Parallel Genetic Algorithms for Constrained Ordering Problems

This paper proposes two different parallel genetic algorithms (PGAs) for constrained ordering problems. Constrained ordering problems are constraint optimization problems (COPs) for which it is possible represent a candidate solution as a permutation of objects. A decoder is used to decode this permutation into an instantiafion of the COP vm-iables. Two examples of such constrmnsd ordering problems are the travel;n~ salesman problem (TSP) and the job shop schedldin~ problem (JSSP). The first PGA we propose (PGA1) implements a GA using p subpopulations, where p is the number of processors. This is known as the island model. What is new is that we use a different selection strategy, called kesp.bemt reproduction (KBR) that favours the parent with higher fitness over the child with lower fitness. Keep-best reproduction has shown better results in the sequential case than the standard selection technique (STDS) of replacing both parents by their two children (Wiese & Goodwin 1997; 1998a; 1998b). The second PGA (PGA2) is different from PGAI: while it also works with independent subpopulations, each subpopulation uses a different crossover operator. It is not a priori known which operator performs the best. PGA2 also uses KBR and its subpopulations exrhange a percentage q of their fittest individuals every x generations. In addition, whenever this exchange takes place, the subpopulation with the best average fitness broadcasts a percentage q~ of its fittest individuals to all other subpopulations. This will enmn~ that for a particular problem instance the operator that works best will have an increasing number of ot~pring sampled in the global population. This design also tAlt~ care of the fact that in the early stages of a GA run different operators can work better than in the later stages. Over time PGA2 will automatically adjust to this new situation. Topic Areas: Search, Distributed AI, Genetic Algorithms, Evolutionary Computing, Constraint Optimization Copyright (~)1998, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. Introduction Many problems in artificial intelligence and simulation can be described in a general framework as a constraint satisfaction problem (CSP) or constraint op timization 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 makespaus (the total time to complete all orders), or different inventory requirements. So in addition to the standard CSP, a constraint optimization problem has a so-called objective function f which assigns a value to each solution of the underlying CSP. A global solution to a COP is a labeling 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 optimum f value, for many problems global optimization is not feasible in practice. That 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 algorithms (Dueck Scheuer 1990), simulated annealing (Cerny 1985; Kirkpatrick, Gelatt Jr., & Vecchi 1983), taboo search (Glover, Talllard, & Werra 1993), 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 optimum. Another optimization technique are genetic algorithms (GAs). Genetic algorithms were originally designed to work on hitstrings. These bitstrings encoded a domain value of a real valued function that was supposed to be optimized. They were originally proposed by Holland (Holland 1975). More recently, researchers have focused on applying GAs to combinatorial optimization problems, including constraint optimization problems such as the traveling salesman problem (TSP) and the job shop scheduling problem (JSSP). Genetic Algorithms 101 From: Proceedings of the Eleventh International FLAIRS Conference. Copyright © 1998, AAAI (www.aaai.org). All rights reserved.