Entropy-based multi-objective genetic algorithm for design optimization

Farhang-Mehr, A.; Azarm, Shapour

doi:10.1007/s00158-002-0247-6

Cited by 39 publications

(18 citation statements)

References 10 publications

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“…In [58], a Euclidean minimum spanning tree (EMST) of individuals in a population is generated, and the density of an individual is estimated by its edges in the EMST. Farhang-Mehr and Azarm calculated the entropy in the population, estimating the density of an individual by considering the influences coming from all other individuals in the population [22].…”

Section: A Density Estimation In Emo Algorithmsmentioning

confidence: 99%

Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization

Yang

Liu

2014

IEEE Trans. Evol. Computat.

559

271

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Abstract-It is commonly accepted that Pareto-based evolutionary multiobjective optimization (EMO) algorithms encounter difficulties in dealing with many-objective problems. In these algorithms, the ineffectiveness of the Pareto dominance relation for a high-dimensional space leads diversity maintenance mechanisms to play the leading role during the evolutionary process, while the preference of diversity maintenance mechanisms for individuals in sparse regions results in the final solutions distributed widely over the objective space but distant from the desired Pareto front. Intuitively, there are two ways to address this problem: 1) modifying the Pareto dominance relation and 2) modifying the diversity maintenance mechanism in the algorithm. In this paper, we focus on the latter and propose a shift-based density estimation (SDE) strategy. The aim of our study is to develop a general modification of density estimation in order to make Pareto-based algorithms suitable for many-objective optimization. In contrast to traditional density estimation which only involves the distribution of individuals in the population, SDE covers both the distribution and convergence information of individuals. The application of SDE in three popular Paretobased algorithms demonstrates its usefulness in handling manyobjective problems. Moreover, an extensive comparison with five state-of-the-art EMO algorithms reveals its competitiveness in balancing convergence and diversity of solutions. These findings not only show that SDE is a good alternative to tackle manyobjective problems, but also present a general extension of Paretobased algorithms in many-objective optimization.

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Section: A Density Estimation In Emo Algorithmsmentioning

confidence: 99%

Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization

Yang

Liu

2014

IEEE Trans. Evol. Computat.

559

271

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“…Entropy has been used in the context of GAs to prevent premature convergence. For example, Farhang-Mehr and Azarm [12] introduce an entropy-based multi-objective genetic algorithm. Tsujimura and Gen [42] calculate the entropy of each gene for the individuals in the population and compare it with a threshold value; when the number of genes whose entropy is lower than the threshold is greater than a given amount, the diversity of the population is increased by a process of allele exchange.…”

Section: Diversity-adaptive Controlmentioning

confidence: 99%

Adaptive generalized crowding for genetic algorithms

Mengshoel

Galán

Dios

2014

Information Sciences

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The genetic algorithm technique known as crowding preserves population diversity by pairing each offspring with a similar individual in the current population (pairing phase) and deciding which of the two will survive (replacement phase). The replacement phase of crowding is usually carried out through deterministic or probabilistic crowding, which have the limitations that they apply the same selective pressure regardless of the problem being solved and the stage of genetic algorithm search. The recently developed generalized crowding approach introduces a scaling factor in the replacement phase, thus generalizing and potentially overcoming the limitations of both deterministic and probabilistic crowding. A key problem not previously addressed, however, is how the scaling factor should be adapted during the search process in order to effectively obtain optimal or near-optimal solutions. The present work investigates this problem by developing and evaluating two methods for adapting, during search, the scaling factor. We call these two methods diversity-adaptive and self-adaptive generalized crowding respectively. Whereas the former method adapts the scaling factor according to the population's diversity, the latter method includes the scaling factor in the chromosome for self-adaptation. Our experiments with real function optimization, Bayesian network inference, and the Traveling Salesman Problem show that both diversity-adaptive and self-adaptive generalized crowding are consistent techniques that produce strong results, often outperforming traditional generalized crowding.

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“…What is more, another problem is each set of coefficient combination can only acquire one optimal solution, and it is hard to make sure whether the solution achieved is an optimal one. However, in engineering design domains, more and more attentions have been paid on multi-objective genetic algorithm (MOGA), which mimics the natural selection process in which a superior creature evolves whilst inferior creatures fade out from their population as generations go by Farhang-Mehr and Azarm, 2002;Hiroyasu et al, 2002). Many advantages of MOGA are very attractive (Kasprzak and Lewis, 2000), such as the capability of exploring a large design space and the merit of none gradients information is needed.…”

Section: Introductionmentioning

confidence: 99%