is debatable when talking about technical sciences. However, considering the second assumption of the stationary process, the function of the availability is introduced. It represents the measure between (...) the reliability and the benefit of maintaining the components and the system as a whole one. An additional and the last reason for analyzing constructing machine as a whole one has an economic reason. From the aspect of the total cost and the capacity of the system, the function of the availability is catching more and more impact in the process of determinating the total cost in bill of quantities as the most important part of tender documents. Until former works, techno-economic optimisation usually ran over when choosing the system of the construction machines. In the work, there are shown the methodologies for gathering and analyzing the indicators of availabilities per unit of a company's machine park. The time of demission and reparation have been investigated among 34 components in the period of 6 years. Based on the obtained result for different conditions of machine exploitation and facilities, it is suggested the methodology of the future behaviour of the corresponding within the model optimization availability of constructing production system with the aim of eliminating extra criterion. The suggested model takes in consideration the total cost of the components when they are functional, and when they are not. This kind of approach enables the one who take choices decision of the height of profits, in the lenght of work in function of the projection of cash flow and managing with real indicators of functioning the system at the project level. Given the fact that the maintanance policy of machines is based on availability, and not on reliability of components, with the aim of maximizing the availability of different budget scenarios, a logical approach to the selection of the objective function in the terms of management of construction production systems is to minimize costs for a given availability of system constructing machinery is based on the use of historical data base with the values of the operational availability of components, conditions in which they function, in the process of forecasting the project availability for projects that follow. Ranking variant solutions is the result of the adopted function of the aim as a consequence due to enlargement methods of availability for serial parallel systems with the associated restrictions. For optimal system availability is taken a value that belongs to minimal total cost. However, it is predicted that after the end of the financial year, the real and projected indicators of system functions get compared to each other. Informational support to the proposed model is informational company system, which was built in the PHP programming language on the Linux software platform, and with data based in My SQL. The suggested model is tested on the system for the production and embedding bitumen bound materials on the specific project. Obtained results confirm the assumptions used in work. (shrink)

In this paper, the optimization of the enterprise HR information system is studied based on IoT first-off technology, the system demand phase is analysed, and the edge control system is designed and built. The hardware and software system and edge node management platform are implemented first, and then the communication scenarios between the edge layer of the system and the sensing layer, the edge layer, and the cloud layer are analysed, and the business type-driven link selection algorithm and the (...) northbound multilink switching algorithm are designed and implemented, respectively, to guarantee the communication reliability between different layers of the system. Based on the implementation of the above functions, the edge control system can meet the intelligence, expandability, and security requirements of IoT applications. An in-depth investigation and research are launched mainly on the enterprise demand to determine the functional requirements and performance requirements of the enterprise and to achieve the basic logical structure; in the system design phase, the system architecture and other aspects of the design are realized. According to the conditions of the system function structure, a number of system module functions are designed in detail. The system is composed of the following modules, namely, personnel change management, organization management, and salary and benefits management. The system consists of the following modules, namely, personnel change management, organization management, compensation and benefits management, and personnel information management. The system modules run through the process of human resource management; in the system implementation stage, the system coding and page operation are realized based on the development tools and software development techniques. The system finally achieves the system design objectives and is put on a trial operation to meet its actual business requirements. (shrink)

An improved variant of the Jaya optimization algorithm, called Jaya2, is proposed to enhance the performance of the original Jaya sacrificing its algorithmic design. The proposed approach arranges the solutions in a ring topology to reduce the likelihood of premature convergence. In addition, the population size reduction is used to automatically adjust the population size during the optimization process. Moreover, the translation dependency problem of the original Jaya is discussed, and an alternative solution update operation is proposed. (...) To test Jaya2, we compare it with nine different optimization methods on the CEC 2020 benchmark functions and the CEC 2011 real-world optimization problems. The results show that Jaya2 is highly competitive on the tested problems where it generally outperforms most approaches. Having an easy-to-implement approach with little parameter tuning is highly desirable since researchers from different disciplines with basic programming skills can use it to solve their optimization problems. (shrink)

Economic dispatch plays an important role in power system operation, since it can decrease the operating cost, save energy resources, and reduce environmental load. This paper presents an improved particle swarm optimization called biogeography-based learning particle swarm optimization for solving the ED problems involving different equality and inequality constraints, such as power balance, prohibited operating zones, and ramp-rate limits. In the proposed BLPSO, a biogeography-based learning strategy is employed in which particles learn from each other based on (...) the quality of their personal best positions, and thus it can provide a more efficient balance between exploration and exploitation. The proposed BLPSO is applied to solve five ED problems and compared with other optimization techniques in the literature. Experimental results demonstrate that the BLPSO is a promising approach for solving the ED problems. (shrink)

