The Quadratic Assignment Problem (QAP) is a well-known combinatorial optimization problem with a wide variety of practical applications. Although many heuristics and semi-enumerative procedures for QAP have been proposed, no dominant algorithm has emerged. In this paper, we describe a Genetic Algorithm (GA) approach to QAP. Genetic algorithms are a class of randomized parallel search heuristics which emulate biological natural selection on a population of feasible solutions. We present computational results which show that this GA approach finds solutions competitive with those of the best previously-known heuristics, and argue that genetic algorithms provide a particularly robust method for QAP and its more complex extensions. 5 A Genetic Approach to the Quadratic Assignment Problem David M. Tate and Alice E. Smith Department of Industrial Engineering 1048 Benedum Hall University of Pittsburgh Pittsburgh, PA 15261 412-624-9837 412-624-9831 (Fax) 1. Introduction The Quadrat...

. Selection is an essential component of evolutionary algorithms, playing an important role especially in solving hard optimization problems. Most previous studies on selection have focused on more or less ideal properties based on asymptotic analysis. In this paper, we address the selection problem from a more practical point of view by considering solution quality achievable within acceptable time. The repertoire of methods we compare includes proportional selection, ranking selection, linear ranking, tournament, Genitor selection, simulated annealing, and hill-climbing. All these methods use genetic operators in one form or another to create new search points. Experiments are performed in the context of the machine layout design problem. This problem is a real industrial application having both continuous and discrete optimization characteristics. The experimental results for solving two-row machine layout problems of size ranging from 10 to 50 show strong evidence that ranking and tournament selection are, in general, more effective in both solution quality and convergence time than proportional selection and other methods. We provide a theoretical explanation of the experimental results using a predictive model of evolutionary optimization based on selection differential and response to selection. Keywords: Evolutionary optimization, machine layout design, selection methods, selection differential, response to selection, heritability 1.

Abstract. Selection is an essential component of evolutionary algorithms, playing an important role especially in solving optimization problems. We compare three most pop~ar selection schemes: proportional, ranking, and tournament selection. Experiments have been performed in the context of the machine layout design problem. This problem provides a useful benchmark due to its scalability of problem complexity and its having poth discrete and continuous optimization. Our empirical results suggest that ranking and tournament selection be, in general, more effective in solution quality and computational costs for optimization than proportional selection.

In this paper a general model for embedding an assembly process on different plant layout configurations is presented. A combinatorial optimization model is given, which generalizes many well known problems in production planning and scheduling, such as machine loading, machine layout, and several routing and scheduling models. The problems of finding feasible as well as optimal solutions with respect to makespan minimization are addressed in this context, and their computational complexity is analyzed in several relevant cases.