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

Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)

Recently, increasing works have proposed to drive evolutionary algorithms using machine learning models. Usually, the performance of such model based evolutionary algorithms is highly dependent on the training qualities of the adopted models. Since it usually requires a certain amount of data (i.e. the candidate solutions generated by the algorithms) for model training, the performance deteriorates rapidly with the increase of the problem scales, due to the curse of dimensionality. To address this issue, we propose a multi-objective evolutionary algorithm driven by the generative adversarial networks (GANs). At each generation of the proposed algorithm, the parent solutions are first classified into real and fake samples to train the GANs; then the offspring solutions are sampled by the trained GANs. Thanks to the powerful generative ability of the GANs, our proposed algorithm is capable of generating promising offspring solutions in high-dimensional decision space with limited training data. The proposed algorithm is tested on 10 benchmark problems with up to 200 decision variables. Experimental results on these test problems demonstrate the effectiveness of the proposed algorithm

CES-485 Approximating the Set of Pareto Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm

Most existing multiobjective evolutionary algorithms aim at approximating the PF, the distribution of the Pareto optimal solutions in the objective space. In many real-life applications, however, a good approximation to the PS, the distribution of the Pareto optimal solutions in the decision space, is also required by a decision maker. This paper considers a class of MOPs, in which the dimensionalities of the PS and PF are different so that a good approximation to the PF might not approximate the PS very well. It proposes a probabilistic model based multiobjective evolutionary algorithm, called MMEA, for approximating the PS and the PF simultaneously for a MOP in this class. In the modelling phase of MMEA, the population is clustered into a number of subpopulations based on their distribution in the objective space, the PCA technique is used to detect the dimensionality of the centroid of each subpopulation, and then a probabilistic model is built for modelling the distribution of the Pareto optimal solutions in the decision space. Such modelling procedure could promote the population diversity in both the decision and objective spaces. To ease the burden of setting the number of subpopulations, a dynamic strategy for periodically adjusting it has been adopted in MMEA. The experimental comparison between MMEA and the two other methods, KP1 and Omni-Optimizer on a set of test instances, some of which are proposed in this paper, have been made in this paper. It is clear from the experiments that MMEA has a big advantage over the two other methods in approximating both the PS and the PF of a MOP when the PS is a nonlinear manifold, although it might not be able to perform significantly better in the case when the PS is a linear manifold

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