When Hillclimbers Beat Genetic Algorithms in Multimodal Optimization

It has been shown in the past that a multistart hillclimbing strategy compares favourably to a standard genetic algorithm with respect to solving instances of the multimodal problem generator. We extend that work and verify if the utilization of diversity preservation techniques in the genetic algorithm changes the outcome of the comparison. We do so under two scenarios: (1) when the goal is to find the global optimum, (2) when the goal is to find all optima. A mathematical analysis is performed for the multistart hillclimbing algorithm and a through empirical study is conducted for solving instances of the multimodal problem generator with increasing number of optima, both with the hillclimbing strategy as well as with genetic algorithms with niching. Although niching improves the performance of the genetic algorithm, it is still inferior to the multistart hillclimbing strategy on this class of problems. An idealized niching strategy is also presented and it is argued that its performance should be close to a lower bound of what any evolutionary algorithm can do on this class of problems

A Partition-Based Random Search Method for Multimodal Optimization

Practical optimization problems are often too complex to be formulated exactly. Knowing multiple good alternatives can help decision-makers easily switch solutions when needed, such as when faced with unforeseen constraints. A multimodal optimization task aims to find multiple global optima as well as high-quality local optima of an optimization problem. Evolutionary algorithms with niching techniques are commonly used for such problems, where a rough estimate of the optima number is required to determine the population size. In this paper, a partition-based random search method is proposed, in which the entire feasible domain is partitioned into smaller and smaller subregions iteratively. Promising regions are partitioned faster than unpromising regions, thus, promising areas will be exploited earlier than unpromising areas. All promising areas are exploited in parallel, which allows multiple good solutions to be found in a single run. The proposed method does not require prior knowledge about the optima number and it is not sensitive to the distance parameter. By cooperating with local search to refine the obtained solutions, the proposed method demonstrates good performance in many benchmark functions with multiple global optima. In addition, in problems with numerous local optima, high-quality local optima are captured earlier than low-quality local optima

Signal synthesis by means of evolutionary algorithms

In this article, we investigate a procedure for generating signals with genetic algorithms. Signals are obtained from elementary patterns characterized by different degrees of freedom. These patterns are repeated and combined in order to reach specific signal shapes. The whole signal parametrization has to be determined by solving a difficult inverse problem of high dimensionality and strong multimodality. This can be carried out using evolutionary algorithms with the aim of finding all pattern configurations in the signal. The different signal synthesis schemes are evaluated, tested and applied to the generation of particular railway driving profiles

Uncertainty evaluation of reservoir simulation models using particle swarms and hierarchical clustering

History matching production data in finite difference reservoir simulation models has been and always will be a challenge for the industry. The principal hurdles that need to be overcome are finding a match in the first place and more importantly a set of matches that can capture the uncertainty range of the simulation model and to do this in as short a time as possible since the bottleneck in this process is the length of time taken to run the model. This study looks at the implementation of Particle Swarm Optimisation (PSO) in history matching finite difference simulation models. Particle Swarms are a class of evolutionary algorithms that have shown much promise over the last decade. This method draws parallels from the social interaction of swarms of bees, flocks of birds and shoals of fish. Essentially a swarm of agents are allowed to search the solution hyperspace keeping in memory each individual’s historical best position and iteratively improving the optimisation by the emergent interaction of the swarm. An intrinsic feature of PSO is its local search capability. A sequential niching variation of the PSO has been developed viz. Flexi-PSO that enhances the exploration and exploitation of the hyperspace and is capable of finding multiple minima. This new variation has been applied to history matching synthetic reservoir simulation models to find multiple distinct history 3 matches to try to capture the uncertainty range. Hierarchical clustering is then used to post-process the history match runs to reduce the size of the ensemble carried forward for prediction. The success of the uncertainty modelling exercise is then assessed by checking whether the production profile forecasts generated by the ensemble covers the truth case

Exploring and Exploiting Models of the Fitness Landscape: a Case Against Evolutionary Optimization

In recent years, the theories of natural selection and biological evolution have proved popular metaphors for understanding and solving optimization problems in engineering design. This thesis identifies some fundamental problems associated with this use of such metaphors. Key objections are the failure of evolutionary optimization techniques to represent explicitly the goal of the optimization process, and poor use of knowledge developed during the process. It is also suggested that convergent behaviour of an optimization algorithm is an undesirable quality if the algorithm is to be applied to multimodal problems. An alternative approach to optimization is suggested, based on the explicit use of knowledge and/or assumptions about the nature of the optimization problem to construct Bayesian probabilistic models of the surface being optimized and the goal of the optimization. Distinct exploratory and exploitative strategies are identified for carrying out optimization based on such models—exploration based on attempting to reduce maximally an entropy-based measure of the total uncertainty concerning the satisfaction of the optimization goal over the space, exploitation based on evalutation of the point judged most likely to achieve the goal—together with a composite strategy which combines exploration and exploitation in a principled manner. The behaviour of these strategies is empirically investigated on a number of test problems. Results suggest that the approach taken may well provide effective optimization in a way which addresses the criticisms made of the evolutionary metaphor, subject to issues of the computational cost of the approach being satisfactorily addressed

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