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

Two enhancements for improving the convergence speed of a robust multi-objective coevolutionary algorithm.

We describe two enhancements that significantly improve the rapid convergence behavior of DECM02 - a previously proposed robust coevolutionary algorithm that integrates three different multi-objective space exploration paradigms: differential evolution, two-tier Pareto-based selection for survival and decomposition-based evolutionary guidance. The first enhancement is a refined active search adaptation mechanism that relies on run-time sub-population performance indicators to estimate the convergence stage and dynamically adjust and steer certain parts of the coevolutionary process in order to improve its overall efficiency. The second enhancement consists in a directional intensification operator that is applied in the early part of the run during the decomposition-based search phases. This operator creates new random local linear individuals based on the recent historically successful solution candidates of a given directional decomposition vector. As the two efficiency-related enhancements are complementary, our results show that the resulting coevolutionary algorithm is a highly competitive improvement of the baseline strategy when considering a comprehensive test set aggregated from 25 (standard) benchmark multi-objective optimization problems

Empirical Investigations of Reference Point Based Methods When Facing a Massively Large Number of Objectives: First Results

EMO 2017: 9th International Conference on Evolutionary Multi-Criterion Optimization, 19-22 March 2017, Münster, GermanyThis is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.Multi-objective optimization with more than three objectives has become one of the most active topics in evolutionary multi-objective optimization (EMO). However, most existing studies limit their experiments up to 15 or 20 objectives, although they claimed to be capable of handling as many objectives as possible. To broaden the insights in the behavior of EMO methods when facing a massively large number of objectives, this paper presents some preliminary empirical investigations on several established scalable benchmark problems with 25, 50, 75 and 100 objectives. In particular, this paper focuses on the behavior of the currently pervasive reference point based EMO methods, although other methods can also be used. The experimental results demonstrate that the reference point based EMO method can be viable for problems with a massively large number of objectives, given an appropriate choice of the distance measure. In addition, sufficient population diversity should be given on each weight vector or a local niche, in order to provide enough selection pressure. To the best of our knowledge, this is the first time an EMO methodology has been considered to solve a massively large number of conflicting objectives.This work was partially supported by EPSRC (Grant No. EP/J017515/1

An analysis of the Taguchi method for tuning a memetic algorithm with reduced computational time budget

Determining the best initial parameter values for an algorithm, called parameter tuning, is crucial to obtaining better algorithm performance; however, it is often a time-consuming task and needs to be performed under a restricted computational budget. In this study, the results from our previous work on using the Taguchi method to tune the parameters of a memetic algorithm for cross-domain search are further analysed and extended. Although the Taguchi method reduces the time spent finding a good parameter value combination by running a smaller size of experiments on the training instances from different domains as opposed to evaluating all combinations, the time budget is still larger than desired. This work investigates the degree to which it is possible to predict the same good parameter setting faster by using a reduced time budget. The results in this paper show that it was possible to predict good combinations of parameter settings with a much reduced time budget. The good final parameter values are predicted for three of the parameters, while for the fourth parameter there is no clear best value, so one of three similarly performing values is identified at each time instant

An ensemble indicator-based density estimator for evolutionary multi-objective optimization

International audienceEnsemble learning is one of the most employed methods in machine learning. Its main ground is the construction of stronger mechanisms based on the combination of elementary ones. In this paper, we employ AdaBoost, which is one of the most well-known ensemble methods, to generate an ensemble indicator-based density estimator for multi-objective optimization. It combines the search properties of five density estimators, based on the hypervolume, R2, IGD+, ε+, and ∆p quality indicators. Through the multi-objective evolutionary search process, the proposed ensemble mechanism adapts itself using a learning process that takes the preferences of the underlying quality indicators into account. The proposed method gives rise to the ensemble indicator-based multi-objective evolutionary algorithm (EIB-MOEA) that shows a robust performance on different multi-objective optimization problems when compared with respect to several existing indicator-based multi-objective evolutionary algorithms

A multi-objective evolutionary algorithm fitness function for case-base maintenance.

Case-Base Maintenance (CBM) has two important goals. On the one hand, it aims to reduce the size of the case-base. On the other hand, it has to improve the accuracy of the CBR system. CBM can be represented as a multi-objective optimization problem to achieve both goals. Multi-Objective Evolutionary Algorithms (MOEAs) have been recognised as appropriate techniques for multi-objective optimisation because they perform a search for multiple solutions in parallel. In the present paper we introduce a fitness function based on the Complexity Profiling model to perform CBM with MOEA, and we compare its results against other known CBM approaches. From the experimental results, CBM with MOEA shows regularly good results in many case-bases, despite the amount of redundant and noisy cases, and with a significant potential for improvement

A simulated annealing based genetic local search algorithm for multi-objective multicast routing problems

This paper presents a new hybrid evolutionary algorithm to solve multi-objective multicast routing problems in telecommunication networks. The algorithm combines simulated annealing based strategies and a genetic local search, aiming at a more flexible and effective exploration and exploitation in the search space of the complex problem to find more non-dominated solutions in the Pareto Front. Due to the complex structure of the multicast tree, crossover and mutation operators have been specifically devised concerning the features and constraints in the problem. A new adaptive mutation probability based on simulated annealing is proposed in the hybrid algorithm to adaptively adjust the mutation rate according to the fitness of the new solution against the average quality of the current population during the evolution procedure. Two simulated annealing based search direction tuning strategies are applied to improve the efficiency and effectiveness of the hybrid evolutionary algorithm. Simulations have been carried out on some benchmark multi-objective multicast routing instances and a large amount of random networks with five real world objectives including cost, delay, link utilisations, average delay and delay variation in telecommunication networks. Experimental results demonstrate that both the simulated annealing based strategies and the genetic local search within the proposed multi-objective algorithm, compared with other multi-objective evolutionary algorithms, can efficiently identify high quality non-dominated solution set for multi-objective multicast routing problems and outperform other conventional multi-objective evolutionary algorithms in the literature

ParadisEO-MOEO: A Software Framework for Evolutionary Multi-Objective Optimization

This chapter presents ParadisEO-MOEO, a white-box object-oriented software framework dedicated to the flexible design of metaheuristics for multi-objective optimization. This paradigm-free software proposes a unified view for major evolutionary multi-objective metaheuristics. It embeds some features and techniques for multi-objective resolution and aims to provide a set of classes allowing to ease and speed up the development of computationally efficient programs. It is based on a clear conceptual distinction between the solution methods and the problems they are intended to solve. This separation confers a maximum design and code reuse. This general-purpose framework provides a broad range of fitness assignment strategies, the most common diversity preservation mechanisms, some elitistrelated features as well as statistical tools. Furthermore, a number of state-of-the-art search methods, including NSGA-II, SPEA2 and IBEA, have been implemented in a user-friendly way, based on the fine-grained ParadisEO-MOEO components