Convergence versus diversity in multiobjective optimization

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkConvergence and diversity are two main goals in multiobjective optimization. In literature, most existing multiobjective optimization evolutionary algorithms (MOEAs) adopt a convergence-first-and-diversity-second environmental selection which prefers nondominated solutions to dominated ones, as is the case with the popular nondominated sorting based selection method. While convergence-first sorting has continuously shown effectiveness for handling a variety of problems, it faces challenges to maintain well population diversity due to the overemphasis of convergence. In this paper, we propose a general diversity-first sorting method for multiobjective optimization. Based on the method, a new MOEA, called DBEA, is then introduced. DBEA is compared with the recently-developed nondominated sorting genetic algorithm III (NSGA-III) on different problems. Experimental studies show that the diversity-first method has great potential for diversity maintenance and is very competitive for many-objective optimization

Stochastic Fractal Based Multiobjective Fruit Fly Optimization

The fruit fly optimization algorithm (FOA) is a global optimization algorithm inspired by the foraging behavior of a fruit fly swarm. In this study, a novel stochastic fractal model based fruit fly optimization algorithm is proposed for multiobjective optimization. A food source generating method based on a stochastic fractal with an adaptive parameter updating strategy is introduced to improve the convergence performance of the fruit fly optimization algorithm. To deal with multiobjective optimization problems, the Pareto domination concept is integrated into the selection process of fruit fly optimization and a novel multiobjective fruit fly optimization algorithm is then developed. Similarly to most of other multiobjective evolutionary algorithms (MOEAs), an external elitist archive is utilized to preserve the nondominated solutions found so far during the evolution, and a normalized nearest neighbor distance based density estimation strategy is adopted to keep the diversity of the external elitist archive. Eighteen benchmarks are used to test the performance of the stochastic fractal based multiobjective fruit fly optimization algorithm (SFMOFOA). Numerical results show that the SFMOFOA is able to well converge to the Pareto fronts of the test benchmarks with good distributions. Compared with four state-of-the-art methods, namely, the non-dominated sorting generic algorithm (NSGA-II), the strength Pareto evolutionary algorithm (SPEA2), multi-objective particle swarm optimization (MOPSO), and multiobjective self-adaptive differential evolution (MOSADE), the proposed SFMOFOA has better or competitive multiobjective optimization performance

Stochastic Fractal Based Multiobjective Fruit Fly Optimization

The fruit fly optimization algorithm (FOA) is a global optimization algorithm inspired by the foraging behavior of a fruit fly swarm. In this study, a novel stochastic fractal model based fruit fly optimization algorithm is proposed for multiobjective optimization. A food source generating method based on a stochastic fractal with an adaptive parameter updating strategy is introduced to improve the convergence performance of the fruit fly optimization algorithm. To deal with multiobjective optimization problems, the Pareto domination concept is integrated into the selection process of fruit fly optimization and a novel multiobjective fruit fly optimization algorithm is then developed. Similarly to most of other multiobjective evolutionary algorithms (MOEAs), an external elitist archive is utilized to preserve the nondominated solutions found so far during the evolution, and a normalized nearest neighbor distance based density estimation strategy is adopted to keep the diversity of the external elitist archive. Eighteen benchmarks are used to test the performance of the stochastic fractal based multiobjective fruit fly optimization algorithm (SFMOFOA). Numerical results show that the SFMOFOA is able to well converge to the Pareto fronts of the test benchmarks with good distributions. Compared with four state-of-the-art methods, namely, the non-dominated sorting generic algorithm (NSGA-II), the strength Pareto evolutionary algorithm (SPEA2), multi-objective particle swarm optimization (MOPSO), and multiobjective self-adaptive differential evolution (MOSADE), the proposed SFMOFOA has better or competitive multiobjective optimization performance

Decomposition-Based-Sorting and Angle-Based-Selection for Evolutionary Multiobjective and Many-Objective Optimization

Multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem (MOP) into a number of scalar optimization subproblems and then solves them in parallel. In many MOEA/D variants, each subproblem is associated with one and only one solution. An underlying assumption is that each subproblem has a different Pareto-optimal solution, which may not be held, for irregular Pareto fronts (PFs), e.g., disconnected and degenerate ones. In this paper, we propose a new variant of MOEA/D with sorting-and-selection (MOEA/D-SAS). Different from other selection schemes, the balance between convergence and diversity is achieved by two distinctive components, decomposition-based-sorting (DBS) and angle-based-selection (ABS). DBS only sorts ${L}$ closest solutions to each subproblem to control the convergence and reduce the computational cost. The parameter ${L}$ has been made adaptive based on the evolutionary process. ABS takes use of angle information between solutions in the objective space to maintain a more fine-grained diversity. In MOEA/D-SAS, different solutions can be associated with the same subproblems; and some subproblems are allowed to have no associated solution, more flexible to MOPs or many-objective optimization problems (MaOPs) with different shapes of PFs. Comprehensive experimental studies have shown that MOEA/D-SAS outperforms other approaches; and is especially effective on MOPs or MaOPs with irregular PFs. Moreover, the computational efficiency of DBS and the effects of ABS in MOEA/D-SAS are also investigated and discussed in detail

An evolutionary algorithm with double-level archives for multiobjective optimization

Existing multiobjective evolutionary algorithms (MOEAs) tackle a multiobjective problem either as a whole or as several decomposed single-objective sub-problems. Though the problem decomposition approach generally converges faster through optimizing all the sub-problems simultaneously, there are two issues not fully addressed, i.e., distribution of solutions often depends on a priori problem decomposition, and the lack of population diversity among sub-problems. In this paper, a MOEA with double-level archives is developed. The algorithm takes advantages of both the multiobjective-problemlevel and the sub-problem-level approaches by introducing two types of archives, i.e., the global archive and the sub-archive. In each generation, self-reproduction with the global archive and cross-reproduction between the global archive and sub-archives both breed new individuals. The global archive and sub-archives communicate through cross-reproduction, and are updated using the reproduced individuals. Such a framework thus retains fast convergence, and at the same time handles solution distribution along Pareto front (PF) with scalability. To test the performance of the proposed algorithm, experiments are conducted on both the widely used benchmarks and a set of truly disconnected problems. The results verify that, compared with state-of-the-art MOEAs, the proposed algorithm offers competitive advantages in distance to the PF, solution coverage, and search speed

Hybridizing Non-dominated Sorting Algorithms: Divide-and-Conquer Meets Best Order Sort

Many production-grade algorithms benefit from combining an asymptotically efficient algorithm for solving big problem instances, by splitting them into smaller ones, and an asymptotically inefficient algorithm with a very small implementation constant for solving small subproblems. A well-known example is stable sorting, where mergesort is often combined with insertion sort to achieve a constant but noticeable speed-up. We apply this idea to non-dominated sorting. Namely, we combine the divide-and-conquer algorithm, which has the currently best known asymptotic runtime of $O(N (\log N)^{M - 1})$, with the Best Order Sort algorithm, which has the runtime of $O(N^2 M)$ but demonstrates the best practical performance out of quadratic algorithms. Empirical evaluation shows that the hybrid's running time is typically not worse than of both original algorithms, while for large numbers of points it outperforms them by at least 20%. For smaller numbers of objectives, the speedup can be as large as four times.Comment: A two-page abstract of this paper will appear in the proceedings companion of the 2017 Genetic and Evolutionary Computation Conference (GECCO 2017

Ergonomic Chair Design by Fusing Qualitative and Quantitative Criteria using Interactive Genetic Algorithms

This paper emphasizes the necessity of formally bringing qualitative and quantitative criteria of ergonomic design together, and provides a novel complementary design framework with this aim. Within this framework, different design criteria are viewed as optimization objectives; and design solutions are iteratively improved through the cooperative efforts of computer and user. The framework is rooted in multi-objective optimization, genetic algorithms and interactive user evaluation. Three different algorithms based on the framework are developed, and tested with an ergonomic chair design problem. The parallel and multi-objective approaches show promising results in fitness convergence, design diversity and user satisfaction metrics