Geometric generalisation of surrogate model-based optimisation to combinatorial and program spaces

Open access journalSurrogate models (SMs) can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with solutions that can be encoded as integer vectors. We show how radial basis functions can provide a generalised SM for combinatorial problems which have a geometric solution representation, through the conversion of that representation to a different metric space. This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation. We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs. © 2014 Yong-Hyuk Kim et al

A New Adaptive Hungarian Mating Scheme in Genetic Algorithms

In genetic algorithms, selection or mating scheme is one of the important operations. In this paper, we suggest an adaptive mating scheme using previously suggested Hungarian mating schemes. Hungarian mating schemes consist of maximizing the sum of mating distances, minimizing the sum, and random matching. We propose an algorithm to elect one of these Hungarian mating schemes. Every mated pair of solutions has to vote for the next generation mating scheme. The distance between parents and the distance between parent and offspring are considered when they vote. Well-known combinatorial optimization problems, the traveling salesperson problem, and the graph bisection problem are used for the test bed of our method. Our adaptive strategy showed better results than not only pure and previous hybrid schemes but also existing distance-based mating schemes

Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces

Surrogate models (SMs) can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with solutions that can be encoded as integer vectors. We show how radial basis functions can provide a generalised SM for combinatorial problems which have a geometric solution representation, through the conversion of that representation to a different metric space. This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation. We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs

Quotient geometric crossovers and redundant encodings

Copyright © 2012 Elsevier. NOTICE: this is the author’s version of a work that was accepted for publication in Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Theoretical Computer Science Vol. 425 (2012), DOI: 10.1016/j.tcs.2011.08.015We extend a geometric framework for the interpretation of search operators to encompass the genotype–phenotype mapping derived from an equivalence relation defined by an isometry group. We show that this mapping can be naturally interpreted using the concept of quotient space, in which the original space corresponds to the genotype space and the quotient space corresponds to the phenotype space. Using this characterization, it is possible to define induced geometric crossovers on the phenotype space (called quotient geometric crossovers). These crossovers have very appealing properties for non-synonymously redundant encodings, such as reducing the size of the search space actually searched, removing the low locality from the encodings, and allowing a more informed search by utilizing distances better tailored to the specific solution interpretation. Interestingly, quotient geometric crossovers act on genotypes but have an effect equivalent to geometric crossovers acting directly on the phenotype space. This property allows us to actually implement them even when phenotypes cannot be represented directly. We give four example applications of quotient geometric crossovers for non-synonymously redundant encodings and demonstrate their superiority experimentally