Multi-Objective Optimization Algorithm for Grouping Decision Variables Based on Extreme Point Pareto Frontier

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.

Large-Scale Multi-Objective Optimization Algorithm Based on Weighted Overlapping Grouping of Decision Variables

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.

A decision support system for satellite layout integrating multi-objective optimization and multi-attribute decision making

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.

Multi-objective optimization in highway pavement maintenance and rehabilitation project selection and scheduling:A state-of-the-art review

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.

Time-Variant Reliability-Based Multi-Objective Fuzzy Design Optimization for Anti-Roll Torsion Bar of EMU

Although various types of anti-roll torsion bars have been developed to inhibit excessive roll angle of the electric multiple unit(EMU)car body,it is critical to ensure the reliability of structural design due to the complexity of the problems involving time and uncertainties.To address this issue,amulti-objective fuzzy design optimization model is constructed considering time-variant stiffness and strength reliability constraints for the anti-roll torsion bar.A hybrid optimization strategy combining the design of experiment(DoE)sampling and non-linear programming by quadratic lagrangian(NLPQL)is presented to deal with the design optimization model.To characterize the effect of time on the structural performance of the torsion bar,the continuous-time model combined with Ito lemma is proposed to establish the time-variant stiffness and strength reliability constraints.Fuzzy mathematics is employed to conduct uncertainty quantification for the design parameters of the torsion bar.A physical programming approach is used to improve the designer’s preference and to make the optimization results more consistent with engineering practices.Moreover,the effectiveness of the proposed method has been validated by comparing with current methods in a practical engineering case.

Group Decision Making Based Fuzzy Pattern Recognition Model for Lectotype Optimization of Offshore Platforms 1

This paper develops a fuzzy pattern recognition model for group decision making to solve the problem of lectotype optimization of offshore platforms. The lack of data and the inexact or incomplete information for criteria are the main cause of uncertainty in the evaluation process, therefore it is necessary to integrate the judgments from different decision makers with different experience, knowledge and preference. This paper first uses a complementary principle based pairwise comparison method to obtain the subjective weight of the criteria from each decision maker. A fuzzy pattern recognition model is then developed to integrate the judgments from all the decision makers and the information from the criteria, under the supervision of the subjective weights. Finally a case study is given to show the efficiency and robustness of the proposed model.

Multi-objective fuzzy particle swarm optimization based on elite archiving and its convergence

A fuzzy particle swarm optimization （PSO） on the basis of elite archiving is proposed for solving multi-objective optimization problems. First, a new perturbation operator is designed, and the concepts of fuzzy global best and fuzzy personal best are given on basis of the new operator. After that, particle updating equations are revised on the basis of the two new concepts to discourage the premature convergence and enlarge the potential search space; second, the elite archiving technique is used during the process of evolution, namely, the elite particles are introduced into the swarm, whereas the inferior particles are deleted. Therefore, the quality of the swarm is ensured. Finally, the convergence of this swarm is proved. The experimental results show that the nondominated solutions found by the proposed algorithm are uniformly distributed and widely spread along the Pareto front.

Exploring a Promising Region and Enhancing Decision Space Diversity for Multimodal Multi-Objective Optimization

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.

