Multimodal Optimization by Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations

During the recent decades, many niching methods have been proposed and empirically verified on some available test problems. They often rely on some particular assumptions associated with the distribution, shape, and size of the basins, which can seldom be made in practical optimization problems. This study utilizes several existing concepts and techniques, such as taboo points, normalized Mahalanobis distance, and the Ursem's hill-valley function in order to develop a new tool for multimodal optimization, which does not make any of these assumptions. In the proposed method, several subpopulations explore the search space in parallel. Offspring of a subpopulation are forced to maintain a sufficient distance to the center of fitter subpopulations and the previously identified basins, which are marked as taboo points. The taboo points repel the subpopulation to prevent convergence to the same basin. A strategy to update the repelling power of the taboo points is proposed to address the challenge of basins of dissimilar size. The local shape of a basin is also approximated by the distribution of the subpopulation members converging to that basin. The proposed niching strategy is incorporated into the covariance matrix self-adaptation evolution strategy (CMSA-ES), a potent global optimization method. The resultant method, called the covariance matrix self-adaptation with repelling subpopulations (RS-CMSA), is assessed and compared to several state-of-the-art niching methods on a standard test suite for multimodal optimization. An organized procedure for parameter setting is followed which assumes a rough estimation of the desired/expected number of minima available. Performance sensitivity to the accuracy of this estimation is also studied by introducing the concept of robust mean peak ratio. Based on the numerical results using the available and the introduced performance measures, RS-CMSA emerges as the most successful method when robustness and efficiency are considered at the same time.FWN – Publicaties zonder aanstelling Universiteit Leide

Static and Dynamic Multimodal Optimization by Improved Covariance Matrix Self-Adaptation Evolution Strategy with Repelling Subpopulations

The covariance matrix self-adaptation evolution strategy with repelling subpopulations (RS-CMSA-ES) is one of the most successful multimodal optimization (MMO) methods currently available. However, some of its components may become inefficient in certain situations. This study introduces the second variant of this method, called RS-CMSA-ESII. It improves the adaptation schemes for the normalized taboo distances of the archived solutions and the covariance matrix of the subpopulation, the termination criteria for the subpopulations, and the way in which the infeasible solutions are treated. It also improves the time complexity of RS-CMSA-ES by updating the initialization procedure of a subpopulation and developing a more accurate metric for determining critical taboo regions. The effects of these modifications are illustrated by designing controlled numerical simulations. RS-CMSA-ESII is then compared with the most successful and recent niching methods for MMO on a widely adopted test suite. The results obtained reveal the superiority of RS-CMSA-ESII over these methods, including the winners of the competition on niching methods for MMO in previous years. Besides, this study extends RS-CMSA-ESII to dynamic MMO and compares it with a few recently proposed methods on the modified moving peak benchmark functions

Fitness landscape analysis in the optimization of coefficients of curve parametrizations

Este documento se considera que es una ponencia de congresos en lugar de un capítulo de libro.Computer Aided Systems Theory - EUROCAST 2017, 19-24 February, Las Palmas de Gran Canaria, Spain.J.R. Sendra is member of the Research Group ASYNACS (Ref.CT-CE2019/683)Parametric representations of geometric objects, such as curves or surfaces, may have unnecessarily huge integer coefficients. Our goal is to search for an alternative parametric representation of the same object with significantly smaller integer coefficients. We have developed and implemented an evolutionary algorithm that is able to find solutions to this problem in an efficient as well as robust way. In this paper we analyze the fitness landscapes associated with this evolutionary algorithm. We here discuss the use of three different strategies that are used to evaluate and order partial solutions. These orderings lead to different landscapes of combinations of partial solutions in which the optimal solutions are searched. We see that the choice of this ordering strategy has a huge inuence on the characteristics of the resulting landscapes, which are in this paper analyzed using a set of metrics, and also on the quality of the solutions that can be found by the subsequent evolutionary search.Ministerio de Economía y CompetitividadEuropean Regional Development FundAustrian Research Promotion Agenc

