Keep-best reproduction: a selection strategy for genetic algorithms

This paper presents an empirical study of a new intermediate selection strategy for genetic algori thms for constraint optimization problems. In a s tandard genetic algorithm the children replace their parents. The idea behind this is that both parents pass on their good genetic material to their children. In practice however, children can have worse fitnesses than their parents. We therefore propose another intermediate selection step, which we will call keep-best reproduction, which works as follows: After two parents are chosen for reproduction, the crossover operator is applied with its probability setting. Then the newly created offspring are evaluated. The worst offspring is replaced by the best parent. This makes sure that new genetic information is entered into the gene pool in the fortr~ of the best child, as well as ensuring that good previous genetic material is being preserved in the form of the best parent. Then mutat ion is applied to these strings with a certain probabili ty and the resulting encodings are inserted into the new population. We will demonstra te the superiority of keep-best reproduction on several instances of the traveling salesman problem. Keep-best reproduction not only finds better solutions, but also finds better solutions faster than the s tandard generational replacement. nission to make digital/hard copy of all or part of this work ibr personal or sroom use is granted without t~e provided that copies are not made or ributed for profit or commercial advantage, the copyright notice, the title of the lication and its date appear, and notice is given that copying is by permission of M. Inc. ]'o cop',' othe~vise, to republish, to post on servers or to redistribute to • requires prior specific permission and/or a the. <-? 1998 ACM 0-89791-969-6/98/0002 3.50 Many problems in artificial intelligence and simulation can be described in a general framework as a constraint satisfaction problem (CSP) or a constraint optimization problem (COP). Informally a CSP (in its finite domain formulation) is a problem composed of a finite set of variables, each of which has a finite domain, and a set of constraints that restrict the values that the variables can simultaneously take. For many problem domains however not all solutions to a CSP are equally good. For example in the case of job shop scheduling different schedules which all satisfy the resource and capacity constraints can have different makespans (the total t ime to complete all orders), or different inventory requirements. So in addition to the standard CSP, a constraint optimizat ion problem has a so-called objective function f which assigns a value to each solution of the underlying CSP. A global sohttion to a COP is a labelling of all its variables, so that all constraints are satisfied, and the objective function f is optimized. Since it usually takes a complete search of the search space to find the op t imum f value, for many problems global optimizat ion is not feasible in practice. Tha t is why COP research has focused on local search methods that take a candidate solution to a COP and search in its local neighborhood for improving neighbors. Such techniques include iterative improvement (hill climbing), threshold algori thms [3], simulated annealing [1, 10], t aboo search [4, 5. 6], and variable depth search. Since these methods are only searching a subset of the search space, they are not complete, i.e., are not guaranteed to return the overall opt imum. Another opt imizat ion technique is genetic algorithms (GAs). Genetic algori thms were originally designed to work on bitstrings. These bitstrings encoded a domain value of a real valued function that was supposed to be optimized. They were originally proposed by Holland [9]. More recently, researchers