Effective and personalized treatment relies heavily on skin disease categorization. In the stratification of skin disorders, it is crucial to identify the subtypes of illnesses to provide an efficient therapy. To attain this aim, researchers have focused their attention on cluster algorithms for the stratification of skin disorders in recent decades. But, cluster algorithms have real-world drawbacks, including experimental noises, a large number of dimensions, and a poor ability to comprehend. Cluster algorithms, in particular, determine the quality of clusters using (...) a single internal evaluation operation in the majority of cases. A single internal assessment procedure is difficult to design and robust for all datasets, which is a problem. The multi-objective particle swarm obtained high sensitivity in the existing work, but it is not able to anticipate all kinds of classes. An optimized cluster distance parameter for K-means clustering is determined using a hybrid particle swarm and moth flame optimization. Multi-objective is guided by two cluster value indices, including the K-means clustering misclassification rate and neural network classification rate. Hybrid PSO will solve the multi-objective problem to identify the optimal cluster for clustering. On the dermatological dataset from the UCI repository, MATLAB R2020a will be used to evaluate the proposed method. This will be followed by an evaluation of the proposed method’s performance using the cluster evaluation indices. (shrink)

Packing optimization problems have a wide spectrum of real-word applications. One of the applications of the problems is problem of placement of containers with spent nuclear fuel on the storage platform. The solution of the problem can be reduced to the solution of the problem of finding the optimal placement of a given set of congruent circles into a multiconnected domain taking into account technological restrictions. A mathematical model of the prob-lem is constructed and its peculiarities are considered. Our (...) approach is based on the mathematical modelling of rela-tions between geometric objects by means of phi-function technique. That allowed us to reduce the problem solving to nonlinear programming. Today, an important scientific problem is the problem of creating conditions for safe storage of spent nuclear fuel. In the process of creating any dry spent nuclear fuel storage, the following main stages can be identified: site selection, storage design, construction, operation and decommissioning. A full check for compliance of the repository and its elements with these standards usually begins at the design stage. At the stage of site selection, the inspection for compliance with safety standards is carried out only in terms of the impact of the repository as a whole on the environment. This approach cannot be considered fully appropriate, because, taking into account, for example, all the climatic features of the future storage site, it is possible to adjust the thermal storage regimes of spent nuclear fuel. Similarly, it can be considered necessary to analyze and select the shape of the storage site in order to accommo-date the maximum possible number of spent fuel containers. Such a choice, obviously, should be made taking into ac-count the norms of nuclear, radiation and thermal safety, as well as in compliance with technological limitations. The problem of finding the optimal placement of containers taking into account the given technological limitations can be formulated in the form of the problem of optimization of geometric design. Therefore, the purpose of the study is to build a mathematical model of the problem and study its characteristics to develop effective methods of solution. The proposed approach is based on mathematical modeling of relations between geometric objects using the method of phi-functions. This allowed to reduce the solution of the problem to the problem of nonlinear programming. (shrink)

Four hundred seventy-six nuclear power plants are in operation or under construction around the world. Are concepts for designing and operating plants safely sufficient? Conventional approaches are premised on expectations of predictability and control of radiation release and on assumptions that plant operations are closed systems. Field observations in the industry find, however, that the periodic necessity to refuel, test safety equipment, and continuously upgrade plant designs introduces challenges to control not originally calculated. The social and cultural contexts of (...) markets, regulation, and work systems create additional contingencies. In this dynamic environment, reactor operations produce invaluable data about the states of the entire technology and organizational system. Rereading these dynamics as "experiments" suggests an alternative epistemol ogy that synthesizes science's values of doubt, discovery, and documentation with engineering's values of efficiency, optimization, and problem solving. This redefines plant-based risk handlers as ethologists, geologists, and anthropologists of an ecology of visible and invisible hazards. (shrink)

For enhancing the stability of the microgrid operation, this paper proposes an optimization model considering the small-signal stability constraint. Due to the nonsmooth property of the spectral abscissa function, the droop controller parameters’ optimization is a nonsmooth optimization problem. The Sequential Quadratic Programming with Gradient Sampling is implemented to optimize the droop controller parameters for solving the nonsmooth problem. The SQP-GS method can guarantee the solution of the optimization problem globally and efficiently converges to stationary (...) points with probability of one. In the current iteration, the gradient of the nonsmooth function can be evaluated on a set of randomly generated nearby points by computing closed-form sensitivities. A test on the microgrid system shows that the optimality and the efficiency of the SQP-GS are better than those of the heuristic algorithms. (shrink)

Resource saving has become an integral aspect of manufacturing in industry 4.0. This paper proposes a multisystem optimization algorithm, inspired by implicit parallelism of heuristic methods, to solve an integrated production scheduling with resource saving problem in textile printing and dyeing. First, a real-world integrated production scheduling with resource saving is formulated as a multisystem optimization problem. Then, the MSO algorithm is proposed to solve multisystem optimization problems that consist of several coupled subsystems, and each of the (...) subsystems may contain multiple objectives and multiple constraints. The proposed MSO algorithm is composed of within-subsystem evolution and cross-subsystem migration operators, and the former is to optimize each subsystem by excellent evolution operators and the later is to complete information sharing between multiple subsystems, to accelerate the global optimization of the whole system. Performance is tested on a set of multisystem benchmark functions and compared with improved NSGA-II and multiobjective multifactorial evolutionary algorithm. Simulation results show that the MSO algorithm is better than compared algorithms for the benchmark functions studied in this paper. Finally, the MSO algorithm is successfully applied to the proposed integrated production scheduling with resource saving problem, and the results show that MSO is a promising algorithm for the studied problem. (shrink)

