Generalized decomposition and cross entropy methods for many-objective optimization

Decomposition-based algorithms for multi-objective optimization problems have increased in popularity in the past decade. Although their convergence to the Pareto optimal front (PF) is in several instances superior to that of Pareto-based algorithms, the problem of selecting a way to distribute or guide these solutions in a high-dimensional space has not been explored. In this work, we introduce a novel concept which we call generalized decomposition. Generalized decomposition provides a framework with which the decision maker (DM) can guide the underlying evolutionary algorithm toward specific regions of interest or the entire Pareto front with the desired distribution of Pareto optimal solutions. Additionally, it is shown that generalized decomposition simplifies many-objective problems by unifying the three performance objectives of multi-objective evolutionary algorithms – convergence to the PF, evenly distributed Pareto optimal solutions and coverage of the entire front – to only one, that of convergence. A framework, established on generalized decomposition, and an estimation of distribution algorithm (EDA) based on low-order statistics, namely the cross-entropy method (CE), is created to illustrate the benefits of the proposed concept for many objective problems. This choice of EDA also enables the test of the hypothesis that low-order statistics based EDAs can have comparable performance to more elaborate EDAs

A novel multi-objective evolutionary algorithm based on space partitioning

To design an e ective multi-objective optimization evolutionary algorithms (MOEA), we need to address the following issues: 1) the sensitivity to the shape of true Pareto front (PF) on decomposition-based MOEAs; 2) the loss of diversity due to paying so much attention to the convergence on domination-based MOEAs; 3) the curse of dimensionality for many-objective optimization problems on grid-based MOEAs. This paper proposes an MOEA based on space partitioning (MOEA-SP) to address the above issues. In MOEA-SP, subspaces, partitioned by a k-dimensional tree (kd-tree), are sorted according to a bi-indicator criterion de ned in this paper. Subspace-oriented and Max-Min selection methods are introduced to increase selection pressure and maintain diversity, respectively. Experimental studies show that MOEA-SP outperforms several compared algorithms on a set of benchmarks

Component-level study of a decomposition-based multi-objective optimizer on a limited evaluation budget

Decomposition-based algorithms have emerged as one of the most popular classes of solvers for multi-objective optimization. Despite their popularity, a lack of guidance exists for how to configure such algorithms for real-world problems, based on the features or contexts of those problems. One context that is important for many real-world problems is that function evaluations are expensive, and so algorithms need to be able to provide adequate convergence on a limited budget (e.g. 500 evaluations). This study contributes to emerging guidance on algorithm configuration by investigating how the convergence of the popular decomposition-based optimizer MOEA/D, over a limited budget, is affected by choice of component level configuration. Two main aspects are considered: (1) impact of sharing information; (2) impact of normalisation scheme. The empirical test framework includes detailed trajectory analysis, as well as more conventional performance indicator analysis, to help identify and explain the behaviour of the optimizer. Use of neighbours in generating new solutions is found to be highly disruptive for searching on a small budget, leading to better convergence in some areas but far worse convergence in others. The findings also emphasise the challenge and importance of using an appropriate normalisation scheme

MaOMFO: Many-objective moth flame optimizer using reference-point based non-dominated sorting mechanism for global optimization problems

Many-objective optimization (MaO) deals with a large number of conflicting objectives in optimization problems to acquire a reliable set of appropriate non-dominated solutions near the true Pareto front, and for the same, a unique mechanism is essential. Numerous papers have reported multi-objective evolutionary algorithms to explain the absence of convergence and diversity variety in many-objective optimization problems. One of the most encouraging methodologies utilizes many reference points to segregate the solutions and guide the search procedure. The above-said methodology is integrated into the basic version of the Moth Flame Optimization (MFO) algorithm for the first time in this paper. The proposed Many-Objective Moth Flame Optimization (MaOMFO) utilizes a set of reference points progressively decided by the hunt procedure of the moth flame. It permits the calculation to combine with the Pareto front yet synchronize the decent variety of the Pareto front. MaOMFO is employed to solve a wide range of unconstrained and constrained benchmark functions and compared with other competitive algorithms, such as non-dominated sorting genetic algorithm, multi-objective evolutionary algorithm based on dominance and decomposition, and novel multi-objective particle swarm optimization using different performance metrics. The results demonstrate the superiority of the algorithm as a new many-objective algorithm for complex many-objective optimization problems

Multiobjective evolutionary algorithm based on vector angle neighborhood

Selection is a major driving force behind evolution and is a key feature of multiobjective evolutionary algorithms. Selection aims at promoting the survival and reproduction of individuals that are most fitted to a given environment. In the presence of multiple objectives, major challenges faced by this operator come from the need to address both the population convergence and diversity, which are conflicting to a certain extent. This paper proposes a new selection scheme for evolutionary multiobjective optimization. Its distinctive feature is a similarity measure for estimating the population diversity, which is based on the angle between the objective vectors. The smaller the angle, the more similar individuals. The concept of similarity is exploited during the mating by defining the neighborhood and the replacement by determining the most crowded region where the worst individual is identified. The latter is performed on the basis of a convergence measure that plays a major role in guiding the population towards the Pareto optimal front. The proposed algorithm is intended to exploit strengths of decomposition-based approaches in promoting diversity among the population while reducing the user's burden of specifying weight vectors before the search. The proposed approach is validated by computational experiments with state-of-the-art algorithms on problems with different characteristics. The obtained results indicate a highly competitive performance of the proposed approach. Significant advantages are revealed when dealing with problems posing substantial difficulties in keeping diversity, including many-objective problems. The relevance of the suggested similarity and convergence measures are shown. The validity of the approach is also demonstrated on engineering problems.This work was supported by the Portuguese Fundacao para a Ciencia e Tecnologia under grant PEst-C/CTM/LA0025/2013 (Projecto Estrategico - LA 25 - 2013-2014 - Strategic Project - LA 25 - 2013-2014).info:eu-repo/semantics/publishedVersio