Genetically controlled random search: a global optimization method for continuous multidimensional functions☆
Introduction
A recurring problem in many applications is that of finding the global minimum of a function. This problem may be stated as: Determine The nonempty set considered here, is a hyper box defined as:
Recently several methods have been proposed for the solution of the global optimization problem. These methods can be divided in two main categories, deterministic and stochastic. Random search methods are widely used in the field of global optimization, because they are easy to implement and also since they do not depend critically on a priori information about the objective function. Various random search methods have been proposed, such as the Random Line Search [1], Adaptive Random Search [2], Competitive Evolution [3], Controlled Random Search [4], Simulated Annealing [5], [6], [7], [8], Genetic Algorithms [9], [10], Differential Evolution [11], [12], methods based on Tabu Search [23], etc. This article introduces a new sampling technique for use with conjunction with Controlled Random Search. The method is based on the genetic programming procedure known as Grammatical Evolution. Performance comparison to other methods is quite favorable as might be verified by inspecting the reported results of our computational experiments in Table 1, Section 3.2. The suggested approach uses a population of randomly created moves, that guide the underlying stochastic search towards the global minimum. These random moves are produced by applying the method of grammatical evolution. Grammatical evolution is an evolutionary process that can produce code in an arbitrary language. The production is performed using a mapping process governed by a grammar expressed in Backus Naur Form. Grammatical evolution has been applied successfully to problems such as symbolic regression [14], discovery of trigonometric identities [15], robot control [16], caching algorithms [17], financial prediction [18], etc. The rest of this article is organized as follows: in Section 2 we give a brief presentation of the grammatical evolution and of the suggested algorithms. In Section 3 we list some experimental results from the application of the proposed method and a comparison is made against traditional global optimization methods and in Section 4 we present the installation and the execution procedures of the GenPrice.
Section snippets
Grammatical evolution
Grammatical evolution is an evolutionary algorithm that can produce code in any programming language. The algorithm requires the grammar of the target language in BNF syntax and the proper fitness function. Chromosomes in grammatical evolution, in contrast to classical genetic programming [20], are not expressed as parse trees, but as vectors of integers. Each integer denotes a production rule from the BNF grammar. The algorithm starts from the start symbol of the grammar and gradually creates
Experimental results
The Genetically Controlled Random Search (GCRS) was tested against
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The original Controlled Random Search (CRS).
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The modified Controlled Random Search (PCRS) as described in [26].
The comparison is made using a suite of well-known test problems.
Distribution
The package is distributed in a tar.gz file named GenPrice.tar.gz and under UNIX systems the user must issue the following commands to extract the associated files:
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gunzip GenPrice.tar.gz.
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tar xfv GenPrice.tar.
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bin: A directory which is initially empty. After compilation of the package, it will contain the executable make_genprice.
- 2.
examples: A directory that contains the test functions used in this article, written in ANSI
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Cited by (12)
GenMin: An enhanced genetic algorithm for global optimization
2008, Computer Physics CommunicationsGenAnneal: Genetically modified Simulated Annealing
2006, Computer Physics CommunicationsAn improved controlled random search method
2021, SymmetryA hybrid one dimensional optimization
2015, Electronics, Communications and Networks IV - Proceedings of the 4th International Conference on Electronics, Communications and Networks, CECNet2014
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This paper and its associated computer program are available via the Computer Physics Communications homepage on ScienceDirect (http://www.sciencedirect.com/science/journal/00104655).