Benchmarking evolutionary multiobjective optimization algorithms

Choosing and tuning an optimization procedure for a given class of nonlinear optimization problems is not an easy task. One way to proceed is to consider this as a tournament, where each procedure will compete in different ‘disciplines’. Here, disciplines could either be different functions, which we want to optimize, or specific performance measures of the optimization procedure. We would then be interested in the algorithm that performs best in a majority of cases or whose average performance is maximal. We will focus on evolutionary multiobjective optimization algorithms (EMOA), and will present a novel approach to the design and analysis of evolutionary multiobjective benchmark experiments based on similar work from the context of machine learning. We focus on deriving a consensus among several benchmarks over different test problems and illustrate the methodology by reanalyzing the results of the CEC 2007 EMOA competition

Evolutionary multiobjective optimization of the multi-location transshipment problem

We consider a multi-location inventory system where inventory choices at each location are centrally coordinated. Lateral transshipments are allowed as recourse actions within the same echelon in the inventory system to reduce costs and improve service level. However, this transshipment process usually causes undesirable lead times. In this paper, we propose a multiobjective model of the multi-location transshipment problem which addresses optimizing three conflicting objectives: (1) minimizing the aggregate expected cost, (2) maximizing the expected fill rate, and (3) minimizing the expected transshipment lead times. We apply an evolutionary multiobjective optimization approach using the strength Pareto evolutionary algorithm (SPEA2), to approximate the optimal Pareto front. Simulation with a wide choice of model parameters shows the different trades-off between the conflicting objectives

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

On the Impact of Multiobjective Scalarizing Functions

Recently, there has been a renewed interest in decomposition-based approaches for evolutionary multiobjective optimization. However, the impact of the choice of the underlying scalarizing function(s) is still far from being well understood. In this paper, we investigate the behavior of different scalarizing functions and their parameters. We thereby abstract firstly from any specific algorithm and only consider the difficulty of the single scalarized problems in terms of the search ability of a (1+lambda)-EA on biobjective NK-landscapes. Secondly, combining the outcomes of independent single-objective runs allows for more general statements on set-based performance measures. Finally, we investigate the correlation between the opening angle of the scalarizing function's underlying contour lines and the position of the final solution in the objective space. Our analysis is of fundamental nature and sheds more light on the key characteristics of multiobjective scalarizing functions.Comment: appears in Parallel Problem Solving from Nature - PPSN XIII, Ljubljana : Slovenia (2014

MIJ2K Optimization using evolutionary multiobjective optimization algorithms

This paper deals with the multiobjective definition of video compression and its optimization. The optimization will be done using NSGA-II, a well-tested and highly accurate algorithm with a high convergence speed developed for solving multiobjective problems. Video compression is defined as a problem including two competing objectives. We try to find a set of optimal, so-called Pareto-optimal solutions, instead of a single optimal solution. The two competing objectives are quality and compression ratio maximization. The optimization will be achieved using a new patent pending codec, called MIJ2K, also outlined in this paper. Video will be compressed with the MIJ2K codec applied to some classical videos used for performance measurement, selected from the Xiph.org Foundation repository. The result of the optimization will be a set of near-optimal encoder parameters. We also present the convergence of NSGA-II with different encoder parameters and discuss the suitability of MOEAs as opposed to classical search-based techniques in this field.This work was supported in part by Projects CICYT TIN2008- 06742-C02-02/TSI, CICYT TEC2008-06732-C02-02/TEC, SINPROB, CAM MADRINET S-0505/TIC/0255 and DPS2008-07029-C02-02.publicad