Evolutionary Many-objective Optimization Research Articles

Adaptive Control of Dominance Area of Solutions in Evolutionary Many-Objective Optimization

Controlling the dominance area of solutions (CDAS) relaxes the concept of Pareto dominance with an user-defined parameter S. CDAS with S < 0.5 expands the dominance area and improves the search performance of multi-objective evolutionary algorithms (MOEAs) especially in many-objective optimization problems (MaOPs) by enhancing convergence of solutions toward the optimal Pareto front. However, there is a problem that CDAS with an expanded dominance area (S < 0.5) generally cannot approximate entire Pareto front. To overcome this problem we propose an adaptive CDAS (A-CDAS) that adaptively controls the dominance area of solutions during the solutions search. Our method improves the search performance in MaOPs by approximating the entire Pareto front while keeping high convergence. In early generations, A-CDAS tries to converge solutions toward the optimal Pareto front by using an expanded dominance area with S < 0.5. When we detect convergence of solutions, we gradually increase S and contract the dominance area of solutions to obtain Pareto optimal solutions (POS) covering the entire optimal Pareto front. We verify the effectiveness and the search performance of the proposed A-CDAS on concave and convex DTLZ3 benchmark problems with 2–8 objectives, and show that the proposed A-CDAS achieves higher search performance than conventional non-dominated sorting genetic algorithm II (NSGA-II) and CDAS with an expanded dominance area.

Large-scale parallelization of the Borg multiobjective evolutionary algorithm to enhance the management of complex environmental systems

The Borg MOEA is a self-adaptive multiobjective evolutionary algorithm capable of solving complex, many-objective environmental systems problems efficiently and reliably. Water and environmental resources problems pose significant computational challenges due to their potential for large Pareto optimal sets, the presence of disjoint Pareto-optimal regions that arise from discrete choices, multi-modal suboptimal regions, and expensive objective function calculations. This work develops two large-scale parallel implementations of the Borg MOEA, the master–slave and multi-master Borg MOEA, and applies them to a highly challenging risk-based water supply portfolio planning problem. The performance and scalability of both implementations are compared on up to 16384 processors. The multi-master Borg MOEA is shown to scale efficiently on tens of thousands of cores while dramatically improving the reliability of attaining high-quality solutions. Our results dramatically expand the scale and scope of complex environmental systems that can be addressed using many-objective evolutionary optimization.

An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach

In the precursor paper, a many-objective optimization method (NSGA-III), based on the NSGA-II framework, was suggested and applied to a number of unconstrained test and practical problems with box constraints alone. In this paper, we extend NSGA-III to solve generic constrained many-objective optimization problems. In the process, we also suggest three types of constrained test problems that are scalable to any number of objectives and provide different types of challenges to a many-objective optimizer. A previously suggested MOEA/D algorithm is also extended to solve constrained problems. Results using constrained NSGA-III and constrained MOEA/D show an edge of the former, particularly in solving problems with a large number of objectives. Furthermore, the NSGA-III algorithm is made adaptive in updating and including new reference points on the fly. The resulting adaptive NSGA-III is shown to provide a denser representation of the Pareto-optimal front, compared to the original NSGA-III with an identical computational effort. This, and the original NSGA-III paper, together suggest and amply test a viable evolutionary many-objective optimization algorithm for handling constrained and unconstrained problems. These studies should encourage researchers to use and pay further attention in evolutionary many-objective optimization.

An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints

Having developed multiobjective optimization algorithms using evolutionary optimization methods and demonstrated their niche on various practical problems involving mostly two and three objectives, there is now a growing need for developing evolutionary multiobjective optimization (EMO) algorithms for handling many-objective (having four or more objectives) optimization problems. In this paper, we recognize a few recent efforts and discuss a number of viable directions for developing a potential EMO algorithm for solving many-objective optimization problems. Thereafter, we suggest a reference-point-based many-objective evolutionary algorithm following NSGA-II framework (we call it NSGA-III) that emphasizes population members that are nondominated, yet close to a set of supplied reference points. The proposed NSGA-III is applied to a number of many-objective test problems with three to 15 objectives and compared with two versions of a recently suggested EMO algorithm (MOEA/D). While each of the two MOEA/D methods works well on different classes of problems, the proposed NSGA-III is found to produce satisfactory results on all problems considered in this paper. This paper presents results on unconstrained problems, and the sequel paper considers constrained and other specialties in handling many-objective optimization problems.

Evolutionary Many-Objective Optimization Combined CCG Crossover with Self-Controlling Dominance Area of Solutions

Evolutionary Many-Objective Optimization Combined CCG Crossover with Self-Controlling Dominance Area of Solutions

Variable space diversity, crossover and mutation in MOEA solving many-objective knapsack problems

In this work, we analyze variable space diversity of Pareto optimal solutions (POS) and study the effectiveness of crossover and mutation operators in evolutionary many-objective optimization. Firs...

