The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly...The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.展开更多
The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the intera...The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.展开更多
The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attr...The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.展开更多
A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the...A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.展开更多
Management of forest lands considering multi-functional approaches is the basis to sustain or enhance the provi-sion of specific benefits,while minimizing negative impacts to the environment.Defining a desired managem...Management of forest lands considering multi-functional approaches is the basis to sustain or enhance the provi-sion of specific benefits,while minimizing negative impacts to the environment.Defining a desired management itinerary to a forest depends on a variety of factors,including the forest type,its ecological characteristics,and the social and economic needs of local communities.A strategic assessment of the forest use suitability(FUS)(namely productive,protective,conservation-oriented,social and multi-functional)at regional level,based on the provision of forest ecosystem services and trade-offs between FUS alternatives,can be used to develop management strategies that are tailored to the specific needs and conditions of the forest.The present study assesses the provision of multiple forest ecosystem services and employs a decision model to identify the FUS that sup-ports the most present and productive ecosystem services in each stand in Catalonia.For this purpose,we apply the latest version of the Ecosystem Management Decision Support(EMDS)system,a spatially oriented decision support system that provides accurate results for multi-criteria management.We evaluate 32 metrics and 12 as-sociated ecosystem services indicators to represent the spatial reality of the region.According to the results,the dominant primary use suitability is social,followed by protective and productive.Nevertheless,final assignment of uses is not straightforward and requires an exhaustive analysis of trade-offs between all alternative options,in many cases identifying flexible outcomes,and increasing the representativeness of multi-functional use.The assignment of forest use suitability aims to significantly improve the definition of the most adequate management strategy to be applied.展开更多
The motivation for cost-effective management of highway pavements is evidenced not only by the massive expenditures associated with these activities at a national level but also by the consequences of poor pavement co...The motivation for cost-effective management of highway pavements is evidenced not only by the massive expenditures associated with these activities at a national level but also by the consequences of poor pavement condition on road users.This paper presents a state-of-the-art review of multi-objective optimization(MOO)problems that have been formulated and solution techniques that have been used in selecting and scheduling highway pavement rehabilitation and maintenance activities.First,the paper presents a taxonomy and hierarchy for these activities,the role of funding sources,and levels of jurisdiction.The paper then describes how three different decision mechanisms have been used in past research and practice for project selection and scheduling(historical practices,expert opinion,and explicit mathematical optimization)and identifies the pros and cons of each mechanism.The paper then focuses on the optimization mechanism and presents the types of optimization problems,formulations,and objectives that have been used in the literature.Next,the paper examines various solution algorithms and discusses issues related to their implementation.Finally,the paper identifies some barriers to implementing multi-objective optimization in selecting and scheduling highway pavement rehabilitation and maintenance activities,and makes recommendations to overcome some of these barriers.展开更多
The class of multiple attribute decision making (MADM) problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score fun...The class of multiple attribute decision making (MADM) problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.展开更多
From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept: project entropy and the de...From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept: project entropy and the decision is taken according to the values. The validity and scientific nature of the given is proven.展开更多
To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute d...To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy. Firstly, the definitions of the optimal membership and the relative entropy are given. Secondly, for all alternatives, a set of preference weight vectors are obtained by solving a set of linear programming models whose goals axe all to maximize the optimal membership. Thirdly, a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined. Based on this optimal weight vector, the algorithm of deviation degree minimization is proposed to rank all the alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new model.展开更多