The widespread use of Internet technology has changed people’s traditional life mode and created a new market transaction mode, namely, e-commerce platform. The Internet of Things can carry out real-time monitoring and management of any product in e-commerce and not only can realize information sharing in commercial activities but also can play a greater role in the protection of personal and enterprise information security. In this context, the efficiency and low cost of information flow, cash flow, logistics, and human resources (...) among enterprises are particularly important. The Internet of Things technology is a means to effectively improve and optimize the operation mode of the supply chain. This paper analyzes the status of traditional supply chain management, which discusses the development of a supply chain management based on the Internet of Things technology. Finally, this paper analyzes how to realize the optimization strategy of e-commerce supply chain management based on the Internet of Things technology, which provides strong support for the informatization of e-commerce supply chain management. Through the application of the Internet of Things technology, small- and medium-sized enterprises can optimize the workflow and circulation links of the e-commerce supply chain management, enhance the matching level of product value and information transmission, improve the supply chain operation mechanism, and increase economic benefits. (shrink)

With the rapid development of the Internet information age, social networks, mobile Internet, and e-commerce have expanded the scope of Internet applications. The “big data” era is a challenge and chance for companies and has a great impact on social economy, politics, culture, and people’s lives. An accurate marketing system is developed based on J2EE, and the architecture is selected from the user layer, business logic layer, and data layer and the B/S3 layer application, including three layers of crip-dm and (...) semma. And, other process methods are used. Data-mining-based marketing system information solutions consist of several parts, such as requirement analysis, design, implementation, and testing. This paper introduces data mining technology to the marketing business based on the practical use and design IT solutions for precision marketing, attribute selection tools, attribute analysis tools, modeling prediction tools, and others. This paper introduces a precision marketing system based on data mining technology. The system passes the actual test and the deployment and the operation of this system are confirmed. The system, which can improve marketing activity, is tested, and the development and operation of this system markedly increase the company’s earnings. (shrink)

Major events such as the COVID-19 pandemic, Olympic Games, and G20 Summit bring about supplier disruption risks and challenges to supply chain management. To help deal with these risks, a virtual dual-sourcing production-inventory system can be deployed. In this paper, we study such a system which consists of a raw material supplier, a manufacturer, and a virtual dual-sourcing contingency supplier. The manufacturer needs to determine the production, procurement, and inventory plan of raw materials. When its supplier is interrupted, the manufacturer (...) may need to adjust the production and inventory plan and work with the contingency supplier. We develop a system dynamics method to simulate the operations in this production-inventory system to identify the approximately optimal order-up-to-level inventory policies. We find that the virtual dual production-inventory strategy can be the optimal contingency policy to deal with supplier dynamic disruption risks. Furthermore, for disruption risk with low frequency and long duration, the manufacturer should increase the safety inventory level before the disruption. Otherwise, it should increase the safety inventory level in every cycle. (shrink)

This article evaluates learners’ thinking in the complex environment of teaching level and cognitive construct process and examines learners within the framework of cognitive factors, as well as the degree of consistency in the training process, in the social practice as the teaching of teachers and students to provide timely and dynamic feedback, first of all to “evidence centered” education evaluation of design patterns and cognitive framework theory as the theoretical basis. An evaluation model based on learners’ cognitive network analysis (...) is designed and constructed by integrating cognitive visualization analysis techniques such as network analysis. Secondly, at the beginning of action research, the teaching framework structure sequence is established under the guidance of the implementation model of flipped classroom, and the investigation results of the current situation are designed under the guidance of operational steps and organizational strategies, and categories and autonomous learning theories are divided, so as to preliminarily construct strategies to improve the ability of autonomous learning. Then through three rounds of iterative action research to improve the flip classroom teaching middle school students’ autonomous learning ability of teaching strategy, the interview method is used; the questionnaire and autonomous learning process to improve the students’ autonomous learning ability training effect evaluation questionnaire is analyzed, and finally a complete set of reverse ascending of classroom teaching is formed to improve students’ autonomous learning ability of effective classroom strategies. (shrink)

