On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem

Schütze, Oliver; Lara, Adriana; Coello, Carlos A. Coello

doi:10.1109/tevc.2010.2064321

Cited by 142 publications

(60 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Specifically, given a translated objective vector f ′ t,i in subpopulation j, the convergence criterion can be naturally represented by the distance from f ′ t,i to the ideal point 4 , i.e., ∥f ′ t,i ∥; and the diversity criterion is represented by the acute angle between f ′ t,i and v t,j , i.e., θ t,i,j , as the inverse function value of cos θ t,i,j calculated in (6). In order to balance between the convergence criterion ∥f ′ t,i ∥ and the diversity criterion θ t,i,j , a scalarization approach, i.e., the angle-penalized distance (APD) is proposed as follows: …”

Section: ) Angle-penalized Distance (Apd) Calculationmentioning

confidence: 99%

A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization

Cheng

Jin

Olhofer

et al. 2016

IEEE Trans. Evol. Computat.

1,291

697

View full text Add to dashboard Cite

Abstract-In evolutionary multi-objective optimization, maintaining a good balance between convergence and diversity is particularly crucial to the performance of the evolutionary algorithms. In addition, it becomes increasingly important to incorporate user preferences because it will be less likely to achieve a representative subset of the Pareto optimal solutions using a limited population size as the number of objectives increases. This paper proposes a reference vector guided evolutionary algorithm for many-objective optimization. The reference vectors can not only be used to decompose the original multiobjective optimization problem into a number of single-objective sub-problems, but also to elucidate user preferences to target a preferred subset of the whole Pareto front. In the proposed algorithm, a scalarization approach, termed angle penalized distance, is adopted to balance convergence and diversity of the solutions in the high-dimensional objective space. An adaptation strategy is proposed to dynamically adjust the distribution of the reference vectors according to the scales of the objective functions. Our experimental results on a variety of benchmark test problems show that the proposed algorithm is highly competitive in comparison with five state-of-the-art evolutionary algorithms for many-objective optimization. In addition, we show that reference vectors are effective and cost-efficient for preference articulation, which is particularly desirable for many-objective optimization. Furthermore, a reference vector regeneration strategy is proposed for handling irregular Pareto fronts. Finally, the proposed algorithm is extended for solving constrained many-objective optimization problems.

show abstract

Section: ) Angle-penalized Distance (Apd) Calculationmentioning

confidence: 99%

A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization

Cheng

Jin

Olhofer

et al. 2016

IEEE Trans. Evol. Computat.

1,291

697

View full text Add to dashboard Cite

show abstract

“…2k). It would have been possible to conduct evolution using three objectives rather than two, but there are known challenges with increasing the number of objectives [21] and this would have made a fair comparison to the first two algorithm variants (both of which employ two objectives) more difficult.…”

Section: Combining Fitness-based Search and Preference-based Policy Lmentioning

confidence: 99%

Combining fitness-based search and user modeling in evolutionary robotics

Bongard

Hornby

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

View full text Add to dashboard Cite

Methodologies are emerging in many branches of computer science that demonstrate how human users and automated algorithms can collaborate on a problem such that their combined solutions outperform those produced by either humans or algorithms alone. The problem of behavior optimization in robotics seems particularly well-suited for this approach because humans have intuitions about how animals-and thus robots-should and should not behave, and can visually detect non-optimal behaviors that are trapped in local optima. Here we introduce a multiobjective approach in which a surrogate user (which stands in for a human user) deflects search away from local optima and a traditional fitness function eventually leads search toward the global optimum. We show that this approach produces superior solutions for a deceptive robotics problem compared to a similar search method that is guided by just a surrogate user or just a fitness function.

show abstract

“…In the last decade, many-objective optimization has gained growing attention in the EMO community [12], [24], [39], [57]. One of the important reasons is due to the rapid increase of difficulties with the number of objectives in multiobjective optimization [8], [68], [70]. Most current EMO algorithms, which work well on problems with two or three objectives, noticeably deteriorate their search ability when more objectives are involved [46], [48], [65].…”

Section: Introductionmentioning

confidence: 99%

Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization

Yang

Liu

2014

IEEE Trans. Evol. Computat.

558

248

View full text Add to dashboard Cite

Abstract-It is commonly accepted that Pareto-based evolutionary multiobjective optimization (EMO) algorithms encounter difficulties in dealing with many-objective problems. In these algorithms, the ineffectiveness of the Pareto dominance relation for a high-dimensional space leads diversity maintenance mechanisms to play the leading role during the evolutionary process, while the preference of diversity maintenance mechanisms for individuals in sparse regions results in the final solutions distributed widely over the objective space but distant from the desired Pareto front. Intuitively, there are two ways to address this problem: 1) modifying the Pareto dominance relation and 2) modifying the diversity maintenance mechanism in the algorithm. In this paper, we focus on the latter and propose a shift-based density estimation (SDE) strategy. The aim of our study is to develop a general modification of density estimation in order to make Pareto-based algorithms suitable for many-objective optimization. In contrast to traditional density estimation which only involves the distribution of individuals in the population, SDE covers both the distribution and convergence information of individuals. The application of SDE in three popular Paretobased algorithms demonstrates its usefulness in handling manyobjective problems. Moreover, an extensive comparison with five state-of-the-art EMO algorithms reveals its competitiveness in balancing convergence and diversity of solutions. These findings not only show that SDE is a good alternative to tackle manyobjective problems, but also present a general extension of Paretobased algorithms in many-objective optimization.

show abstract

On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem

Cited by 142 publications

References 29 publications

A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization

A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization

Combining fitness-based search and user modeling in evolutionary robotics

Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization

Contact Info

Product

Resources

About