scholarly journals Improved SparseEA for sparse large-scale multi-objective optimization problems

2021 ◽  
Author(s):  
Yajie Zhang ◽  
Ye Tian ◽  
Xingyi Zhang
Keyword(s):  
Real World ◽  
Large Scale ◽  
Optimization Problems ◽  
State Of The Art ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Limited Budget ◽  
Decision Variables ◽  
Real World Applications

AbstractSparse large-scale multi-objective optimization problems (LSMOPs) widely exist in real-world applications, which have the properties of involving a large number of decision variables and sparse Pareto optimal solutions, i.e., most decision variables of these solutions are zero. In recent years, sparse LSMOPs have attracted increasing attentions in the evolutionary computation community. However, all the recently tailored algorithms for sparse LSMOPs put the sparsity detection and maintenance in the first place, where the nonzero variables can hardly be optimized sufficiently within a limited budget of function evaluations. To address this issue, this paper proposes to enhance the connection between real variables and binary variables within the two-layer encoding scheme with the assistance of variable grouping techniques. In this way, more efforts can be devoted to the real part of nonzero variables, achieving the balance between sparsity maintenance and variable optimization. According to the experimental results on eight benchmark problems and three real-world applications, the proposed algorithm is superior over existing state-of-the-art evolutionary algorithms for sparse LSMOPs.

Evolutionary Large-Scale Multi-Objective Optimization: A Survey

2022 ◽  
Vol 54 (8) ◽  
pp. 1-34
Author(s):  
Ye Tian ◽  
Langchun Si ◽  
Xingyi Zhang ◽  
Ran Cheng ◽  
Cheng He ◽  
...  
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Future Research ◽  
Decision Variable ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Space Reduction ◽  
Decision Variables ◽  
Comprehensive Survey

Multi-objective evolutionary algorithms (MOEAs) have shown promising performance in solving various optimization problems, but their performance may deteriorate drastically when tackling problems containing a large number of decision variables. In recent years, much effort been devoted to addressing the challenges brought by large-scale multi-objective optimization problems. This article presents a comprehensive survey of stat-of-the-art MOEAs for solving large-scale multi-objective optimization problems. We start with a categorization of these MOEAs into decision variable grouping based, decision space reduction based, and novel search strategy based MOEAs, discussing their strengths and weaknesses. Then, we review the benchmark problems for performance assessment and a few important and emerging applications of MOEAs for large-scale multi-objective optimization. Last, we discuss some remaining challenges and future research directions of evolutionary large-scale multi-objective optimization.

scholarly journals Evolutionary Computation for Large-scale Multi-objective Optimization: A Decade of Progresses

2021 ◽  
Author(s):  
Wen-Jing Hong ◽  
Peng Yang ◽  
Ke Tang
Keyword(s):  
Evolutionary Computation ◽  
Real World ◽  
Large Scale ◽  
Optimization Problems ◽  
Divide And Conquer ◽  
Research Progress ◽  
Small Scale ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Decision Variables

AbstractLarge-scale multi-objective optimization problems (MOPs) that involve a large number of decision variables, have emerged from many real-world applications. While evolutionary algorithms (EAs) have been widely acknowledged as a mainstream method for MOPs, most research progress and successful applications of EAs have been restricted to MOPs with small-scale decision variables. More recently, it has been reported that traditional multi-objective EAs (MOEAs) suffer severe deterioration with the increase of decision variables. As a result, and motivated by the emergence of real-world large-scale MOPs, investigation of MOEAs in this aspect has attracted much more attention in the past decade. This paper reviews the progress of evolutionary computation for large-scale multi-objective optimization from two angles. From the key difficulties of the large-scale MOPs, the scalability analysis is discussed by focusing on the performance of existing MOEAs and the challenges induced by the increase of the number of decision variables. From the perspective of methodology, the large-scale MOEAs are categorized into three classes and introduced respectively: divide and conquer based, dimensionality reduction based and enhanced search-based approaches. Several future research directions are also discussed.

