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Register a new userA Linear Constrained Optimization Benchmark For Probabilistic Search Algorithms: The Rotated Klee-Minty Problem
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Added by
Michael Hellwig
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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The development, assessment, and comparison of randomized search algorithms heavily rely on benchmarking. Regarding the domain of constrained optimization, the number of currently available benchmark environments bears no relation to the number of distinct problem features. The present paper advances a proposal of a scalable linear constrained optimization problem that is suitable for benchmarking Evolutionary Algorithms. By comparing two recent EA variants, the linear benchmarking environment is demonstrated.
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Benchmarking plays an important role in the development of novel search algorithms as well as for the assessment and comparison of contemporary algorithmic ideas. This paper presents common principles that need to be taken into account when considering benchmarking problems for constrained optimization. Current benchmark environments for testing Evolutionary Algorithms are reviewed in the light of these principles. Along with this line, the reader is provided with an overview of the available problem domains in the field of constrained benchmarking. Hence, the review supports algorithms developers with information about the merits and demerits of the available frameworks.
In this article we provide a comprehensive review of the different evolutionary algorithm techniques used to address multimodal optimization problems, classifying them according to the nature of their approach. On the one hand there are algorithms that address the issue of the early convergence to a local optimum by differentiating the individuals of the population into groups and limiting their interaction, hence having each group evolve with a high degree of independence. On the other hand other approaches are based on directly addressing the lack of genetic diversity of the population by introducing elements into the evolutionary dynamics that promote new niches of the genotypical space to be explored. Finally, we study multi-objective optimization genetic algorithms, that handle the situations where multiple criteria have to be satisfied with no penalty for any of them. Very rich literature has arised over the years on these topics, and we aim at offering an overview of the most important techniques of each branch of the field.
This paper analyses a $(1,lambda)$-Evolution Strategy, a randomised comparison-based adaptive search algorithm, on a simple constraint optimisation problem. The algorithm uses resampling to handle the constraint and optimizes a linear function with a linear constraint. Two cases are investigated: first the case where the step-size is constant, and second the case where the step-size is adapted using path length control. We exhibit for each case a Markov chain whose stability analysis would allow us to deduce the divergence of the algorithm depending on its internal parameters. We show divergence at a constant rate when the step-size is constant. We sketch that with step-size adaptation geometric divergence takes place. Our results complement previous studies where stability was assumed.
The performance of evolutionary algorithms can be heavily undermined when constraints limit the feasible areas of the search space. For instance, while Covariance Matrix Adaptation Evolution Strategy is one of the most efficient algorithms for unconstrained optimization problems, it cannot be readily applied to constrained ones. Here, we used concepts from Memetic Computing, i.e. the harmonious combination of multiple units of algorithmic information, and Viability Evolution, an alternative abstraction of artificial evolution, to devise a novel approach for solving optimization problems with inequality constraints. Viability Evolution emphasizes elimination of solutions not satisfying viability criteria, defined as boundaries on objectives and constraints. These boundaries are adapted during the search to drive a population of local search units, based on Covariance Matrix Adaptation Evolution Strategy, towards feasible regions. These units can be recombined by means of Differential Evolution operators. Of crucial importance for the performance of our method, an adaptive scheduler toggles between exploitation and exploration by selecting to advance one of the local search units and/or recombine them. The proposed algorithm can outperform several state-of-the-art methods on a diverse set of benchmark and engineering problems, both for quality of solutions and computational resources needed.
In this paper, we extend a bio-inspired algorithm called the porcellio scaber algorithm (PSA) to solve constrained optimization problems, including a constrained mixed discrete-continuous nonlinear optimization problem. Our extensive experiment results based on benchmark optimization problems show that the PSA has a better performance than many existing methods or algorithms. The results indicate that the PSA is a promising algorithm for constrained optimization.
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