Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion

Abstract — In our previous work [1], it has been shown that the performance of evolutionary multi-objective algorithms can be greatly enhanced if the regularity in the distribution of Pareto-optimal solutions is taken advantage using a probabilistic model. This paper suggests a new hybrid multi-objective evolutionary algorithm by introducing a convergence based criterion to determine when the model-based method and when the genetics-based method should be used to generate offspring in each generation. The basic idea is that the genetics-based method, i.e., crossover and mutation, should be used when the population is far away from the Pareto front and no obvious regularity in population distribution can be observed. When the population moves towards the Pareto front, the distribution of the individuals will show increasing regularity and in this case, the model-based method should be used to generate offspring. The proposed hybrid method is verified on widely used test problems and our simulation results show that the method is effective in achieving Pareto-optimal solutions compared to two state-of-the-art evolutionary multi-objective algorithms: NSGA-II and SPEA2, and our pervious method in [1]. I

Adaptive modelling strategy for continuous multi-objective optimization

The Pareto optimal set of a continuous multi-objective optimization problem is a piecewise continuous manifold under some mild conditions. We have recently developed several multi-objective evolutionary algorithms based on this property. However, the modelling methods used in these algorithms are rather costly. In this paper, a cheap and effective modelling strategy is proposed for building the probabilistic models of promising solutions. A new criterion is proposed for measuring the convergence of the algorithm. The locality degree of each local model is adjusted according to the proposed convergence criterion. Experimental results show that the algorithm with the proposed strategy is very promising. © 2007 IEEE

Multi-objective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables

This paper proposes a new multi-objective estimation of distribution algorithm (EDA) based on joint modeling of objectives and variables. This EDA uses the multi-dimensional Bayesian network as its probabilistic model. In this way it can capture the dependencies between objectives, variables and objectives, as well as the dependencies learnt between variables in other Bayesian network-based EDAs. This model leads to a problem decomposition that helps the proposed algorithm to find better trade-off solutions to the multi-objective problem. In addition to Pareto set approximation, the algorithm is also able to estimate the structure of the multi-objective problem. To apply the algorithm to many-objective problems, the algorithm includes four different ranking methods proposed in the literature for this purpose. The algorithm is applied to the set of walking fish group (WFG) problems, and its optimization performance is compared with an evolutionary algorithm and another multi-objective EDA. The experimental results show that the proposed algorithm performs significantly better on many of the problems and for different objective space dimensions, and achieves comparable results on some compared with the other algorithms

MB-GNG: Addressing drawbacks in multi-objective optimization estimation of distribution algorithms

We examine the model-building issue related to multi-objective estimation of distribution algorithms (MOEDAs) and show that some of their, as yet overlooked, characteristics render most current MOEDAs unviable when addressing optimization problems with many objectives. We propose a novel model-building growing neural gas (MB-GNG) network that is specially devised for properly dealing with that issue and therefore yields a better performance. Experiments are conducted in order to show from an empirical point of view the advantages of the new algorithm.assigned to this paper for their comments and suggestions. They helped to substantially improve the paper. They also wish to thank Prof. Elisenda Molina for her assistance in the preparation of the manuscript. LM, JG, AB and JMM were supported by projects CICYT TIN2008-06742-C02-02/TSI, CICYT TEC2008-06732-C02-02/TEC, SINPROB, CAM CONTEXTS S2009/TIC-1485 and DPS2008-07029- C02-02. CACC was supported by CONACyT project 103570.Publicad