According to the aggregation method of experts' evaluation information in group decision-making,the existing methods of determining experts' weights based on cluster analysis take into account the expert's preferen...According to the aggregation method of experts' evaluation information in group decision-making,the existing methods of determining experts' weights based on cluster analysis take into account the expert's preferences and the consistency of expert's collating vectors,but they lack of the measure of information similarity.So it may occur that although the collating vector is similar to the group consensus,information uncertainty is great of a certain expert.However,it is clustered to a larger group and given a high weight.For this,a new aggregation method based on entropy and cluster analysis in group decision-making process is provided,in which the collating vectors are classified with information similarity coefficient,and the experts' weights are determined according to the result of classification,the entropy of collating vectors and the judgment matrix consistency.Finally,a numerical example shows that the method is feasible and effective.展开更多
Performance evaluation of facilities management plays a key role in the facilities management process. This paper proposes an optimized multicriteria decision making model to evaluate the performance of facilities man...Performance evaluation of facilities management plays a key role in the facilities management process. This paper proposes an optimized multicriteria decision making model to evaluate the performance of facilities management in schools in Hong Kong. In this model, entropy weights acted as weight coefficients for evaluated criteria in order to avoid uncertainty and randomicity of subjective judgments. Besides, the TOPSIS method was incorporated in this model. Then this model was em- ployed to evaluate the performance of facilities management in classrooms, offices and laboratories and satisfying results were obtained. Moreover, findings indicated that one of the schools could be rehabilitated rather than removed.展开更多
During the past decade,research efforts have been gradually directed to the widely existing yet less noticed multimodal multi-objective optimization problems(MMOPs)in the multi-objective optimization community.Recentl...During the past decade,research efforts have been gradually directed to the widely existing yet less noticed multimodal multi-objective optimization problems(MMOPs)in the multi-objective optimization community.Recently,researchers have begun to investigate enhancing the decision space diversity and preserving valuable dominated solutions to overcome the shortage caused by a preference for objective space convergence.However,many existing methods still have limitations,such as giving unduly high priorities to convergence and insufficient ability to enhance decision space diversity.To overcome these shortcomings,this article aims to explore a promising region(PR)and enhance the decision space diversity for handling MMOPs.Unlike traditional methods,we propose the use of non-dominated solutions to determine a limited region in the PR in the decision space,where the Pareto sets(PSs)are included,and explore this region to assist in solving MMOPs.Furthermore,we develop a novel neighbor distance measure that is more suitable for the complex geometry of PSs in the decision space than the crowding distance.Based on the above methods,we propose a novel dual-population-based coevolutionary algorithm.Experimental studies on three benchmark test suites demonstrates that our proposed methods can achieve promising performance and versatility on different MMOPs.The effectiveness of the proposed neighbor distance has also been justified through comparisons with crowding distance methods.展开更多
This study is to introduce concepts of energy and entropy to describe a robot's emotion decision.It chooses the dimensional approach based on factors of pleasure and arousal for the merit of the interpolation betw...This study is to introduce concepts of energy and entropy to describe a robot's emotion decision.It chooses the dimensional approach based on factors of pleasure and arousal for the merit of the interpolation between emotions.Especially,Circumplex model which has also two axes:pleasure and arousal is used.Besides,the model indicates how emotions are distributed in the two-dimensional plane.Then by the definition of psychodynamicsthe energy states(mental energy and physical energy)are matched to pleasure and arousal respectively that are the basis of Circumplex model.The mental energy is updated by the result of Prospect theory which measures the value of gain and loss as pleasure factor.And the physical energy is updated by the result of hedonic scaling which measures levels of arousal from pleasure computed by Prospect theory,and the result of intensity of stimuli.Then the energy states are fed by entropy.The feedback loop by entropy satisfies the 2nd law of thermodynamics.The energy states generated by stimuli and fed by entropy take a position in the plane of Circumplex model.Then distances between the current position and other emotions are computed to get a level of each emotion,proportional to the inverse of the distance.展开更多