A Memetic Optimization Strategy Based on Dimension Reduction in Decision Space

2015 ◽  
Vol 23 (1) ◽  
pp. 69-100 ◽  
Author(s):  
Handing Wang ◽  
Licheng Jiao ◽  
Ronghua Shang ◽  
Shan He ◽  
Fang Liu
Keyword(s):  
Dimension Reduction ◽  
Optimization Problems ◽  
State Of The Art ◽  
Search Space ◽  
Optimization Strategy ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Decision Space ◽  
Multi Objective ◽  
Decision Variables

There can be a complicated mapping relation between decision variables and objective functions in multi-objective optimization problems (MOPs). It is uncommon that decision variables influence objective functions equally. Decision variables act differently in different objective functions. Hence, often, the mapping relation is unbalanced, which causes some redundancy during the search in a decision space. In response to this scenario, we propose a novel memetic (multi-objective) optimization strategy based on dimension reduction in decision space (DRMOS). DRMOS firstly analyzes the mapping relation between decision variables and objective functions. Then, it reduces the dimension of the search space by dividing the decision space into several subspaces according to the obtained relation. Finally, it improves the population by the memetic local search strategies in these decision subspaces separately. Further, DRMOS has good portability to other multi-objective evolutionary algorithms (MOEAs); that is, it is easily compatible with existing MOEAs. In order to evaluate its performance, we embed DRMOS in several state of the art MOEAs to facilitate our experiments. The results show that DRMOS has the advantage in terms of convergence speed, diversity maintenance, and portability when solving MOPs with an unbalanced mapping relation between decision variables and objective functions.

scholarly journals An Ensemble Framework of Evolutionary Algorithm for Constrained Multi-Objective Optimization

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 116
Author(s):  
Junhua Ku ◽  
Fei Ming ◽  
Wenyin Gong
Keyword(s):  
Evolutionary Algorithms ◽  
Real World ◽  
Optimization Problems ◽  
State Of The Art ◽  
Multi Objective Optimization ◽  
The Real ◽  
Multi Objective ◽  
The Past ◽  
Hypervolume Indicator ◽  
Real World Problems

In the real-world, symmetry or asymmetry widely exists in various problems. Some of them can be formulated as constrained multi-objective optimization problems (CMOPs). During the past few years, handling CMOPs by evolutionary algorithms has become more popular. Lots of constrained multi-objective optimization evolutionary algorithms (CMOEAs) have been proposed. Whereas different CMOEAs may be more suitable for different CMOPs, it is difficult to choose the best one for a CMOP at hand. In this paper, we propose an ensemble framework of CMOEAs that aims to achieve better versatility on handling diverse CMOPs. In the proposed framework, the hypervolume indicator is used to evaluate the performance of CMOEAs, and a decreasing mechanism is devised to delete the poorly performed CMOEAs and to gradually determine the most suitable CMOEA. A new CMOEA, namely ECMOEA, is developed based on the framework and three state-of-the-art CMOEAs. Experimental results on five benchmarks with totally 52 instances demonstrate the effectiveness of our approach. In addition, the superiority of ECMOEA is verified through comparisons to seven state-of-the-art CMOEAs. Moreover, the effectiveness of ECMOEA on the real-world problems is also evaluated for eight instances.

scholarly journals A comparative study of many-objective optimizers on large-scale many-objective software clustering problems

2021 ◽  
Author(s):  
Amarjeet Prajapati
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Software Clustering ◽  
Multi Objective ◽  
The Past ◽  
Decision Variables ◽  
Clustering Problems ◽  
Special Case