A comprehensive introduction to optimization with a focus on practical algorithms for the design of engineering systems. This book offers a comprehensive introduction to optimization with a focus on practical algorithms. The book approaches optimization from an engineering perspective, where the objective is to design a system that optimizes a set of metrics subject to constraints. Readers will learn about computational approaches for a range of challenges, including searching high-dimensional spaces, handling problems where there are multiple competing (...) objectives, and accommodating uncertainty in the metrics. Figures, examples, and exercises convey the intuition behind the mathematical approaches. The text provides concrete implementations in the Julia programming language. Topics covered include derivatives and their generalization to multiple dimensions; local descent and first- and second-order methods that inform local descent; stochastic methods, which introduce randomness into the optimization process; linear constrained optimization, when both the objective function and the constraints are linear; surrogate models, probabilistic surrogate models, and using probabilistic surrogate models to guide optimization; optimization under uncertainty; uncertainty propagation; expression optimization; and multidisciplinary design optimization. Appendixes offer an introduction to the Julia language, test functions for evaluating algorithm performance, and mathematical concepts used in the derivation and analysis of the optimization methods discussed in the text. The book can be used by advanced undergraduates and graduate students in mathematics, statistics, computer science, any engineering field, (including electrical engineering and aerospace engineering), and operations research, and as a reference for professionals. (shrink)

In the automatic detection of epileptic seizures, the monitoring of critically ill patients with time varying EEG signals is an essential procedure in intensive care units. There is an increasing interest in using EEG analysis to detect seizure, and in this study we aim to get a better understanding of how to visualize the information in the EEG time-frequency feature, and design and train a novel random forest algorithm for EEG decoding, especially for multiple-levels of illness. Here, we propose an (...) automatic detection framework for epileptic seizure based on multiple time-frequency analysis approaches; it involves a novel random forest model combined with grid search optimization. The short-time Fourier transformation visualizes seizure features after normalization. The dimensionality of features is reduced through principal component analysis before feeding them into the classification model. The training parameters are optimized using grid search optimization to improve detection performance and diagnostic accuracy by in the recognition of three different levels epileptic of conditions (healthy subjects, seizure-free intervals, seizure activity). Our proposed model was used to classify 500 samples of raw EEG data, and multiple cross-validations were adopted to boost the modeling accuracy. Experimental results were evaluated by an accuracy, a confusion matrix, a receiver operating characteristic curve and an area under the curve. The evaluations indicated that our model achieved the more effective classification than some previous typical methods. Such a scheme for computer-assisted clinical diagnosis of seizures has a potential guiding significance, which not only relieves the suffering of patient with epilepsy to improve quality of life, but also helps neurologists reduce their workload. (shrink)

In this paper, we study solution concepts for cooperative games with stochastic payoffs. we define four kinds of solution concepts, namely the most coalitional (marginal) stable solution and the fairest coalitional (marginal) solution, by minimizing the total variance of excesses of coalitions (individual players). All these four concepts are optimal solutions of corresponding optimal problem under the least square criterion. It turns out that the fairest coalitional (marginal) solution belongs to the set of the most coalitional (marginal) stable solutions. Inspired (...) by the definition of nucleolus, we propose various extended nucleolus based on lexicographic criterion. Furthermore, axiomatizations of the proposed solutions are exhibited through the linkage between the stochastic and deterministic models. (shrink)

Offshore micro integrated energy systems are the basis of offshore oil and gas engineering and play an important role in developing and utilizing marine resources. By introducing offshore wind power generation, the carbon emissions of offshore micro integrated energy systems can be effectively reduced; however, greater challenges have been posted to the reliable operation due to the uncertainty. To reduce the influence brought by the uncertainty, a multiobjective optimization model was proposed based on the chance-constrained programming ; the (...) operating cost and penalty cost of natural gas emission were selected as objectives. Then, the improved hybrid constraints handling strategy based on nondominated sorting genetic algorithm II was introduced to solve the model efficiently. Finally, the numerical studies verified the efficiency of the proposed algorithm, as well as the validity and feasibility of the proposed model in improving the economy of OMIES under uncertainty. (shrink)

E-commerce conceivable future trade, consumption, and service is a new digital employer mode. Therefore, in order to decorate the customary natural environment of operation, it is quintessential to get rid of the preferred desktop in the true field, create a social logistics and transportation administration computing device with commodity agents and distributors as the key features, and mix freight logistics, business enterprise approach waft and data waft advertising and marketing, and advertising and marketing organically. The notion of e-commerce logistics (...) looks alongside the enchantment vogue of neighborhood technological knowledge and social demand. It is an integral part of ending e-commerce authentic economic value. All kinds of cell networks clear up the problem of data flow communication; in the technological know-how of telephone network, digital cost solves the bother of capital flow; at present, logistics is however a long-standing problem of e-commerce. Logistics has grown to be the last and entirely bottleneck of e-commerce. If logistics cannot adapt to the enchantment of e-commerce, it may also additionally lead to the slow enchantment of e-commerce. The purpose of this paper is to supply an Internet of things e-commerce logistics cloud provider platform based totally absolutely on cell communication, which can be combined with e-commerce and beautify the transport tempo of e-commerce. This paper moreover optimizes the e-commerce logistics system, so that it can combine with e-commerce to increase out the distribution of goods, the distribution tempo of e-commerce is doubled, and e-commerce can in a similar fashion develop rapidly. (shrink)

