Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy

2000 ◽  
Vol 8 (2) ◽  
pp. 149-172 ◽  
Author(s):  
Joshua D. Knowles ◽  
David W. Corne
Keyword(s):  
Genetic Algorithm ◽  
Multiobjective Optimization ◽  
Local Search ◽  
Optimization Problems ◽  
Population Based ◽  
Evolution Strategy ◽  
Basic Algorithm ◽  
Pareto Optimal Set ◽  
Candidate Solution ◽  
Multiobjective Optimization Problems

We introduce a simple evolution scheme for multiobjective optimization problems, called the Pareto Archived Evolution Strategy (PAES). We argue that PAES may represent the simplest possible nontrivial algorithm capable of generating diverse solutions in the Pareto optimal set. The algorithm, in its simplest form, is a (1+1) evolution strategy employing local search but using a reference archive of previously found solutions in order to identify the approximate dominance ranking of the current and candidate solution vectors. (1+1)-PAES is intended to be a baseline approach against which more involved methods may be compared. It may also serve well in some real-world applications when local search seems superior to or competitive with population-based methods. We introduce (1+λ) and (μ+λ) variants of PAES as extensions to the basic algorithm. Six variants of PAES are compared to variants of the Niched Pareto Genetic Algorithm and the Nondominated Sorting Genetic Algorithm over a diverse suite of six test functions. Results are analyzed and presented using techniques that reduce the attainment surfaces generated from several optimization runs into a set of univariate distributions. This allows standard statistical analysis to be carried out for comparative purposes. Our results provide strong evidence that PAES performs consistently well on a range of multiobjective optimization tasks.

scholarly journals A Multiobjective Genetic Algorithm Based on a Discrete Selection Procedure

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Qiang Long ◽  
Changzhi Wu ◽  
Xiangyu Wang ◽  
Lin Jiang ◽  
Jueyou Li
Keyword(s):  
Genetic Algorithm ◽  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Selection Procedure ◽  
Population Based ◽  
Pareto Solution ◽  
Multiobjective Genetic Algorithm ◽  
Trade Offs ◽  
Multiobjective Optimization Problems ◽  
Optimum Order

Multiobjective genetic algorithm (MOGA) is a direct search method for multiobjective optimization problems. It is based on the process of the genetic algorithm; the population-based property of the genetic algorithm is well applied in MOGAs. Comparing with the traditional multiobjective algorithm whose aim is to find a single Pareto solution, the MOGA intends to identify numbers of Pareto solutions. During the process of solving multiobjective optimization problems using genetic algorithm, one needs to consider the elitism and diversity of solutions. But, normally, there are some trade-offs between the elitism and diversity. For some multiobjective problems, elitism and diversity are conflicting with each other. Therefore, solutions obtained by applying MOGAs have to be balanced with respect to elitism and diversity. In this paper, we propose metrics to numerically measure the elitism and diversity of solutions, and the optimum order method is applied to identify these solutions with better elitism and diversity metrics. We test the proposed method by some well-known benchmarks and compare its numerical performance with other MOGAs; the result shows that the proposed method is efficient and robust.

scholarly journals A Multiobjective Optimization Algorithm Based on Discrete Bacterial Colony Chemotaxis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhigang Lu ◽  
Tao Feng ◽  
Zhaozheng Liu
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Population Diversity ◽  
Transfer Mechanism ◽  
Bacterial Colony ◽  
Continuous Space ◽  
Pareto Optimal Set ◽  
Crowding Distance ◽  
Multiobjective Optimization Problems ◽  
Definition Of

Bacterial colony chemotaxis algorithm was originally developed for optimal problem with continuous space. In this paper the discrete bacterial colony chemotaxis (DBCC) algorithm is developed to solve multiobjective optimization problems. The basic DBCC algorithm has the disadvantage of being trapped into the local minimum. Therefore, some improvements are adopted in the new algorithm, such as adding chaos transfer mechanism when the bacterium choose their next locations and the crowding distance operation to maintain the population diversity in the Pareto Front. The definition of chaos transfer mechanism is used to retain the elite solution produced during the operation, and the definition of crowding distance is used to guide the bacteria for determinate variation, thus enabling the algorithm obtain well-distributed solution in the Pareto optimal set. The convergence properties of the DBCC strategy are tested on some test functions. At last, some numerical results are given to demonstrate the effectiveness of the results obtained by the new algorithm.

Combining Convergence and Diversity in Evolutionary Multiobjective Optimization

2002 ◽  
Vol 10 (3) ◽  
pp. 263-282 ◽  
Author(s):  
Marco Laumanns ◽  
Lothar Thiele ◽  
Kalyanmoy Deb ◽  
Eckart Zitzler
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Fundamental Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Pareto Optimal Set ◽  
Multiobjective Optimization Problems ◽  
Baseline Algorithm

Over the past few years, the research on evolutionary algorithms has demonstrated their niche in solving multiobjective optimization problems, where the goal is to find a number of Pareto-optimal solutions in a single simulation run. Many studies have depicted different ways evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. However, none of the multiobjective evolutionary algorithms (MOEAs) has a proof of convergence to the true Pareto-optimal solutions with a wide diversity among the solutions. In this paper, we discuss why a number of earlier MOEAs do not have such properties. Based on the concept of ɛ-dominance, new archiving strategies are proposed that overcome this fundamental problem and provably lead to MOEAs that have both the desired convergence and distribution properties. A number of modifications to the baseline algorithm are also suggested. The concept of ɛ-dominance introduced in this paper is practical and should make the proposed algorithms useful to researchers and practitioners alike.

Domination Measure: A New Metric for Solving Multiobjective Optimization

2020 ◽  
Vol 32 (3) ◽  
pp. 565-581 ◽  
Author(s):  
Joshua Q. Hale ◽  
Helin Zhu ◽  
Enlu Zhou
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Solution Space ◽  
Optimization Methods ◽  
Pareto Optimal Set ◽  
Performance Metric ◽  
Multiobjective Optimization Problems ◽  
Global Optima ◽  
Benchmark Test Functions ◽  
Optimal Set

For general multiobjective optimization problems, the usual goal is finding the set of solutions not dominated by any other solutions, that is, a set of solutions as good as any other solution in all objectives and strictly better in at least one objective. In this paper, we propose a novel performance metric called the domination measure to measure the quality of a solution, which can be intuitively interpreted as the probability that an arbitrary solution in the solution space dominates that solution with respect to a predefined probability measure. We then reformulate the original problem as a stochastic and single-objective optimization problem. We further propose a model-based approach to solve it, which leads to an ideal version algorithm and an implementable version algorithm. We show that the ideal version algorithm converges to a set representation of the global optima of the reformulated problem; we demonstrate the numerical performance of the implementable version algorithm by comparing it with numerous existing multiobjective optimization methods on popular benchmark test functions. The numerical results show that the proposed approach is effective in generating a finite and uniformly spread approximation of the Pareto optimal set of the original multiobjective problem and is competitive with the tested existing methods. The concept of domination measure opens the door for potentially many new algorithms, and our proposed algorithm is an instance that benefits from domination measure.

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