Proper treatment of weak subgrade soil is very important to building a highway of good quality. We proposed an entropy-based multi-criterion group decision analysis method for a group of experts to evaluate alternativ...Proper treatment of weak subgrade soil is very important to building a highway of good quality. We proposed an entropy-based multi-criterion group decision analysis method for a group of experts to evaluate alternatives of weak subgrade treatment,with an aim to select the optimum technique which is technically,economically and socially viable. We used fuzzy theory to analyze multiple experts' evaluation on various factors of each alterative treatment. Different experts' evaluations are integrated by the group eigenvalue method. An entropy weight is introduced to minimize the negative influences of subjective human factors of experts. The optimum alternative is identified with ideal point discriminant analysis to calculate the distance of each alternative to the ideal point and prioritize all alternatives according to their distances. A case study on a section of the Shiman Expressway verified that the proposed method can give a rational decision on the optimum method of weak subgrade treatment.展开更多
Fuzzy entropy measures are valuable tools in decision-making when dealing with uncertain or imprecise information.There exist many entropy measures for Pythagorean Fuzzy Sets(PFS)in the literature that fail to deal wi...Fuzzy entropy measures are valuable tools in decision-making when dealing with uncertain or imprecise information.There exist many entropy measures for Pythagorean Fuzzy Sets(PFS)in the literature that fail to deal with the problem of providing reasonable or consistent results to the decision-makers.To deal with the shortcomings of the existing measures,this paper proposes a robust fuzzy entropy measure for PFS to facilitate decision-making under uncertainty.The usefulness of the measure is illustrated through an illustration of decision-making in a supplier selection problem and compared with existing fuzzy entropy measures.The Technique for Order Performance by Similarity to Ideal Solution(TOPSIS)approach is also explored to solve the decision-making problem.The results demonstrate that the proposed measure can effectively capture the degree of uncertainty in the decision-making process,leading to more accurate decision outcomes by providing a reliable and robust ranking of alternatives.展开更多
Climate researchers have observed that the carbon dioxide (CO2) concentration in the atmosphere have been growing significantly over the past century. CO2 from energy represents about 75% of the greenhouse gas (GHG...Climate researchers have observed that the carbon dioxide (CO2) concentration in the atmosphere have been growing significantly over the past century. CO2 from energy represents about 75% of the greenhouse gas (GHG) emissions for Annex B (Developed) countries, and over 60% of global emissions. Because of impermeable cap rocks hydrocarbon reservoirs are able to sequester CO〉 In addition, due to high-demand for oil worldwide, injection of CO2 is a useful way to enhance oil production. Hence, applying an efficient method to co-optimize CO2 storage and oil production is vital. Lack of suitable optimization techniques in the past led most multi-objective optimization problems to be tackled in the same way as a single objective optimization issue. However, there are some basic differences between the multi and single objective optimization methods. In this study, by using a non- dominated sorting genetic algorithm (NSGA-II) for an oil reservoir, some appropriate scenarios are proposed based on simultaneous gas storage and enhanced oil recovery optimization. The advantages of this method allow us to amend production scenarios after implementing the optimization process, by regarding the variation of economic parameters such as oil price and CO2 tax. This leads to reduced risks and time duration of making new decisions based on upcoming situations.展开更多
Maintaining population diversity is an important task in the multimodal multi-objective optimization.Although the zoning search(ZS)can improve the diversity in the decision space,assigning the same computational costs...Maintaining population diversity is an important task in the multimodal multi-objective optimization.Although the zoning search(ZS)can improve the diversity in the decision space,assigning the same computational costs to each search subspace may be wasteful when computational resources are limited,especially on imbalanced problems.To alleviate the above-mentioned issue,a zoning search with adaptive resource allocating(ZS-ARA)method is proposed in the current study.In the proposed ZS-ARA,the entire search space is divided into many subspaces to preserve the diversity in the decision space and to reduce the problem complexity.Moreover,the computational resources can be automatically allocated among all the subspaces.The ZS-ARA is compared with seven algorithms on two different types of multimodal multi-objective problems(MMOPs),namely,balanced and imbalanced MMOPs.The results indicate that,similarly to the ZS,the ZS-ARA achieves high performance with the balanced MMOPs.Also,it can greatly assist a“regular”algorithm in improving its performance on the imbalanced MMOPs,and is capable of allocating the limited computational resources dynamically.展开更多