AbstractOver the past 2 decades, several multi-objective optimizers (MOOs) have been proposed to address the different aspects of multi-objective optimization problems (MOPs). Unfortunately, it has been observed that many of MOOs experiences performance degradation when applied over MOPs having a large number of decision variables and objective functions. Specially, the performance of MOOs rapidly decreases when the number of decision variables and objective functions increases by more than a hundred and three, respectively. To address the challenges caused by such special case of MOPs, some large-scale multi-objective optimization optimizers (L-MuOOs) and large-scale many-objective optimization optimizers (L-MaOOs) have been developed in the literature. Even after vast development in the direction of L-MuOOs and L-MaOOs, the supremacy of these optimizers has not been tested on real-world optimization problems containing a large number of decision variables and objectives such as large-scale many-objective software clustering problems (L-MaSCPs). In this study, the performance of nine L-MuOOs and L-MaOOs (i.e., S3-CMA-ES, LMOSCO, LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA) is evaluated and compared over five L-MaSCPs in terms of IGD, Hypervolume, and MQ metrics. The experimentation results show that the S3-CMA-ES and LMOSCO perform better compared to the LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA in most of the cases. The LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, and DREA, are the average performer, and H-RVEA is the worst performer.

A multi-objective evolutionary algorithm based on niche selection in solving irregular Pareto fronts

2021 ◽  
pp. 1-21
Author(s):  
Xin Li ◽  
Xiaoli Li ◽  
Kang Wang
Keyword(s):  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Environmental Selection ◽  
Optimal Solution Set ◽  
Pareto Fronts

The key characteristic of multi-objective evolutionary algorithm is that it can find a good approximate multi-objective optimal solution set when solving multi-objective optimization problems(MOPs). However, most multi-objective evolutionary algorithms perform well on regular multi-objective optimization problems, but their performance on irregular fronts deteriorates. In order to remedy this issue, this paper studies the existing algorithms and proposes a multi-objective evolutionary based on niche selection to deal with irregular Pareto fronts. In this paper, the crowding degree is calculated by the niche method in the process of selecting parents when the non-dominated solutions converge to the first front, which improves the the quality of offspring solutions and which is beneficial to local search. In addition, niche selection is adopted into the process of environmental selection through considering the number and the location of the individuals in its niche radius, which improve the diversity of population. Finally, experimental results on 23 benchmark problems including MaF and IMOP show that the proposed algorithm exhibits better performance than the compared MOEAs.

A Strength Pareto Gravitational Search Algorithm for Multi-Objective Optimization Problems

2015 ◽  
Vol 29 (06) ◽  
pp. 1559010 ◽  
Author(s):  
Xiaohui Yuan ◽  
Zhihuan Chen ◽  
Yanbin Yuan ◽  
Yuehua Huang ◽  
Xiaopan Zhang
Keyword(s):  
Optimization Problems ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Population Diversity ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Local Optima ◽  
Multi Objective ◽  
Fine Grained ◽  
Gravitational Search

A novel strength Pareto gravitational search algorithm (SPGSA) is proposed to solve multi-objective optimization problems. This SPGSA algorithm utilizes the strength Pareto concept to assign the fitness values for agents and uses a fine-grained elitism selection mechanism to keep the population diversity. Furthermore, the recombination operators are modeled in this approach to decrease the possibility of trapping in local optima. Experiments are conducted on a series of benchmark problems that are characterized by difficulties in local optimality, nonuniformity, and nonconvexity. The results show that the proposed SPGSA algorithm performs better in comparison with other related works. On the other hand, the effectiveness of two subtle means added to the GSA are verified, i.e. the fine-grained elitism selection and the use of SBX and PMO operators. Simulation results show that these measures not only improve the convergence ability of original GSA, but also preserve the population diversity adequately, which enables the SPGSA algorithm to have an excellent ability that keeps a desirable balance between the exploitation and exploration so as to accelerate the convergence speed to the true Pareto-optimal front.

scholarly journals A New Method for Dynamic Multi-Objective Optimization Based on Segment and Cloud Prediction

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 465 ◽  
Author(s):  
Peng Ni ◽  
Jiale Gao ◽  
Yafei Song ◽  
Wen Quan ◽  
Qinghua Xing
Keyword(s):  
Optimization Problems ◽  
Pareto Set ◽  
Benchmark Problems ◽  
Small Range ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Good Convergence ◽  
Multi Objective ◽  
The Law ◽  
Cloud Theory

