Fuzzy-Dominance and Its Application in Evolutionary Many Objective Optimization

IEEE Trans. Evol. Computat.

Jin

Olhofer

et al. 2016

1,299

697

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.

Section: Introductionmentioning

confidence: 99%

A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization

IEEE Trans. Evol. Computat.

Jin

Olhofer

et al. 2016

1,299

697

“…Among various convergence enhancement approaches, dominance modification is the most intuitive one. Examples of modified dominance definitions include Loptimality [15], -dominance [16], [17], fuzzy dominance [18], and grid based dominance [19]. Another typical idea of this category is to introduce new convergence metrics in addition to traditional dominance based mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Many-Objective Optimization of Hybrid Electric Vehicle Control: From General Optimization to Preference Articulation

IEEE Trans. Emerg. Top. Comput. Intell.

Rodemann

Fischer

et al. 2017

104

Abstract-Many real-world optimization problems have more than three objectives, which has triggered increasing research interest in developing efficient and effective evolutionary algorithms for solving many-objective optimization problems. However, most many-objective evolutionary algorithms have only been evaluated on benchmark test functions and few applied to real-world optimization problems. To move a step forward, this paper presents a case study of solving a many-objective hybrid electric vehicle controller design problem using three state-of-the-art algorithms, namely, a decomposition based evolutionary algorithm (MOEA/D), a non-dominated sorting based genetic algorithm (NSGA-III), and a reference vector guided evolutionary algorithm (RVEA). We start with a typical setting aiming at approximating the Pareto front without introducing any user preferences. Based on the analyses of the approximated Pareto front, we introduce a preference articulation method and embed it in the three evolutionary algorithms for identifying solutions that the decision-maker prefers. Our experimental results demonstrate that by incorporating user preferences into many-objective evolutionary algorithms, we are not only able to gain deep insight into the trade-off relationships between the objectives, but also to achieve high-quality solutions reflecting the decision-maker's preferences. In addition, our experimental results indicate that each of the three algorithms examined in this work has its unique advantages that can be exploited when applied to the optimization of real-world problems.

“…To enhance the convergence pressure, the most intuitive idea is to directly modify the definition of traditional Pareto dominance, such as ε-dominance [13], [14], L-optimality [15], fuzzy dominance [16], preference order ranking [17] and θ-dominance [18]. Another idea belonging to this category is to combine the traditional dominance with an additional convergence-related metric, and MOEAs belonging to this category include the substitute distance assignment based NSGA-II [19], grid-based evolutionary algorithm (GrEA) [20], preference-inspired coevolutionary algorithm (PICEA-g) [21], many-objective evolutionary algorithm based on directional diversity and favorable convergence (MaOEA-DDFC) [22], and knee point driven evolutionary algorithm (KnEA) [23].…”

mentioning

confidence: 99%

A Decision Variable Clustering-Based Evolutionary Algorithm for Large-Scale Many-Objective Optimization

Zhang

Tian

IEEE Trans. Evol. Computat.

et al. 2018

446

178

Abstract-The current literature of evolutionary manyobjective optimization is merely focused on the scalability to the number of objectives, while little work has considered the scalability to the number of decision variables. Nevertheless, many real-world problems can involve both many objectives and large-scale decision variables. To tackle such large-scale many-objective optimization problems, this paper proposes a specially tailored evolutionary algorithm based on a decision variable clustering method. To begin with, the decision variable clustering method divides the decision variables into two types: convergence-related variables and diversity-related variables. Afterwards, to optimize the two types of decision variables, a convergence optimization strategy and a diversity optimization strategy are adopted. In addition, a fast non-dominated sorting approach is developed to further improve the computational efficiency of the proposed algorithm. To assess the performance of the proposed algorithm, empirical experiments have been conducted on a variety of large-scale many-objective optimization problems with up to 10 objectives and 5000 decision variables. Our experimental results demonstrate that the proposed algorithm has significant advantages over several state-of-the-art evolutionary algorithms in terms of the scalability to decision variables on many-objective optimization problems.