Inferring Future Landscapes: Sampling the Local Optima Level

Connection patterns among Local Optima Networks (LONs) can inform heuristic design for optimisation. LON research has predominantly required complete enumeration of a fitness landscape, thereby restricting analysis to problems diminutive in size compared to real-life situations. LON sampling algorithms are therefore important. In this paper, we study LON construction algorithms for the Quadratic Assignment Problem (QAP). Using machine learning, we use estimated LON features to predict search performance for competitive heuristics used in the QAP domain. The results show that by using random forest regression, LON construction algorithms produce fitness landscape features which can explain almost all search variance. We find that LON samples better relate to search than enumerated LONs do. The importance of fitness levels of sampled LONs in search predictions is crystallised. Features from LONs produced by different algorithms are combined in predictions for the first time, with promising results for this ‘super-sampling’: a model to predict tabu search success explained 99% of variance. Arguments are made for the use-case of each LON algorithm and for combining the exploitative process of one with the exploratory optimisation of the other

Meta-heuristic combining prior online and offline information for the quadratic assignment problem

The construction of promising solutions for NP-hard combinatorial optimization problems (COPs) in meta-heuristics is usually based on three types of information, namely a priori information, a posteriori information learned from visited solutions during the search procedure, and online information collected in the solution construction process. Prior information reflects our domain knowledge about the COPs. Extensive domain knowledge can surely make the search effective, yet it is not always available. Posterior information could guide the meta-heuristics to globally explore promising search areas, but it lacks local guidance capability. On the contrary, online information can capture local structures, and its application can help exploit the search space. In this paper, we studied the effects of using this information on metaheuristic's algorithmic performances for the COPs. The study was illustrated by a set of heuristic algorithms developed for the quadratic assignment problem. We first proposed an improved scheme to extract online local information, then developed a unified framework under which all types of information can be combined readily. Finally, we studied the benefits of the three types of information to meta-heuristics. Conclusions were drawn from the comprehensive study, which can be used as principles to guide the design of effective meta-heuristic in the future

Simulation-based fitness landscape analysis and optimisation of complex problems

Widespread hard optimisation problems in economics and logistics are characterised by large dimensions, uncertainty and nonlinearity and require more powerful methods of stochastic optimisation that traditional ones. Simulation optimisation is a powerful tool for solving these problems. Moreover, fitness landscape analysis techniques provide an efficient approach to better selection of a suitable optimisation algorithm. The concept and techniques of fitness landscape analysis are described. A formalised scheme for simulation optimisation enhanced with fitness landscape analysis is given. Benchmark fitness landscape analysis is performed to find relations between efficiency of an optimisation algorithm and structural features of a fitness landscape. Case study in simulation optimisation of vehicle routing and scheduling is described. Various optimisation scenarios with application of the fitness landscape analysis are discussed and investigated

Towards the landscape rotation as a perturbation strategy on the quadratic assignment problem.

Recent work in combinatorial optimisation have demonstrated that neighbouring solutions of a local optima may belong to more favourable attraction basins. In this sense, the perturbation strategy plays a critical role on local search based algorithms to kick the search of the algorithm into more prominent areas of the space. In this paper, we investigate the landscape rotation as a perturbation strategy to redirect the search of an stuck algorithm. This technique rearranges the mapping of solutions to different objective values without altering important properties of the problem's landscape such as the number and quality of optima, among others. Particularly, we investigate two rotation based perturbation strategies: (i) a profoundness rotation method and (ii) a broadness rotation method. These methods are applied into the stochastic hill-climbing heuristic and tested and compared on different instances of the quadratic assignment problem against other algorithm versions. Performed experiments reveal that the landscape rotation is an efficient perturbation strategy to shift the search in a controlled way. Nevertheless, an empirical investigation of the landscape rotation demonstrates that it needs to be cautiously manipulated in the permutation space since a small rotation does not necessarily mean a small disturbance in the fitness landscape