With the frequent occurrences of emergency events,emergency decision making(EDM)plays an increasingly significant role in coping with such situations and has become an important and challenging research area in recent...With the frequent occurrences of emergency events,emergency decision making(EDM)plays an increasingly significant role in coping with such situations and has become an important and challenging research area in recent times.It is essential for decision makers to make reliable and reasonable emergency decisions within a short span of time,since inappropriate decisions may result in enormous economic losses and social disorder.To handle emergency effectively and quickly,this paper proposes a new EDM method based on the novel concept of q-rung orthopair fuzzy rough(q-ROPR)set.A novel list of q-ROFR aggregation information,detailed description of the fundamental characteristics of the developed aggregation operators and the q-ROFR entropy measure that determine the unknown weight information of decision makers as well as the criteria weights are specified.Further an algorithm is given to tackle the uncertain scenario in emergency to give reliable and reasonable emergency decisions.By using proposed list of q-ROFR aggregation information all emergency alternatives are ranked to get the optimal one.Besides this,the q-ROFR entropy measure method is used to determine criteria and experts’weights objectively in the EDM process.Finally,through an illustrative example of COVID-19 analysis is compared with existing EDM methods.The results verify the effectiveness and practicability of the proposed methodology.展开更多
In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing f...In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing facility points;2) Maximize the minimum distance from the facility to be located to the existing facility points;3) Maximize the number of existing facility points covered. Area restriction concept has been incor-porated so that the facility to be located should be within certain restricted area. The model developed here is a class of maximal covering problem, that is covering maximum number of points where the facility is within the upper bounds of the corresponding mth feasible region Two types of compromise solution methods have been designed to get a satisfactory solution of the multi-objective problem. A transformed non- linear programming algorithm has been designed for the proposed non-linear model. Rectilinear dis-tance norm has been considered as the distance measure as it is more appropriate to various realistic situa-tions. A numerical example has been presented to illustrate the solution algorithm.展开更多
基金the Liaoning Province Nature Fundation Project(2022-MS-291)the National Programme for Foreign Expert Projects(G2022006008L)+2 种基金the Basic Research Projects of Liaoning Provincial Department of Education(LJKMZ20220781,LJKMZ20220783,LJKQZ20222457)King Saud University funded this study through theResearcher Support Program Number(RSPD2023R704)King Saud University,Riyadh,Saudi Arabia.
文摘The existing algorithms for solving multi-objective optimization problems fall into three main categories:Decomposition-based,dominance-based,and indicator-based.Traditional multi-objective optimization problemsmainly focus on objectives,treating decision variables as a total variable to solve the problem without consideringthe critical role of decision variables in objective optimization.As seen,a variety of decision variable groupingalgorithms have been proposed.However,these algorithms are relatively broad for the changes of most decisionvariables in the evolution process and are time-consuming in the process of finding the Pareto frontier.To solvethese problems,a multi-objective optimization algorithm for grouping decision variables based on extreme pointPareto frontier(MOEA-DV/EPF)is proposed.This algorithm adopts a preprocessing rule to solve the Paretooptimal solution set of extreme points generated by simultaneous evolution in various target directions,obtainsthe basic Pareto front surface to determine the convergence effect,and analyzes the convergence and distributioneffects of decision variables.In the later stages of algorithm optimization,different mutation strategies are adoptedaccording to the nature of the decision variables to speed up the rate of evolution to obtain excellent individuals,thusenhancing the performance of the algorithm.Evaluation validation of the test functions shows that this algorithmcan solve the multi-objective optimization problem more efficiently.
基金supported in part by the Central Government Guides Local Science and TechnologyDevelopment Funds(Grant No.YDZJSX2021A038)in part by theNational Natural Science Foundation of China under(Grant No.61806138)in part by the China University Industry-University-Research Collaborative Innovation Fund(Future Network Innovation Research and Application Project)(Grant 2021FNA04014).
文摘The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.