Diagnostic Assessment of Search Controls and Failure Modes in Many-Objective Evolutionary Optimization

The growing popularity of multiobjective evolutionary algorithms (MOEAs) for solving many-objective problems warrants the careful investigation of their search controls and failure modes. This study contributes a new diagnostic assessment framework for rigorously evaluating the effectiveness, reliability, efficiency, and controllability of MOEAs as well as identifying their search controls and failure modes. The framework is demonstrated using the recently introduced Borg MOEA, [Formula: see text]-NSGA-II, [Formula: see text]-MOEA, IBEA, OMOPSO, GDE3, MOEA/D, SPEA2, and NSGA-II on 33 instances of 18 test problems from the DTLZ, WFG, and CEC 2009 test suites. The diagnostic framework exploits Sobol's variance decomposition to provide guidance on the algorithms' non-separable, multi-parameter controls when performing a many-objective search. This study represents one of the most comprehensive empirical assessments of MOEAs ever completed.

Self-Adaptive Control of the Number of Crossed Genes in Evolutionary Many-Objective Optimization

Self-Adaptive Control of the Number of Crossed Genes in Evolutionary Many-Objective Optimization

Diversity Management in Evolutionary Many-Objective Optimization

In evolutionary multiobjective optimization, the task of the optimizer is to obtain an accurate and useful approximation of the true Pareto-optimal front. Proximity to the front and diversity of solutions within the approximation set are important requirements. Most established multiobjective evolutionary algorithms (MOEAs) have mechanisms that address these requirements. However, in many-objective optimization, where the number of objectives is greater than 2 or 3, it has been found that these two requirements can conflict with one another, introducing problems such as dominance resistance and speciation. In this paper, two diversity management mechanisms are introduced to investigate their impact on overall solution convergence. They are introduced separately, and in combination, and tested on a set of test functions with an increasing number of objectives (6-20). It is found that the inclusion of one of the mechanisms improves the performance of a well-established MOEA in many-objective optimization problems, in terms of both convergence and diversity. The relevance of this for many-objective MOEAs is discussed.

Many-objective Evolutionary Optimization by Self-Controlling Dominance Area of Solutions :

Many-objective Evolutionary Optimization by Self-Controlling Dominance Area of Solutions :

Space Partitioning Evolutionary Many-Objective Optimization: Performance Analysis on MNK-Landscapes

This work proposes space partitioning, a new approach to evolutionary many-objective optimization. The proposed approach instantaneously partitions the objective space into subspaces and concurrently searches in each subspace. A partition strategy is used to define a schedule of subspace sampling, so that different subspaces can be emphasized at different generations. Space partitioning is implemented with adaptive epsilon-ranking, a procedure that re-ranks solutions in each subspace giving selective advantage to a subset of well distributed solutions chosen from the set of solutions initially assigned rank-1 in the high dimensional objective space. Adaptation works to keep the actual number of rank-1 solutions in each subspace close to a desired number. The effects on performance of space partitioning are verified on MNK-Landscapes. Also, a comparison with two substitute distance assignment methods recently proposed for many-objective optimization is included.

Space Partitioning Evolutionary Many-Objective Optimization: Performance Analysis on MNK-Landscapes

Space Partitioning Evolutionary Many-Objective Optimization: Performance Analysis on MNK-Landscapes

Adaptive ε-Ranking on many-objective problems

This work proposes Adaptive e-Ranking to enhance Pareto based selection, aiming to develop effective many-objective evolutionary optimization algorithms. e-Ranking fine grains ranking of solutions after they have been ranked by Pareto dominance, using a randomized sampling procedure combined with e-dominance to favor a good distribution of the samples. In the proposed method, sampled solutions keep their initial rank and solutions located within the virtually expanded e-dominance regions of the sampled solutions are demoted to an inferior rank. The parameter e that determines the expanded regions of dominance of the sampled solutions is adapted at each generation so that the number of best-ranked solutions is kept close to a desired number that is expressed as a fraction of the population size. We enhance NSGA-II with the proposed method and analyze its performance on MNK-Landscapes, showing that the adaptive method works effectively and that compared to NSGA-II convergence and diversity of solutions can be improved remarkably on MNK-Landscapes with 3 ≤ M ≤ 10 objectives. Also, we compare the performance of Adaptive e-Ranking with two representative many-objective evolutionary algorithms on DTLZ continuous functions. Results on DTLZ functions with 3 ≤ M ≤ 10 objectives suggest that the three many-objective approaches emphasize different areas of objective space and could be used as complementary strategies to produce a better approximation of the Pareto front.

進化型多数目的最適化に対するスカラー化関数を用いたＨｙｐｅｒｖｏｌｕｍｅの近似手法の提案

進化型多数目的最適化に対するスカラー化関数を用いたＨｙｐｅｒｖｏｌｕｍｅの近似手法の提案