In multimodal multiobjective optimization problems, multiple Pareto optimal sets, even some good local Pareto optimal sets, should be reserved, which can provide more choices for decision-makers. To solve MMOPs, this paper proposes an evolutionary algorithm with clustering-based assisted selection strategy for multimodal multiobjective optimization, in which the addition operator and deletion operator are proposed to comprehensively consider the diversity in both decision and objective spaces. Specifically, in decision space, the union population is partitioned into multiple clusters by using (...) a density-based clustering method, aiming to assist the addition operator to strengthen the population diversity. Then, a number of weight vectors are adopted to divide population into N subregions in objective space. Moreover, in the deletion operator, the solutions in the most crowded subregion are first collected into previous clusters, and then the worst solution in the most crowded cluster is deleted until there are N solutions left. Our algorithm is compared with other multimodal multiobjective evolutionary algorithms on the well-known benchmark MMOPs. Numerical experiments report the effectiveness and advantages of our proposed algorithm. (shrink)

Service process optimization is conducive to the innovation of enterprise services, but the poor logic design of multiple touchpoints can easily lead to problems in the service process, such as scattered layouts and repeated paths. Aiming at the promotion of service innovation and user experience, this paper takes the optimization of a single service touchpoint as the prerequisite and proposes a service process optimization method based on service touchpoint association and the design structure matrix. The association of (...) service touchpoints is categorized into two types, namely, noncoupled and coupled association. The DSM is used to describe the two types of association between service touchpoints, and the matrix operation is used for modular identification and layering of the two kinds of association. Finally, through the above steps, the problematic service process was replanned. By using the service process optimization of a new retail convenience store as an example, the service process is divided into 6 relatively independent modules, and the order of module execution is arranged. Moreover, the optimal service process of the convenience store system is determined, and the method is verified to be feasible. Through optimization both from single service touchpoint and service process modularization, the study provides a reference for process optimization of the complex service system. (shrink)

Arithmetic optimization algorithm (AOA) is one of the recently proposed population-based metaheuristic algorithms. The algorithmic design concept of the AOA is based on the distributive behavior of arithmetic operators, namely, multiplication (M), division (D), subtraction (S), and addition (A). Being a new metaheuristic algorithm, the need for a performance evaluation of AOA is significant to the global optimization research community and specifically to nature-inspired metaheuristic enthusiasts. This article aims to evaluate the influence of the algorithm control parameters, namely, (...) population size and the number of iterations, on the performance of the newly proposed AOA. In addition, we also investigated and validated the influence of different initialization schemes available in the literature on the performance of the AOA. Experiments were conducted using different initialization scenarios and the first is where the population size is large and the number of iterations is low. The second scenario is when the number of iterations is high, and the population size is small. Finally, when the population size and the number of iterations are similar. The numerical results from the conducted experiments showed that AOA is sensitive to the population size and requires a large population size for optimal performance. Afterward, we initialized AOA with six initialization schemes, and their performances were tested on the classical functions and the functions defined in the CEC 2020 suite. The results were presented, and their implications were discussed. Our results showed that the performance of AOA could be influenced when the solution is initialized with schemes other than default random numbers. The Beta distribution outperformed the random number distribution in all cases for both the classical and CEC 2020 functions. The performance of uniform distribution, Rayleigh distribution, Latin hypercube sampling, and Sobol low discrepancy sequence are relatively competitive with the Random number. On the basis of our experiments’ results, we recommend that a solution size of 6,000, the number of iterations of 100, and initializing the solutions with Beta distribution will lead to AOA performing optimally for scenarios considered in our experiments. (shrink)

Because of the difficulty of music feature recognition due to the complex and varied music theory knowledge influenced by music specialization, we designed a music feature recognition system based on Internet of Things technology. The physical sensing layer of the system places sound sensors at different locations to collect the original music signals and uses a digital signal processor to carry out music signal analysis and processing. The network transmission layer transmits the completed music signals to the music signal database (...) in the application layer of the system. The music feature analysis module of the application layer uses a dynamic time regularization algorithm to obtain the maximum similarity between the test template and the reference. The music feature analysis module of the application layer uses the dynamic time regularization algorithm to obtain the maximum similarity between the test template and the reference template to realize the feature recognition of the music signal and determine the music pattern and music emotion corresponding to the music feature content according to the recognition result. The experimental results show that the system operates stably, can capture high-quality music signals, and can correctly identify music style features and emotion features. The results of this study can meet the needs of composers’ assisted creation and music researchers’ analysis of a large amount of music data, and the results can be further transferred to deep music learning research, human-computer interaction music creation, application-based music creation, and other fields for expansion. (shrink)