In the real world, multi-objective optimization problems always change over time in most projects. Once the environment changes, the distribution of the optimal solutions would also be changed in decision space. Sometimes, such change may obey the law of symmetry, i.e., the minimum of the objective function in such environment is its maximum in another environment. In such cases, the optimal solutions keep unchanged or vibrate in a small range. However, in most cases, they do not obey the law of symmetry. In order to continue the search that maintains previous search advantages in the changed environment, some prediction strategy would be used to predict the operation position of the Pareto set. Because of this, the segment and multi-directional prediction is proposed in this paper, which consists of three mechanisms. First, by segmenting the optimal solutions set, the prediction about the changes in the distribution of the Pareto front can be ensured. Second, by introducing the cloud theory, the distance error of direction prediction can be offset effectively. Third, by using extra angle search, the angle error of prediction caused by the Pareto set nonlinear variation can also be offset effectively. Finally, eight benchmark problems were used to verify the performance of the proposed algorithm and compared algorithms. The results indicate that the algorithm proposed in this paper has good convergence and distribution, as well as a quick response ability to the changed environment.

Multi-objective particle swarm optimization using Pareto-based set and aggregation approach

2017 ◽  
Vol 31 (19-21) ◽  
pp. 1740073 ◽  
Author(s):  
Song Huang ◽  
Yan Wang ◽  
Zhicheng Ji
Keyword(s):  
Particle Swarm Optimization ◽  
Local Search ◽  
Real World ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Pareto Set ◽  
Multi Objective Optimization ◽  
Particle Swarm Optimizer ◽  
Swarm Optimization ◽  
Multi Objective

Multi-objective optimization problems (MOPs) need to be solved in real world recently. In this paper, a multi-objective particle swarm optimization based on Pareto set and aggregation approach was proposed to deal with MOPs. Firstly, velocities and positions were updated similar to PSO. Then, global-best set was defined in particle swarm optimizer to preserve Pareto-based set obtained by the population. Specifically, a hybrid updating strategy based on Pareto set and aggregation approach was introduced to update the global-best set and local search was carried on global-best set. Thirdly, personal-best positions were updated in decomposition way, and global-best position was selected from global-best set. Finally, ZDT instances and DTLZ instances were selected to evaluate the performance of MULPSO and the results show validity of the proposed algorithm for MOPs.

scholarly journals Handling Constrained Multi-objective Optimization By Ignoring Constraints and Using Two Evolutionary Frameworks

2020 ◽  
Author(s):  
Xiang Yi ◽  
Xiaowei Yang ◽  
Han Huang ◽  
Jiahai Wang
Keyword(s):  
Real World ◽  
Optimization Problems ◽  
Evolutionary Process ◽  
Inequality Constraints ◽  
Simultaneous Optimization ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Real World Problem ◽  
Conflicting Objectives ◽  
Two Stages

Constrained multi-objective optimization problems exist widely in real-world applications, and they involve a simultaneous optimization of multiple and often conflicting objectives subject to several equality and/or inequality constraints. To deal with these problems, a crucial issue is how to handle constraints effectively. This paper proposes a simple yet effective constrained decomposition-based multi-objective evolutionary algorithm. In the proposal, the evolutionary process is divided into two stages in which constraints are handled differently. In the first stage, constraints are totally ignored and the population is pulled toward the unconstrained Pareto-optimal front (PF) by optimizing objectives only. This can help the proposed algorithm handle well problems with the following features, i.e., the constrained PF has an intersection with the unconstrained counterpart, and there are infeasible regions blocking the way of convergence. In the second stage, with the purpose of approximating the constrained PF well,constraint satisfaction is emphasized over objective minimization.Moreover, different evolutionary frameworks are adopted in the two stages to promote the performance of the algorithm as much as possible. The proposed algorithm is comprehensively compared with several state-of-the-art algorithms on 39 problems (with 266 test instances in total), including one real-world problem (with 36 instances) in search-based software engineering. As shown by the experimental results, the new algorithm performs best on the majority of these problems, particularly on those with the aforementioned features. In summary, the suggested algorithm provides an effective way of handling constrained multi-objective optimization problems.

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