基金Anhui Province Natural Science Research Project of Colleges and Universities(2023AH040321)Excellent Scientific Research and Innovation Team of Anhui Colleges(2022AH010098).
文摘The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.
基金supported by the National Natural Science Foundation of China(51405499)
文摘A decision support system, including a multi-objective optimization framework and a multi-attribute decision making approach is proposed for satellite equipment layout. Firstly, given three objectives (to minimize the C.G. offset, the cross moments of inertia and the space debris impact risk), we develop a threedimensional layout optimization model. Unlike most of the previous works just focusing on mass characteristics of the system, a space debris impact risk index is developed. Secondly, we develop an efficient optimization framework for the integration of computer-aided design (CAD) software as well as the optimization algorithm to obtain the Pareto front of the layout optimization problem. Thirdly, after obtaining the candidate solutions, we present a multi-attribute decision making approach, which integrates the smart Pareto filter and the correlation coefficient and standard deviation (CCSD) method to select the best tradeoff solutions on the optimal Pareto fronts. Finally, the framework and the decision making approach are applied to a case study of a satellite platform.
基金the Catalan Government Predoctoral Schol-arship(AGAUR-FSE 2020 FI_B200147)SuFoRun Marie Sklodowska-Curie Research and Innovation Staff Exchange(RISE)Program(Grant No.691149)the Spanish Ministry of Science and Innovation(PID2020-120355RB-IOO).
文摘Management of forest lands considering multi-functional approaches is the basis to sustain or enhance the provi-sion of specific benefits,while minimizing negative impacts to the environment.Defining a desired management itinerary to a forest depends on a variety of factors,including the forest type,its ecological characteristics,and the social and economic needs of local communities.A strategic assessment of the forest use suitability(FUS)(namely productive,protective,conservation-oriented,social and multi-functional)at regional level,based on the provision of forest ecosystem services and trade-offs between FUS alternatives,can be used to develop management strategies that are tailored to the specific needs and conditions of the forest.The present study assesses the provision of multiple forest ecosystem services and employs a decision model to identify the FUS that sup-ports the most present and productive ecosystem services in each stand in Catalonia.For this purpose,we apply the latest version of the Ecosystem Management Decision Support(EMDS)system,a spatially oriented decision support system that provides accurate results for multi-criteria management.We evaluate 32 metrics and 12 as-sociated ecosystem services indicators to represent the spatial reality of the region.According to the results,the dominant primary use suitability is social,followed by protective and productive.Nevertheless,final assignment of uses is not straightforward and requires an exhaustive analysis of trade-offs between all alternative options,in many cases identifying flexible outcomes,and increasing the representativeness of multi-functional use.The assignment of forest use suitability aims to significantly improve the definition of the most adequate management strategy to be applied.
基金This work is supported by the Next Generation Transportation Systems Center(NEXTRANS),USDOT's Region 5 University Transportation CenterThe work is also affiliated with Purdue University College of Engineering's Institute for Control,Optimization,and Networks(ICON)and Center for Intelligent Infrastructure(CII)initiatives.
文摘The motivation for cost-effective management of highway pavements is evidenced not only by the massive expenditures associated with these activities at a national level but also by the consequences of poor pavement condition on road users.This paper presents a state-of-the-art review of multi-objective optimization(MOO)problems that have been formulated and solution techniques that have been used in selecting and scheduling highway pavement rehabilitation and maintenance activities.First,the paper presents a taxonomy and hierarchy for these activities,the role of funding sources,and levels of jurisdiction.The paper then describes how three different decision mechanisms have been used in past research and practice for project selection and scheduling(historical practices,expert opinion,and explicit mathematical optimization)and identifies the pros and cons of each mechanism.The paper then focuses on the optimization mechanism and presents the types of optimization problems,formulations,and objectives that have been used in the literature.Next,the paper examines various solution algorithms and discusses issues related to their implementation.Finally,the paper identifies some barriers to implementing multi-objective optimization in selecting and scheduling highway pavement rehabilitation and maintenance activities,and makes recommendations to overcome some of these barriers.
