A New Two-Stage Evolutionary Algorithm for Many-Objective Optimization

© 1997-2012 IEEE. Convergence and diversity are interdependently handled during the evolutionary process by most existing many-objective evolutionary algorithms (MaOEAs). In such a design, the degraded performance of one would deteriorate the other, and only solutions with both are able to improve the performance of MaOEAs. Unfortunately, it is not easy to constantly maintain a population of solutions with both convergence and diversity. In this paper, an MaOEA based on two independent stages is proposed for effectively solving many-objective optimization problems (MaOPs), where the convergence and diversity are addressed in two independent and sequential stages. To achieve this, we first propose a nondominated dynamic weight aggregation method by using a genetic algorithm, which is capable of finding the Pareto-optimal solutions for MaOPs with concave, convex, linear and even mixed Pareto front shapes, and then these solutions are employed to learn the Pareto-optimal subspace for the convergence. Afterward, the diversity is addressed by solving a set of single-objective optimization problems with reference lines within the learned Pareto-optimal subspace. To evaluate the performance of the proposed algorithm, a series of experiments are conducted against six state-of-The-Art MaOEAs on benchmark test problems. The results show the significantly improved performance of the proposed algorithm over the peer competitors. In addition, the proposed algorithm can focus directly on a chosen part of the objective space if the preference area is known beforehand. Furthermore, the proposed algorithm can also be used to effectively find the nadir points.

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A New Two-Stage Evolutionary Algorithm for Many-Objective Optimization

10.26686/wgtn.13158290 ◽

2020 ◽

Author(s):

Y Sun ◽

Bing Xue ◽

Mengjie Zhang ◽

GG Yen

Keyword(s):

Pareto Front ◽

Optimization Problems ◽

Evolutionary Process ◽

Test Problems ◽

Pareto Optimal ◽

Aggregation Method ◽

Objective Space ◽

Series Of Experiments ◽

Improved Performance ◽

Optimal Subspace

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A New Multiobjective Evolutionary Algorithm Based on Decomposition of the Objective Space for Multiobjective Optimization

Journal of Applied Mathematics ◽

10.1155/2014/906147 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 4

Author(s):

Cai Dai ◽

Yuping Wang

Keyword(s):

Multiobjective Optimization ◽

Evolutionary Algorithm ◽

Pareto Front ◽

Optimization Problems ◽

Experimental Studies ◽

Evolutionary Process ◽

Optimal Solution ◽

Multiobjective Evolutionary Algorithm ◽

Multiobjective Optimization Problems ◽

Objective Space

In order to well maintain the diversity of obtained solutions, a new multiobjective evolutionary algorithm based on decomposition of the objective space for multiobjective optimization problems (MOPs) is designed. In order to achieve the goal, the objective space of a MOP is decomposed into a set of subobjective spaces by a set of direction vectors. In the evolutionary process, each subobjective space has a solution, even if it is not a Pareto optimal solution. In such a way, the diversity of obtained solutions can be maintained, which is critical for solving some MOPs. In addition, if a solution is dominated by other solutions, the solution can generate more new solutions than those solutions, which makes the solution of each subobjective space converge to the optimal solutions as far as possible. Experimental studies have been conducted to compare this proposed algorithm with classic MOEA/D and NSGAII. Simulation results on six multiobjective benchmark functions show that the proposed algorithm is able to obtain better diversity and more evenly distributed Pareto front than the other two algorithms.

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Using Objective Clustering for Solving Many-Objective Optimization Problems

Mathematical Problems in Engineering ◽

10.1155/2013/584909 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12 ◽

Cited By ~ 12

Author(s):

Xiaofang Guo ◽

Yuping Wang ◽

Xiaoli Wang

Keyword(s):

Clustering Algorithm ◽

Optimization Problems ◽

Computational Cost ◽

Special Kind ◽

Test Problems ◽

Pareto Optimal ◽

Pareto Optimal Front ◽

Engineering Design Problem ◽

Objective Space ◽

Practical Engineering

Many-objective optimization problems involving a large number (more than four) of objectives have attracted considerable attention from the evolutionary multiobjective optimization field recently. With the increasing number of objectives, many-objective optimization problems may lead to stagnation in search process, high computational cost, increased dimensionality of Pareto-optimal front, and difficult visualization of the objective space. In this paper, a special kind of many-objective problems which has redundant objectives and which can be degenerated to a lower dimensional Pareto-optimal front has been investigated. Different from the works in the previous literatures, a novel metric, interdependence coefficient, which represents the nonlinear relationship between pairs of objectives, is introduced in this paper. In order to remove redundant objectives, PAM clustering algorithm is employed to identify redundant objectives by merging the less conflict objectives into the same cluster, and one of the least conflict objectives is removed. Furthermore, the potential of the proposed algorithm is demonstrated by a set of benchmark test problems scaled up to 20 objectives and a practical engineering design problem.

