scholarly journals Comparison of Multiobjective Evolutionary Algorithms: Empirical Results

2000 ◽  
Vol 8 (2) ◽  
pp. 173-195 ◽  
Author(s):  
Eckart Zitzler ◽  
Kalyanmoy Deb ◽  
Lothar Thiele
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Experimental Results ◽  
Pareto Optimal ◽  
Multiobjective Evolutionary Algorithms ◽  
Test Functions ◽  
Test Function ◽  
Pareto Optimal Front ◽  
Systematic Comparison ◽  
Empirical Results

In this paper, we provide a systematic comparison of various evolutionary approaches to multiobjective optimization using six carefully chosen test functions. Each test function involves a particular feature that is known to cause difficulty in the evolutionary optimization process, mainly in converging to the Pareto-optimal front (e.g., multimodality and deception). By investigating these different problem features separately, it is possible to predict the kind of problems to which a certain technique is or is not well suited. However, in contrast to what was suspected beforehand, the experimental results indicate a hierarchy of the algorithms under consideration. Furthermore, the emerging effects are evidence that the suggested test functions provide sufficient complexity to compare multiobjective optimizers. Finally, elitism is shown to be an important factor for improving evolutionary multiobjective search.

APPLICATION OF NOVEL CLONAL ALGORITHM IN MULTIOBJECTIVE OPTIMIZATION

2010 ◽  
Vol 09 (02) ◽  
pp. 239-266 ◽  
Author(s):  
JIANYONG CHEN ◽  
QIUZHEN LIN ◽  
QINGBIN HU
Keyword(s):  
Multiobjective Optimization ◽  
Coarse Grained ◽  
Pareto Optimal ◽  
Pareto Optimal Front ◽  
Fine Grained ◽  
Initial Stage ◽  
Speed Up ◽  
Main Notion ◽  
Hybrid Mutation Operator ◽  
Cooling Schedule

In this paper, a novel clonal algorithm applied in multiobjecitve optimization (NCMO) is presented, which is designed from the improvement of search operators, i.e. dynamic mutation probability, dynamic simulated binary crossover (D-SBX) operator and hybrid mutation operator combining with Gaussian and polynomial mutations (GP-HM) operator. The main notion of these approaches is to perform more coarse-grained search at initial stage in order to speed up the convergence toward the Pareto-optimal front. Once the solutions are getting close to the Pareto-optimal front, more fine-grained search is performed in order to reduce the gaps between the solutions and the Pareto-optimal front. Based on this purpose, a cooling schedule is adopted in these approaches, reducing the parameters gradually to a minimal threshold, the aim of which is to keep a desirable balance between fine-grained search and coarse-grained search. By this means, the exploratory capabilities of NCMO are enhanced. When compared with various state-of-the-art multiobjective optimization algorithms developed recently, simulation results show that NCMO has remarkable performance.

Global WASF-GA: An Evolutionary Algorithm in Multiobjective Optimization to Approximate the Whole Pareto Optimal Front

2017 ◽  
Vol 25 (2) ◽  
pp. 309-349 ◽  
Author(s):  
Rubén Saborido ◽  
Ana B. Ruiz ◽  
Mariano Luque
Keyword(s):  
Multiobjective Optimization ◽  
Evolutionary Algorithm ◽  
Fitness Function ◽  
Weight Vector ◽  
Reference Points ◽  
Pareto Optimal ◽  
Computational Results ◽  
Nsga Ii ◽  
Nondominated Solutions ◽  
Pareto Optimal Front

In this article, we propose a new evolutionary algorithm for multiobjective optimization called Global WASF-GA ( global weighting achievement scalarizing function genetic algorithm), which falls within the aggregation-based evolutionary algorithms. The main purpose of Global WASF-GA is to approximate the whole Pareto optimal front. Its fitness function is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, in which two reference points are considered (both utopian and nadir objective vectors) and the weight vector used is taken from a set of weight vectors whose inverses are well-distributed. At each iteration, all individuals are classified into different fronts. Each front is formed by the solutions with the lowest values of the ASF for the different weight vectors in the set, using the utopian vector and the nadir vector as reference points simultaneously. Varying the weight vector in the ASF while considering the utopian and the nadir vectors at the same time enables the algorithm to obtain a final set of nondominated solutions that approximate the whole Pareto optimal front. We compared Global WASF-GA to MOEA/D (different versions) and NSGA-II in two-, three-, and five-objective problems. The computational results obtained permit us to conclude that Global WASF-GA gets better performance, regarding the hypervolume metric and the epsilon indicator, than the other two algorithms in many cases, especially in three- and five-objective problems.

scholarly journals An MOEA/D-ACO with PBI for Many-Objective Optimization

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Tianbai Ling ◽  
Chen Wang
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Selection Pressure ◽  
Optimization Problems ◽  
State Of The Art ◽  
Experimental Results ◽  
Significant Problem ◽  
Adjustment Method ◽  
Multiobjective Optimization Problems ◽  
Single Objective

Evolutionary algorithms (EAs) are an important instrument for solving the multiobjective optimization problems (MOPs). It has been observed that the combined ant colony (MOEA/D-ACO) based on decomposition is very promising for MOPs. However, as the number of optimization objectives increases, the selection pressure will be released, leading to a significant reduction in the performance of the algorithm. It is a significant problem and challenge in the MOEA/D-ACO to maintain the balance between convergence and diversity in many-objective optimization problems (MaOPs). In the proposed algorithm, an MOEA/D-ACO with the penalty based boundary intersection distance (PBI) method (MOEA/D-ACO-PBI) is intended to solve the MaOPs. PBI decomposes the problems with many single-objective problems, a weighted vector adjustment method based on clustering, and uses different pheromone matrices to solve different single objectives proposed. Then the solutions are constructed and pheromone was updated. Experimental results on both CF1-CF4 and suits of C-DTLZ benchmarks problems demonstrate the superiority of the proposed algorithm in comparison with three state-of-the-art algorithms in terms of both convergence and diversity.