基金supported by the National Science Fund for Distinguished Young Scholars of China(70625005).
文摘The class of multiple attribute decision making (MADM) problems is studied, where the attribute values are intuitionistic fuzzy numbers, and the information about attribute weights is completely unknown. A score function is first used to calculate the score of each attribute value and a score matrix is constructed, and then it is transformed into a normalized score matrix. Based on the normalized score matrix, an entropy-based procedure is proposed to derive attribute weights. Furthermore, the additive weighted averaging operator is utilized to fuse all the normalized scores into the overall scores of alternatives, by which the ranking of all the given alternatives is obtained. This paper is concluded by extending the above results to interval-valued intuitionistic fuzzy set theory, and an illustrative example is also provided.
文摘From the viewpoint of entropy, this paper investigates a hybrid multiple attribute decision making problem with precision number, interval number and fuzzy number. It defines a new concept: project entropy and the decision is taken according to the values. The validity and scientific nature of the given is proven.
基金supported by the National Natural Science Foundation of China(70771041)Chinese Astronautics SupportTechnology Foundation and the Excellent Youth Project of Hubei Provincial Department of Education(Q20082705)
文摘To study the problems of multi-attribute decision making in which the attribute values are given in the form of linguistic fuzzy numbers and the information of attribute weights are incomplete, a new multi-attribute decision making model is presented based on the optimal membership and the relative entropy. Firstly, the definitions of the optimal membership and the relative entropy are given. Secondly, for all alternatives, a set of preference weight vectors are obtained by solving a set of linear programming models whose goals axe all to maximize the optimal membership. Thirdly, a relative entropy model is established to aggregate the preference weight vectors, thus an optimal weight vector is determined. Based on this optimal weight vector, the algorithm of deviation degree minimization is proposed to rank all the alternatives. Finally, a decision making example is given to demonstrate the feasibility and rationality of this new model.
文摘According to the aggregation method of experts' evaluation information in group decision-making,the existing methods of determining experts' weights based on cluster analysis take into account the expert's preferences and the consistency of expert's collating vectors,but they lack of the measure of information similarity.So it may occur that although the collating vector is similar to the group consensus,information uncertainty is great of a certain expert.However,it is clustered to a larger group and given a high weight.For this,a new aggregation method based on entropy and cluster analysis in group decision-making process is provided,in which the collating vectors are classified with information similarity coefficient,and the experts' weights are determined according to the result of classification,the entropy of collating vectors and the judgment matrix consistency.Finally,a numerical example shows that the method is feasible and effective.
基金This paper is supported by National Natural Science Foundation of China under Grant No.70372011.
文摘Performance evaluation of facilities management plays a key role in the facilities management process. This paper proposes an optimized multicriteria decision making model to evaluate the performance of facilities management in schools in Hong Kong. In this model, entropy weights acted as weight coefficients for evaluated criteria in order to avoid uncertainty and randomicity of subjective judgments. Besides, the TOPSIS method was incorporated in this model. Then this model was em- ployed to evaluate the performance of facilities management in classrooms, offices and laboratories and satisfying results were obtained. Moreover, findings indicated that one of the schools could be rehabilitated rather than removed.
基金supported by the National Natural Science Foundation of China(No.62076225).
文摘During the past decade,research efforts have been gradually directed to the widely existing yet less noticed multimodal multi-objective optimization problems(MMOPs)in the multi-objective optimization community.Recently,researchers have begun to investigate enhancing the decision space diversity and preserving valuable dominated solutions to overcome the shortage caused by a preference for objective space convergence.However,many existing methods still have limitations,such as giving unduly high priorities to convergence and insufficient ability to enhance decision space diversity.To overcome these shortcomings,this article aims to explore a promising region(PR)and enhance the decision space diversity for handling MMOPs.Unlike traditional methods,we propose the use of non-dominated solutions to determine a limited region in the PR in the decision space,where the Pareto sets(PSs)are included,and explore this region to assist in solving MMOPs.Furthermore,we develop a novel neighbor distance measure that is more suitable for the complex geometry of PSs in the decision space than the crowding distance.Based on the above methods,we propose a novel dual-population-based coevolutionary algorithm.Experimental studies on three benchmark test suites demonstrates that our proposed methods can achieve promising performance and versatility on different MMOPs.The effectiveness of the proposed neighbor distance has also been justified through comparisons with crowding distance methods.