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Improved Trust Region Based MPS Method for High-Dimensional Expensive Black-Box Problems

Volume 3B: 39th Design Automation Conference ◽

10.1115/detc2013-12665 ◽

2013 ◽

Author(s):

George H. Cheng ◽

Adel Younis ◽

Kambiz Haji Hajikolaei ◽

G. Gary Wang

Keyword(s):

Optimization Problems ◽

Trust Region ◽

Black Box ◽

High Dimensional ◽

Test Problems ◽

Design Variables ◽

Low Dimensionality ◽

Improve Algorithm ◽

Improved Performance ◽

Better Than

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

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Presorting as a method of acceleration of algorithms in multi-objective optimization problems

Computer Science and Mathematical Modelling ◽

10.5604/01.3001.0009.7758 ◽

2016 ◽

Vol 0 (0) ◽

pp. 5-11

Author(s):

Andrzej Ameljańczyk

Keyword(s):

Distance Function ◽

Pareto Front ◽

Optimization Problems ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Multi Objective Optimization ◽

Minkowski Distance ◽

Finite Set ◽

Feasible Solutions

The paper presents a method of algorithms acceleration for determining Pareto-optimal solutions (Pareto Front) multi-criteria optimization tasks, consisting of pre-ordering (presorting) set of feasible solutions. It is proposed to use the generalized Minkowski distance function as a presorting tool that allows build a very simple and fast algorithm Pareto Front for the task with a finite set of feasible solutions.

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Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

Evolutionary Computation ◽

10.1162/106365605774666895 ◽

2005 ◽

Vol 13 (4) ◽

pp. 501-525 ◽

Cited By ~ 377

Author(s):

Kalyanmoy Deb ◽

Manikanth Mohan ◽

Shikhar Mishra

Keyword(s):

Steady State ◽

Evolutionary Algorithm ◽

Optimization Problems ◽

Computational Time ◽

Test Problems ◽

Pareto Optimal ◽

Pareto Optimal Solutions ◽

Optimal Solutions ◽

Nsga Ii ◽

Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

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Archive of Useful Solutions for Directed Mating in Evolutionary Constrained Multiobjective Optimization

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2014.p0221 ◽

2014 ◽

Vol 18 (2) ◽

pp. 221-231 ◽

Cited By ~ 2

Author(s):

Minami Miyakawa ◽

◽

Keiki Takadama ◽

Hiroyuki Sato

Keyword(s):

Pareto Front ◽

Optimization Problems ◽

Selection Process ◽

Benchmark Problems ◽

Search Performance ◽

Next Generation ◽

Multi Objective ◽

Objective Space ◽

Feasible Solutions ◽

Constrained Multiobjective Optimization

As an evolutionary approach to solve multi-objective optimization problems involving several constraints, recently a multi-objective evolutionary algorithm (MOEA) using two-stage non-dominated sorting and directed mating (TNSDM) has been proposed. In TNSDM, directed mating utilizes infeasible solutions dominating feasible solutions in the objective space to generate offspring. In our previous studies, significant contribution of directed mating to the improvement of the search performancewas verified on several benchmark problems. However, in the conventional TNSDM, infeasible solutions utilized in directed mating are discarded in the selection process of parents (elites) population and cannot be utilized in the next generation. TNSDM has potential to further improve the search performance by archiving useful solutions for directed mating to the next generation and repeatedly utilizing them in directed mating. To further improve effects of directed mating in TNSDM, in this work, we propose an archiving strategy of useful solutions for directed mating. We verify the search performance of TNSDM using the proposed archive by varying the size of archive, and compare its search performance with the conventional CNSGA-II and RTS onmobjectiveskknapsacks problems. As results, we show that the search performance of TNSDM is improved by introducing the proposed archive in aspects of diversity of the obtained solutions in the objective space and convergence of solutions toward the optimal Pareto front.