Multiway join queries incur high-cost I/Os operations over large-scale data. Exploiting sharing join opportunities among multiple multiway joins could be beneficial to reduce query execution time and shuffled intermediate data. Although multiway join optimization has been carried out in MapReduce, different design principles are not considered. To bridge the gap of not considering the optimization of Big Data platforms, an end-to-end multiway join over Flink, which is called Join-MOTH system, is proposed to exploit sharing data granularity, sharing join (...) granularity, and sharing implicit sorts within multiple join queries. For sharing data, our previous work, Multiquery Optimization using Tuple Size and Histogram system, has been introduced to consider the granularity of sharing data opportunities among multiple queries. For sharing sort, our previous work, Sort-Based Optimizer for Big Data Multiquery, has been introduced to consider the implicit sorts among join queries. For sharing join, additional modules have been tailored to the J-MOTH optimizer to optimize sharing work by exploiting shared pipelined multiway join among multiple multiway join queries. The experimental evaluation has demonstrated that the J-MOTH system outperforms the naive and the state-of-the-art techniques by 44% for query execution time using TPC-H queries. Also, the proposed J-MOTH system introduces maximal intermediate data size reduction by 30% in average over Hadoop-like infrastructures. (shrink)

Schizophrenia is a serious mental disease whose pathogenesis has not been fully elucidated. Its clinical evaluation and diagnosis still highly depend on the clinical experience of doctors. It is of great scientific value and clinical significance to study the inducing factors and neuropathological mechanism of schizophrenia. Based on the four research problems of schizophrenia, this paper analyzes the data types that need to be stored in clinical trials and scientific research, including basic information, case report data, neuropsychological and cognitive function (...) evaluation, magnetic resonance data, electroencephalogram data, and intestinal flora data. Through the demand analysis of the system, including the data management part, data analysis part, the functional demand of the system management part, and the overall nonfunctional demand of the system, the overall architecture design, functional module division, and database table structure design of the system are completed. Adopting Browser/Server architecture and front-end and back-end separation mode and applying Java and Python programming language, based on spring framework and database, a multidimensional information management system for schizophrenia is designed and implemented, which includes four modules: data analysis, data management, system management, and security control. In addition, each functional module of the system is designed and implemented in detail, and the software operation flow of each module is illustrated with the sequence diagram. Finally, the multidimensional data of schizophrenia collected in our laboratory were used for system test to verify whether the system can meet the needs of clinical big data management of schizophrenia and the multidimensional information management system of schizophrenia can meet the needs of clinical big data management. The information management system helps schizophrenic researchers to carry out data management and data analysis. It also has advantages that are easy to use, safe, and efficient and has strong scalability in data management, data analysis, and scalability. It reflects the innovation of the system and provides a good platform for the management, research, and analysis of clinical big data of schizophrenia. (shrink)

SummaryThe problems of operations research, optimized at the tactical and strategic level, have a domain of interest much broader than many of its earlier suboptimization problems. Its appeal to scientific method requires the construction of a model from which predictions can be made. This model must have the comprehensive character of those proposed by philosophy and the sciences. Such a model is available in the form of war gaming, a traditional military training vehicle transformed in such a way as to (...) make it a research tool of great power and flexibility and which can assume a multitude of forms. The war game as a new research tool, when applied to the important problems at a high level of optimization, carries with it the excitement of a pioneering venture and the promise of contributions of greatly increased importance to the development of military science. (shrink)

A large number of modern communication technologies and sensing technologies are incorporated into the smart grid, which makes its structure unique. The centralized optimized dispatch method of traditional power grids is difficult to achieve effective dispatch of smart grids. Based on the analysis of power generation plan and maintenance plan optimization model, this paper establishes a smart grid power generation and maintenance collaborative optimization model with distributed renewable energy. The objective function of this collaborative optimization problem is (...) the operating cost of conventional units, the cost of wind power generation, and the cost of overhauling units; the constraints considered mainly include system constraints and overhaul constraints. The solution method of combinatorial optimization is analyzed, and the genetic optimization algorithm adopted in this paper is selected and discussed. According to the characteristics of the system, various loads are modeled, and power supply constraints are considered. By establishing an effective objective function, the adjustable load scheduling problem is transformed into a solvable optimal control problem. Taking into account the uncertain factors in the system, the advantage of the real-time control system is that it can realize the dynamic update scheduling of the load, so it is more in line with the requirements of the actual system. The real-time algorithm proposed in the paper is based on a distributed control strategy, which can not only realize dynamic compensation for random fluctuations in renewable energy power generation but also satisfy the load curve optimization under the premise of making full use of power supply resources. In addition, simulation experiments compare the load dispatching capabilities of the proposed algorithm with the existing algorithms, thereby verifying the performance of the proposed method. (shrink)

The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent introduction of new classes of monotones, like injective monotones or strict monotone multi-utilities, we present the classification of preordered spaces in terms of both the existence and cardinality of real-valued monotones and the cardinality of the quotient space. In particular, we take advantage of a characterization of real-valued (...) monotones in terms of separating families of increasing sets to obtain a more complete classification consisting of classes that are strictly different from each other. As a result, we gain new insight into both complexity and optimization, and clarify their interplay in preordered spaces. (shrink)