基金supported by the MKE(The Ministry of Knowledge Economy),Korea,under the ITRC(Information Technology Research Center)support program supervised by the NIPA(National IT Industry Promotion Agency)(NIPA-2009-(C1090-0902-0007))
文摘This study is to introduce concepts of energy and entropy to describe a robot's emotion decision.It chooses the dimensional approach based on factors of pleasure and arousal for the merit of the interpolation between emotions.Especially,Circumplex model which has also two axes:pleasure and arousal is used.Besides,the model indicates how emotions are distributed in the two-dimensional plane.Then by the definition of psychodynamicsthe energy states(mental energy and physical energy)are matched to pleasure and arousal respectively that are the basis of Circumplex model.The mental energy is updated by the result of Prospect theory which measures the value of gain and loss as pleasure factor.And the physical energy is updated by the result of hedonic scaling which measures levels of arousal from pleasure computed by Prospect theory,and the result of intensity of stimuli.Then the energy states are fed by entropy.The feedback loop by entropy satisfies the 2nd law of thermodynamics.The energy states generated by stimuli and fed by entropy take a position in the plane of Circumplex model.Then distances between the current position and other emotions are computed to get a level of each emotion,proportional to the inverse of the distance.
基金the National Natural Science Foundation of China (No.50478090)the Key Plan of Science and Technology of Hubei Provincial Communication Department (No.2005jtkj361)
文摘Proper treatment of weak subgrade soil is very important to building a highway of good quality. We proposed an entropy-based multi-criterion group decision analysis method for a group of experts to evaluate alternatives of weak subgrade treatment,with an aim to select the optimum technique which is technically,economically and socially viable. We used fuzzy theory to analyze multiple experts' evaluation on various factors of each alterative treatment. Different experts' evaluations are integrated by the group eigenvalue method. An entropy weight is introduced to minimize the negative influences of subjective human factors of experts. The optimum alternative is identified with ideal point discriminant analysis to calculate the distance of each alternative to the ideal point and prioritize all alternatives according to their distances. A case study on a section of the Shiman Expressway verified that the proposed method can give a rational decision on the optimum method of weak subgrade treatment.
文摘Fuzzy entropy measures are valuable tools in decision-making when dealing with uncertain or imprecise information.There exist many entropy measures for Pythagorean Fuzzy Sets(PFS)in the literature that fail to deal with the problem of providing reasonable or consistent results to the decision-makers.To deal with the shortcomings of the existing measures,this paper proposes a robust fuzzy entropy measure for PFS to facilitate decision-making under uncertainty.The usefulness of the measure is illustrated through an illustration of decision-making in a supplier selection problem and compared with existing fuzzy entropy measures.The Technique for Order Performance by Similarity to Ideal Solution(TOPSIS)approach is also explored to solve the decision-making problem.The results demonstrate that the proposed measure can effectively capture the degree of uncertainty in the decision-making process,leading to more accurate decision outcomes by providing a reliable and robust ranking of alternatives.
