Impact analysis of crossovers in a multi-objective evolutionary algorithm

Multi-objective optimization has become mainstream because several real-world problems are naturally posed as a Multi-objective optimization problems (MOPs) in all fields of engineering and science. Usually MOPs consist of more than two conflicting objective functions and that demand trade-off solutions. Multi-objective evolutionary algorithms (MOEAs) are extremely useful and well-suited for solving MOPs due to population based nature. MOEAs evolve its population of solutions in a natural way and searched for compromise solutions in single simulation run unlike traditional methods. These algorithms make use of various intrinsic search operators in efficient manners. In this paper, we experimentally study the impact of different multiple crossovers in multi-objective evolutionary algorithm based on decomposition (MOEA/D) framework and evaluate its performance over test instances of 2009 IEEE congress on evolutionary computation (CEC?09) developed for MOEAs competition. Based on our carried out experiment, we observe that used variation operators are considered to main source to improve the algorithmic performance of MOEA/D for dealing with CEC?09 complicated test problems

Hybrid non-dominated sorting genetic algorithm with adaptive operators selection

Multiobjective optimization entails minimizing or maximizing multiple objective functions subject to a set of constraints. Many real world applications can be formulated as multi-objective optimization problems (MOPs), which often involve multiple conflicting objectives to be optimized simultaneously. Recently, a number of multi-objective evolutionary algorithms (MOEAs) were developed suggested for these MOPs as they do not require problem specific information. They find a set of non-dominated solutions in a single run. The evolutionary process on which they are based, typically relies on a single genetic operator. Here, we suggest an algorithm which uses a basket of search operators. This is because it is never easy to choose the most suitable operator for a given problem. The novel hybrid non-dominated sorting genetic algorithm (HNSGA) introduced here in this paper and tested on the ZDT (Zitzler-Deb-Thiele) and CEC’09 (2009 IEEE Conference on Evolutionary Computations) benchmark problems specifically formulated for MOEAs. Numerical results prove that the proposed algorithm is competitive with state-of-the-art MOEAs

Hybrid adaptive evolutionary algorithm based on decomposition

The performance of search operators varies across the different stages of the search/optimization process of evolutionary algorithms (EAs). In general, a single search operator may not do well in all these stages when dealing with different optimization and search problems. To mitigate this, adaptive search operator schemes have been introduced. The idea is that when a search operator hits a difficult patch (under-performs) in the search space, the EA scheme “reacts” to that by potentially calling upon a different search operator. Hence, several multiple-search operator schemes have been proposed and employed within EA. In this paper, a hybrid adaptive evolutionary algorithm based on decomposition (HAEA/D) that employs four different crossover operators is suggested. Its performance has been evaluated on the well-known IEEE CEC’09 test instances. HAEA/D has generated promising results which compare well against several well-known algorithms including MOEA/D, on a number of metrics such as the inverted generational distance (IGD), the hyper-volume, the Gamma and Delta functions. These results are included and discussed in this paper

A theoretical and empirical study on unbiased boundary-extended crossover for real-valued representation

Copyright © 2012 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Information Sciences. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Information Sciences Vol. 183 Issue 1 (2012), DOI: 10.1016/j.ins.2011.07.013We present a new crossover operator for real-coded genetic algorithms employing a novel methodology to remove the inherent bias of pre-existing crossover operators. This is done by transforming the topology of the hyper-rectangular real space by gluing opposite boundaries and designing a boundary extension method for making the fitness function smooth at the glued boundary. We show the advantages of the proposed crossover by comparing its performance with those of existing ones on test functions that are commonly used in the literature, and a nonlinear regression on a real-world dataset

Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem

In this paper, we consider the symmetric multi-type non-negative matrix tri-factorization problem (SNMTF), which attempts to factorize several symmetric non-negative matrices simultaneously. This can be considered as a generalization of the classical non-negative matrix tri-factorization problem and includes a non-convex objective function which is a multivariate sixth degree polynomial and a has convex feasibility set. It has a special importance in data science, since it serves as a mathematical model for the fusion of different data sources in data clustering. We develop four methods to solve the SNMTF. They are based on four theoretical approaches known from the literature: the fixed point method (FPM), the block-coordinate descent with projected gradient (BCD), the gradient method with exact line search (GM-ELS) and the adaptive moment estimation method (ADAM). For each of these methods we offer a software implementation: for the former two methods we use Matlab and for the latter Python with the TensorFlow library. We test these methods on three data-sets: the synthetic data-set we generated, while the others represent real-life similarities between different objects. Extensive numerical results show that with sufficient computing time all four methods perform satisfactorily and ADAM most often yields the best mean square error ($\mathrm{MSE}$). However, if the computation time is limited, FPM gives the best $\mathrm{MSE}$ because it shows the fastest convergence at the beginning. All data-sets and codes are publicly available on our GitLab profile

A novel two-archive strategy for evolutionary many-objective optimization algorithm based on reference points

Current evolutionary many-objective optimization algorithms face two challenges: one is to ensure population diversity for searching the entire solution space. The other is to ensure quick convergence to the optimal solution set. In this paper, we propose a novel two-archive strategy for evolutionary many-objective optimization algorithm. The uniform archive strategy, based on reference points, is used to keep population diversity in the evolutionary process, and to ensure that an evolutionary algorithm is able to search the entire solution space. The single elite archive strategy is used to ensure that individuals with the best single objective value are able to evolve into the next generation and have more opportunities to generate offspring. This strategy aims to improve the convergence rate. Then this novel two-archive strategy is applied to improving the Non-dominated Sorting Genetic Algorithm (NSGA-III). Simulation experiments are conducted on benchmark test sets and experimental results show that our proposed algorithm with the two-archive strategy has a better performance than other state-of-art algorithms