This article uses a research method that combines theoretical research and empirical analysis. It first introduces the relevant theories of energy service city distribution sites in the context of e-commerce and then the types of energy service city distribution sites and the composition of energy service city distribution systems. The network layout of the service city distribution site and the location objectives, principles, and processes of the model is studied to determine the network layout plan of the energy service city (...) distribution system in this paper. This paper fully considers the characteristics of the network operation mode of the energy service city distribution site and establishes an optimization model for the location selection and vehicle routing of the distribution center with the lowest total system cost under the simultaneous delivery service mode; based on the hierarchical solution strategy, a combination of deep learning is designed. Algorithms mainly include two-stage hybrid heuristic algorithm of cluster analysis, maximum coverage and genetic algorithm; simulation analysis is conducted to verify the effectiveness of the model and algorithm by data simulation, finally get the integrated optimization plan of distribution center location and routing, and put forward the operation strategy through the result expansion analysis. This paper studies the planning model based on the network layout planning of the energy service city distribution system under the e-commerce environment, aiming to promote the breakthrough development of urban smart logistics and prove the importance of the energy service city distribution station network layout planning. The purpose and results of the research are to reduce traffic and environmental pressures, achieve joint direct distribution, improve the efficiency of urban logistics and distribution, and solve the problem of the last mile of the city. (shrink)

For the application of the standard genetic algorithm in illustration art design, there are still problems such as low search efficiency and high complexity. This paper proposes an illustration art design model based on operator and clustering optimization genetic algorithm. First, during the operation of the genetic algorithm, the values of the crossover probability and the mutation probability are dynamically adjusted according to the characteristics of the population to improve the search efficiency of the algorithm, then the k-medoids (...) algorithm is introduced to optimize the clustering of the genetic algorithm, and a cost function is used to carry out and evaluate the quality of clustering to optimize the complexity of the original algorithm. In addition, a multiobjective optimization genetic algorithm with complex constraints based on group classification is proposed. This algorithm focuses on the problem of group diversity and uses k-means cluster analysis operation to solve the problem of group diversity. The algorithm divides the entire group into four subgroups and assigns appropriate fitness values to reflect the optimal preservation strategy. A large number of computer simulation calculations show that the algorithm can obtain a widely distributed and uniform Pareto optimal solution, the evolution speed is fast, usually only a few iterations can achieve a good optimization effect, and finally the improved genetic algorithm is used to design the random illustration art. The example simulation shows that the improved algorithm proposed in this paper can achieve higher artistic and innovative illustration art design. (shrink)

Urbanization poses significant challenges to healthcare systems, including overcrowded hospitals, inequitable access to care, and rising costs. Artificial Intelligence (AI) and the Internet of Things (IoT) offer transformative solutions for optimizing healthcare delivery in smart cities. This paper explores how AI-driven predictive analytics, combined with IoT-enabled wearable devices and telemedicine platforms, can enhance patient outcomes, streamline resource allocation, and reduce urban health disparities. By analyzing real-time health data and predicting disease outbreaks, this study demonstrates the potential of AI to revolutionize (...) urban healthcare systems. Experimental results highlight improvements in diagnostic accuracy, emergency response times, and operational efficiency, paving the way for equitable and sustainable healthcare in smart cities. (shrink)

In a fiercely competitive business landscape, the optimization of supply chain management (SCM) strategies and the integration of robust corporate digital competencies stand as pivotal determinants for sustained success across various industries, including the fast-moving consumer goods (FMCG) sector. The study investigates the dynamic interplay between SCM strategies, corporate digital competencies, and operational performance. Through a hypothesis testing research design, the examination sought to determine the influence of these variables. The study revealed strong support for the hypothesis that SCM (...) strategies significantly impact corporate digital competencies and, in turn, operational performance. The results indicated a direct positive relationship between SCM strategies and operational performance while corporate digital competencies indirectly influenced operational performance through their mediation between SCM strategies and operational effectiveness. The findings underscored the integral role of corporate digital competencies in enhancing the efficacy of SCM strategies, amplifying operational performance, and driving customer-centric value. These implications stress the imperative for businesses to strategically align their SCM processes with digital competencies to effectively navigate market complexities and ensure long-term competitiveness. (shrink)