Hybrid Multi-Object Optimization Method for Tapping Center Machines

This paper proposes a hybrid multi-object optimization method integrating a uniform design,an adaptive network-based fuzzy inference system(ANFIS),and a multi-objective particle swarm optimizer(MOPSO)to optimize the rigid tapping parameters and minimize the synchronization errors and cycle times of computer numerical control(CNC)machines.First,rigid tapping parameters and uniform(including 41-level and 19-level)layouts were adopted to collect representative data for modeling.Next,ANFIS was used to build the model for the collected 41-level and 19-level uniform layout experiment data.In tapping center machines,the synchronization errors and cycle times are important consid-erations,so these two objects were used to build the ANFIS models.Then,a MOPSO algorithm was used to search for the optimal parameter combinations for the two ANFIS models simultaneously.The experimental results showed that the proposed method obtains suitable parameter values and optimal parameter combinations compared with the nonsystematic method.Additionally,the optimal parameter combination was used to optimize existing CNC tools during the commissioning process.Adjusting the proportional and integral gains of the spindle could improve resistance to deformation during rigid tapping.The posi-tion gain and prefeedback coefficient can reduce the synchronization errors significantly,and the acceleration and deceleration times of the spindle affect both the machining time and synchronization errors.The proposed method can quickly and accurately minimize synchronization errors from 107 to 19.5 pulses as well as the processing time from 3,600 to 3,248 ms;it can also shorten the machining time significantly and reduce simultaneous errors to improve tapping yield,there-by helping factories achieve carbon reduction.

Autonomous air combat maneuver decision using Bayesian inference and moving horizon optimization

To reach a higher level of autonomy for unmanned combat aerial vehicle(UCAV) in air combat games, this paper builds an autonomous maneuver decision system. In this system,the air combat game is regarded as a Markov process, so that the air combat situation can be effectively calculated via Bayesian inference theory. According to the situation assessment result,adaptively adjusts the weights of maneuver decision factors, which makes the objective function more reasonable and ensures the superiority situation for UCAV. As the air combat game is characterized by highly dynamic and a significant amount of uncertainty,to enhance the robustness and effectiveness of maneuver decision results, fuzzy logic is used to build the functions of four maneuver decision factors. Accuracy prediction of opponent aircraft is also essential to ensure making a good decision; therefore, a prediction model of opponent aircraft is designed based on the elementary maneuver method. Finally, the moving horizon optimization strategy is used to effectively model the whole air combat maneuver decision process. Various simulations are performed on typical scenario test and close-in dogfight, the results sufficiently demonstrate the superiority of the designed maneuver decision method.

Co-optimization of carbon dioxide storage and enhanced oil recovery in oil reservoirs using a multi-objective genetic algorithm(NSGA-Ⅱ)

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.

Zoning Search With Adaptive Resource Allocating Method for Balanced and Imbalanced Multimodal Multi-Objective Optimization

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.

Overview of multi-objective optimization methods

To assist readers to have a comprehensive understanding, the classical and intelligent methods roundly based on precursory research achievements are summarized in this paper. First, basic conception and description about multi-objective (MO) optimization are introduced. Then some definitions and related terminologies are given. Furthermore several MO optimization methods including classical and current intelligent methods are discussed one by one succinctly. Finally evaluations on advantages and disadvantages about these methods are made at the end of the paper.

The Coalition Cooperative Game Method and Its Application in Multi-objective Optimization Design

This paper proposes a multi-objective optimization design method based on the coalition cooperative game theory where the three design goals have been seen as three game players. By calculating the affecting factors and fuzzy clustering, the design variables are divided into different strategic spaces which belong to each player, then it constructs a payoff function based on the coalition mechanism. Each game player takes its own revenue function as a target and obtains the best strategy versus other players. The best strategies of all players consist of the strategy permutation of a round game and it obtains the final game solutions through multi-round games according to the convergence criterion. A multi-objective optimization example of the luff mechanism of compensative sheave block shows the effectiveness of the coalition cooperative game method.

Sustainable Multi-Objective Multi-Reservoir Optimization Considering Environmental Flow