文摘Climate researchers have observed that the carbon dioxide (CO2) concentration in the atmosphere have been growing significantly over the past century. CO2 from energy represents about 75% of the greenhouse gas (GHG) emissions for Annex B (Developed) countries, and over 60% of global emissions. Because of impermeable cap rocks hydrocarbon reservoirs are able to sequester CO〉 In addition, due to high-demand for oil worldwide, injection of CO2 is a useful way to enhance oil production. Hence, applying an efficient method to co-optimize CO2 storage and oil production is vital. Lack of suitable optimization techniques in the past led most multi-objective optimization problems to be tackled in the same way as a single objective optimization issue. However, there are some basic differences between the multi and single objective optimization methods. In this study, by using a non- dominated sorting genetic algorithm (NSGA-II) for an oil reservoir, some appropriate scenarios are proposed based on simultaneous gas storage and enhanced oil recovery optimization. The advantages of this method allow us to amend production scenarios after implementing the optimization process, by regarding the variation of economic parameters such as oil price and CO2 tax. This leads to reduced risks and time duration of making new decisions based on upcoming situations.
基金This work was partially supported by the Shandong Joint Fund of the National Nature Science Foundation of China(U2006228)the National Nature Science Foundation of China(61603244).
文摘Maintaining population diversity is an important task in the multimodal multi-objective optimization.Although the zoning search(ZS)can improve the diversity in the decision space,assigning the same computational costs to each search subspace may be wasteful when computational resources are limited,especially on imbalanced problems.To alleviate the above-mentioned issue,a zoning search with adaptive resource allocating(ZS-ARA)method is proposed in the current study.In the proposed ZS-ARA,the entire search space is divided into many subspaces to preserve the diversity in the decision space and to reduce the problem complexity.Moreover,the computational resources can be automatically allocated among all the subspaces.The ZS-ARA is compared with seven algorithms on two different types of multimodal multi-objective problems(MMOPs),namely,balanced and imbalanced MMOPs.The results indicate that,similarly to the ZS,the ZS-ARA achieves high performance with the balanced MMOPs.Also,it can greatly assist a“regular”algorithm in improving its performance on the imbalanced MMOPs,and is capable of allocating the limited computational resources dynamically.
基金This Project was funded by the Deanship of Scientific Research(DSR),King Abdulaziz University,Jeddah,under the Grant No.(G:578-135-1441)The authors,therefore,acknowledge with thanks DSR for technical and financial support.
文摘With the frequent occurrences of emergency events,emergency decision making(EDM)plays an increasingly significant role in coping with such situations and has become an important and challenging research area in recent times.It is essential for decision makers to make reliable and reasonable emergency decisions within a short span of time,since inappropriate decisions may result in enormous economic losses and social disorder.To handle emergency effectively and quickly,this paper proposes a new EDM method based on the novel concept of q-rung orthopair fuzzy rough(q-ROPR)set.A novel list of q-ROFR aggregation information,detailed description of the fundamental characteristics of the developed aggregation operators and the q-ROFR entropy measure that determine the unknown weight information of decision makers as well as the criteria weights are specified.Further an algorithm is given to tackle the uncertain scenario in emergency to give reliable and reasonable emergency decisions.By using proposed list of q-ROFR aggregation information all emergency alternatives are ranked to get the optimal one.Besides this,the q-ROFR entropy measure method is used to determine criteria and experts’weights objectively in the EDM process.Finally,through an illustrative example of COVID-19 analysis is compared with existing EDM methods.The results verify the effectiveness and practicability of the proposed methodology.
文摘In this paper a Vertex Covering Obnoxious Facility Location model on a Plane has been designed with a combination of three interacting criteria as follows: 1) Minimize the overall importance of the various exist-ing facility points;2) Maximize the minimum distance from the facility to be located to the existing facility points;3) Maximize the number of existing facility points covered. Area restriction concept has been incor-porated so that the facility to be located should be within certain restricted area. The model developed here is a class of maximal covering problem, that is covering maximum number of points where the facility is within the upper bounds of the corresponding mth feasible region Two types of compromise solution methods have been designed to get a satisfactory solution of the multi-objective problem. A transformed non- linear programming algorithm has been designed for the proposed non-linear model. Rectilinear dis-tance norm has been considered as the distance measure as it is more appropriate to various realistic situa-tions. A numerical example has been presented to illustrate the solution algorithm.