The economical/environmental scheduling problem of the ship integrated energy system has high computational complexity, which includes more than one optimization objective, various types of constraints, and frequently fluctuated load demand. Therefore, the intelligent scheduling strategies cannot be applied to the ship energy management system online, which has limited computing power and storage space. Aiming at realizing green computing on SEMS, in this paper a typical SIES-EESP optimization model is built, considering the form of decision vectors, the economical/environmental (...) class='Hi'>optimization objectives, and various types of real-world constraints of the SIES. Based on the complexity of SIES-EESPs, a two-stage offline-to-online multiobjective optimization strategy for SIES-EESP is proposed, which transfers part of the energy dispatch online computing task to the offline high-performance computer systems. The specific constraints handling methods are designed to reduce both continuous and discrete constraints violations of SIES-EESPs. Then, an establishment method of energy scheduling scheme-base is proposed. By using the big data offline, the economical/environmental scheduling solutions of a typical year can be obtained and stored with more computing resources and operation time on land. Thereafter, a short-term multiobjective offline-to-online optimization approach by SEMS is considered, with the application of multiobjective evolutionary algorithm and typical schemes corresponding to the actual SIES-EESPs. Simulation results show that the proposed strategy can obtain enough feasible Pareto solutions in a shorter time and get well-distributed Pareto sets with better convergence performance, which can well adapt to the features of real-world SIES-EESPs and save plenty of operation time and storage space for the SEMS. (shrink)

Path selection is one of the key technologies of wireless sensor network. A reasonable choice of coverage path can improve the service quality of WSN and extend the life cycle of WSN. Biogeography-based optimization is widely used in the field of cluster intelligent optimization because its search method has a better incentive mechanism for population evolution. In this paper, the move-in and move-out operation and mutation operation of the BBO algorithm enable WSN to find an efficient (...) routing path. In this paper, simulation experiments are carried out in two scenarios of regular deployment and random deployment of WSN nodes. The experimental results show that the quality of the WSN coverage path solution optimized by the BBO algorithm in the two scenarios is better than that of the particle swarm algorithm and genetic algorithm. (shrink)

The field service scheduling problem is the key problem in field services. Field service pays particular attention to customer experience, that is, customer satisfaction. Customer satisfaction described by customer behavior characteristics based on the prospect theory is considered as the primary optimization goal in this paper. The knowledge of the insertion feasibility on the solution is analysed based on the skill constraint and time window. According to the knowledge, an initialization method based on the nearest heuristic algorithm is constructed. (...) Based on the prior knowledge of the FSSP and the endowment of the Fruit Fly Optimization Algorithm, two operators are defined according to the matrix encoding method. Based on these two operators, three search strategies are then proposed, and the smell-based search strategy and vision-based search strategy for the FOA are redesigned. To verify the performance of the algorithms, the proposed operators and strategies are tested and analysed in the well-known benchmark. Through comparison with the state-of-the-art algorithms, the results show that the proposed HFOA is an effective and efficient method to solve the FSSP with customer satisfaction. (shrink)

This paper introduces Nymity’s Privacy Risk Optimization Process (PROP), a process that enables the implementation of privacy into operational policies and procedures, which embodies in Privacy by Design for business practices. The PROP is based on the International Organization for Standardization (ISO) concept that risk can be positive and negative; and further defines Risk Optimization as a process whereby organizations strive to maximize positive risks and mitigate negative ones. The PROP uses these concepts to implement privacy into operational (...) policies and procedures. This paper was produced by Nymity and the Office of the Information and Privacy Commissioner of Ontario, Canada. It was presented by Terry McQuay, President of Nymity, at Privacy by Design: The Definitive Workshop, in Madrid, Spain, on November 2nd, 2009. The workshop was hosted by Dr. Ann Cavoukian, Information and Privacy Commissioner of Ontario, Canada, and Yoram Hacohen, Head of the Israeli Law, Information and Technology Authority. (shrink)

Based on the concept of “passengers self-help hubbing,” we build a flight schedule optimization model where maximizing the number of feasible flight connections, indicating transfer opportunities, as one objective and minimizing total slot displacements as the other objective. At the same time, the “Demand Smoothing Model” is introduced into the flight schedule optimization model to reduce the queuing delays for arrival and departure flights. We take into account all aircraft itineraries, the difficulty level of schedule coordination, and the (...) maximum displacement of any single flight acceptable to airlines when optimizing flight schedule. Given an original schedule, the model produces a feasible modified schedule that obeys the slot limits specified for an airport without canceling any flights, increases transfer opportunities, and improves on-time performance for hub airports while reducing interference with airline scheduling preferences. The model was verified with the operating data of the Urumqi international airport, and the results show that minor adjustments to flight schedules can increase the transfer opportunities of the airport and significantly reduce flight queuing delays. (shrink)

In an earlier article [Found. Phys. 30, 1191 (2000)], a quasiclassical phase space approximation for quantum projection operators was presented, whose accuracy increases in the limit of large basis size (projection subspace dimensionality). In a second paper [J. Chem. Phys. 111, 4869 (1999)], this approximation was used to generate a nearly optimal direct-product basis for representing an arbitrary (Cartesian) quantum Hamiltonian, within a given energy range of interest. From a few reduced-dimensional integrals, the method determines the optimal 1D marginal Hamiltonians, (...) whose eigenstates comprise the direct-product basis. In the present paper, this phase space optimized direct-product basis method is generalized to incorporate non-Cartesian coordinate spaces, composed of radii and angles, that arise in molecular applications. Analytical results are presented for certain standard systems, including rigid rotors, and three-body vibrators. (shrink)