Increasing demand for water from all sectors presents a challenge for policy makers to improve water allocation policies for storage reservoirs. In addition, there are many other organisms and species present in river waters that also require water for their survival. Due to the lack of awareness many times the minimum required quantity and quality of water for river ecosystem is not made available at downstream of storage reservoirs. So, a sustainable approach is required in reservoir operations to maintain the river ecosystem with environmental flow while meeting the other demands. Multi-objective, multi-reservoir operation model developed with Python programming using Fuzzy Linear Programing method incorporating environmental flow requirement of river is presented in this paper. Objective of maximization of irrigation release is considered for first run. In second run maximization of releases for hydropower generation is considered as objective. Further both objectives are fuzzified by incorporating linear membership function and solved to maximize fuzzified objective function simultaneously by maximizing satisfaction level indicator (λ). The optimal reservoir operation policy is presented considering constraints including Irrigation release, Turbine release, Reservoir storage, Environmental flow release and hydrologic continuity. Model applied for multi-reservoir system consists of four reservoirs, i.e., Jayakwadi Stage-I Reservoir (R1), Jayakwadi Stage-II Reservoir (R2), Yeldari Reservoir (R3), Siddheshwar Reservoir (R4) in Godavari River sub-basin from Marathwada region of Maharashtra State, India.

A New Integrated Design Method Based on Fuzzy Matter-Element Optimization

This paper puts forward a new integrated design met ho d based on fuzzy matter-element optimization.On the based of analyzing the mod el of multi-objective fuzzy matter-element , the paper defines the m atter-element weightily and changes solving multi-objective fuzzy optimization into solving dependent function K(x) of the single-objective optimization according to the optimization criterion. The paper particularly describes the realization approach of GA process of multi -objective fuzzy matter-element optimization: encode, produce initial populati on, confirm fitness function, select operator, etc. In the process, the adaptive macro genetic algorithms (AMGA) is applied to enhancing the evolution speed. Th e paper improves the two genetic operators: crossover and mutation operator. The modified adaptive macro genetic algorithms (MAMGA) is put forward simultane ously. It is adopted to solve the optimization problem. Three optimization methods, namely fuzzy matter-element optimization method, li nearity weighted method and fuzzy optimization method, are compared by using the table and figure, it shows that not only MAMGA is a little better than the AMGA , but also it reaches the extent to which the effective iteration generation is 62.2% of simple genetic algorithms (SGA). By the calculation of optimum exam ple, the improved method of genetic in the paper is much better than the method in reference of paper.

A Fuzzy Sequential Optimization Method for the Antenna Structures with Multiple Objectives

This paper presents a fuzzy sequential optimization method for the antenna structures with multiple objectives (structural displacement, weight, cost, nature frequency characteristic) based on fuzzy sets. This has led to a set of new concepts which are discussed here. The paper establishes a sequential optimization model, in which the cost function is constructed, the membership function of single objective is defined as extended quadratic function, the membership function in decision making is constructed with linearly weighted and power product weighted models and the objectives are classed. In addition, the paper presents two methods, namely the linear extended method and the secondary constrained sequential optimization method, by which effective satisfactory design can be found. A computer program is given, optimization computing of the truss- type and antenna structures are described. It is shown that the method is practical and effective.

Kind of Fuzzy Method Determining Index Weight on Multi-Objctive Decision Making

Based on fuzzy characteristic of dicision-making thought, matrix of priority relation has been introduced and blurrized. A kind of fuzzy method, which is to determine the index weight on multi-objective decision making, has been put forward by means of the sequence root method for analysis of hierarchical process (AHP). Using this method an example which is to define the index weigbt on multi-objective decision making in thc scheme optimization of mine design has been given.

Optimization in Site Selection of Wind Turbine for Energy Using Fuzzy Logic System and GIS—A Case Study for Gujarat

The development of new wind energy project requires studying of many parameters to achieve maximum benefits at the cost of minimum environmental impacts. Using Geographic Information System (GIS), an analytical framework has been developed in this paper with fuzzy logic to evaluate the suitable site for turbines for optimum energy output. The criteria for suitable site for energy optimization are environmental, physical and human factors. The present study helps to assess the appropriate sites for the wind turbines in Gujarat. The result obtained from the study conveys the suitability of the development of wind turbines along the western parts of Gujarat. The suggested model could be used for the future site selection of the wind turbine which in turn could be of orientation for energy planners and decision makers.