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An evolutionary based framework for many-objective optimization problems

Engineering Computations ◽

10.1108/ec-08-2017-0296 ◽

2018 ◽

Vol 35 (4) ◽

pp. 1805-1828 ◽

Cited By ~ 1

Author(s):

Kimia Bazargan Lari ◽

Ali Hamzeh

Keyword(s):

Optimization Problems ◽

State Of The Art ◽

Fitness Function ◽

Population Diversity ◽

Numerical Results ◽

Superior Performance ◽

High Dimensional ◽

Test Problems ◽

Content Type ◽

Objective Space

Purpose Recently, many-objective optimization evolutionary algorithms have been the main issue for researchers in the multi-objective optimization community. To deal with many-objective problems (typically for four or more objectives) some modern frameworks are proposed which have the potential of achieving the finest non-dominated solutions in many-objective spaces. The effectiveness of these algorithms deteriorates greatly as the problem’s dimension increases. Diversity reduction in the objective space is the main reason of this phenomenon. Design/methodology/approach To properly deal with this undesirable situation, this work introduces an indicator-based evolutionary framework that can preserve the population diversity by producing a set of discriminated solutions in high-dimensional objective space. This work attempts to diversify the objective space by proposing a fitness function capable of discriminating the chromosomes in high-dimensional space. The numerical results prove the potential of the proposed method, which had superior performance in most of test problems in comparison with state-of-the-art algorithms. Findings The achieved numerical results empirically prove the superiority of the proposed method to state-of-the-art counterparts in the most test problems of a known artificial benchmark. Originality/value This paper provides a new interpretation and important insights into the many-objective optimization realm by emphasizing on preserving the population diversity.

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An Environmental Selection and Transfer Learning Based Dynamic Multiobjective Optimization Evolutionary Algorithm

10.21203/rs.3.rs-320752/v1 ◽

2021 ◽

Author(s):

Qiang He ◽

Zheng Xiang ◽

Peng Ren

Keyword(s):

Multiobjective Optimization ◽

Evolutionary Algorithm ◽

Transfer Learning ◽

Optimization Problems ◽

Evolutionary Process ◽

Pareto Optimal ◽

Nsga Ii ◽

Environmental Selection ◽

Dynamic Multiobjective Optimization ◽

Prediction Strategy

Abstract In recent years, the dynamic multiobjective optimization problems (DMOPs), whose major strategy is to track the varying PS (Pareto Optimal Solution, PS) and/or PF (Pareto Optimal Frontier), caused a great deal of attention worldwide. As a promising solution, reusing of “experiences” to establish a prediction model is proved to be very useful and widely used in practice. However, most existing methods overlook the importance of environmental selection in the evolutionary processes. In this paper, we propose a dynamic multiobjective optimal evolutionary algorithm which is based on environmental selection and transfer learning (DMOEA-ESTL). This approach makes full use of the environmental selection and transfer learning technique to generate individuals for a new environment by reusing experience to maintain the diversity of the population and speed up the evolutionary process. As experimental validation, we embed this new scheme in the NSGA-II (non-dominated sorting genetic algorithm). We test the proposed algorithm with the help of six benchmark functions as well as compare it with the other two prediction based strategies FPS (Forward-looking Prediction Strategy, FPS) and PPS (Population Prediction Strategy, PPS). The experimental results testify that the proposed strategy can deal with the DMOPs effectively.

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Performances Assessment of MOMA-Plus Method on Multiobjective Optimization Problems

European Journal of Pure and Applied Mathematics ◽

10.29020/nybg.ejpam.v1i1.3581 ◽

2020 ◽

Vol 13 (1) ◽

pp. 48-68

Author(s):

Alexandre Som ◽

Kounhinir Some ◽

Abdoulaye Compaore ◽

Blaise Some

Keyword(s):

Multiobjective Optimization ◽

Comparative Study ◽

Pareto Front ◽

Optimization Problems ◽

Test Problems ◽

Nsga Ii ◽

Multiobjective Problems ◽

Multiobjective Optimization Problems ◽

Non Linear

This work is devoted to evaluate the performances of the MOMA-plus method in solving multiobjective optimization problems. This assessment is doing on the complexity of its algorithm, the convergence and the diversity of solutions in relation to the Pareto front. All these parameters were evaluated on non-linear multiobjective test problems and obtained solutions are compared with those provided by the NSGA-II method. This comparative study made it possible tohighlight the performances of MOMA-plus method for solving non-linear multiobjective problems.

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