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.

Pareto-adaptive ε-dominance

2007 ◽  
Vol 15 (4) ◽  
pp. 493-517 ◽  
Author(s):  
Alfredo G. Hernández-Díaz ◽  
Luis V. Santana-Quintero ◽  
Carlos A. Coello Coello ◽  
Julián Molina
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Multiobjective Evolutionary Algorithms ◽  
Pareto Dominance ◽  
Nondominated Solutions ◽  
Evolutionary Multiobjective Optimization ◽  
The Way

Efficiency has become one of the main concerns in evolutionary multiobjective optimization during recent years. One of the possible alternatives to achieve a faster convergence is to use a relaxed form of Pareto dominance that allows us to regulate the granularity of the approximation of the Pareto front that we wish to achieve. One such relaxed forms of Pareto dominance that has become popular in the last few years is ε-dominance, which has been mainly used as an archiving strategy in some multiobjective evolutionary algorithms. Despite its advantages, ε-dominance has some limitations. In this paper, we propose a mechanism that can be seen as a variant of ε-dominance, which we call Pareto-adaptive ε-dominance (paε-dominance). Our proposed approach tries to overcome the main limitation of ε-dominance: the loss of several nondominated solutions from the hypergrid adopted in the archive because of the way in which solutions are selected within each box.

Hybridisation of Evolutionary Algorithms for Solving Multi-Objective Simulation Optimisation Problems

2009 ◽  
Vol 39 (1) ◽  
pp. 9-15
Author(s):  
Liana Napalkova
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Optimal ◽  
Approximation Accuracy ◽  
Pareto Optimal Front ◽  
Computational Costs ◽  
Multi Objective ◽  
Taxonomic Analysis ◽  
Simulation Optimisation

Hybridisation of Evolutionary Algorithms for Solving Multi-Objective Simulation Optimisation ProblemsThe paper presents a taxonomic analysis of existing hybrid multi-objective evolutionary algorithms aimed at solving multi-objective simulation optimisation problems. For that, the properties of evolutionary algorithms and the requirements made to solving the problem considered are determined. Finally, a combination of the properties, which allows one to increase the approximation accuracy of the Pareto-optimal front at relatively low computational costs, is revealed.

IMPROVING THE PERFORMANCE OF MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS USING THE ISLAND PARALLEL MODEL

2007 ◽  
Vol 17 (02) ◽  
pp. 127-139 ◽  
Author(s):  
A. MÁRQUEZ ◽  
C. GIL ◽  
R. BAÑOS ◽  
J. GÓMEZ
Keyword(s):  
Parallel Processing ◽  
Evolutionary Algorithms ◽  
Population Size ◽  
Test Problems ◽  
Pareto Optimal ◽  
Parallel Model ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective

Recently, the research interest in multi-objective optimization has increased remarkably. Most of the proposed methods use a population of solutions that are simultaneously improved trying to approximate them to the Pareto-optimal front. When the population size increases, the quality of the solutions tends to be better, but the runtime is higher. This paper presents how to apply parallel processing to enhance the convergence to the Pareto-optimal front, without increasing the runtime. In particular, we present an island-based parallelization of five multi-objective evolutionary algorithms: NSGAII, SPEA2, PESA, msPESA, and a new hybrid version we propose. Experimental results in some test problems denote that the quality of the solutions tends to improve when the number of islands increases.

scholarly journals Evaluating Multiobjective Evolutionary Algorithms Using MCDM Methods

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaobing Yu ◽  
YiQun Lu ◽  
Xianrui Yu
Keyword(s):  
Decision Making ◽  
Experimental Study ◽  
Evolutionary Algorithms ◽  
Performance Metrics ◽  
Multiple Criteria Decision Making ◽  
Multiple Criteria ◽  
Experimental Results ◽  
Multiobjective Evolutionary Algorithms

The evaluation of multiobjective evolutionary algorithms (MOEAs) involves many metrics, it can be considered as a multiple-criteria decision making (MCDM) problem. A framework is proposed to estimate MOEAs, in which six MOEAs, five performance metrics, and two MCDM methods are used. An experimental study is designed and thirteen benchmark functions are selected to validate the proposed framework. The experimental results have indicated that the framework is effective in evaluating MOEAs.

scholarly journals A Review of Surrogate Assisted Multiobjective Evolutionary Algorithms

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Alan Díaz-Manríquez ◽  
Gregorio Toscano ◽  
Jose Hugo Barron-Zambrano ◽  
Edgar Tello-Leal
Keyword(s):  
Evolutionary Algorithms ◽  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
State Of The Art ◽  
Surrogate Models ◽  
Multiobjective Evolutionary Algorithms ◽  
Advantages And Disadvantages ◽  
Multiobjective Optimization Problems ◽  
Computationally Expensive

Multiobjective evolutionary algorithms have incorporated surrogate models in order to reduce the number of required evaluations to approximate the Pareto front of computationally expensive multiobjective optimization problems. Currently, few works have reviewed the state of the art in this topic. However, the existing reviews have focused on classifying the evolutionary multiobjective optimization algorithms with respect to the type of underlying surrogate model. In this paper, we center our focus on classifying multiobjective evolutionary algorithms with respect to their integration with surrogate models. This interaction has led us to classify similar approaches and identify advantages and disadvantages of each class.

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