Short abstract, isn't it? P.A.C.S. numbers 05.20, 02.50, 87.10 1 Introduction Large Numbers "...the optimal tour displayed (see Figure 6) is the possible unique tour having one arc fixed from among 10 655 tours that are possible among 318 points and have one arc fixed. Assuming that one could possibly enumerate 10 9 tours per second on a computer it would thus take roughly 10 639 years of computing to establish the optimality of this tour by exhaustive enumeration." This quote shows the real difficulty of a combinatorial optimization problem. The huge number of configurations is the primary difficulty when dealing with one of these problems. The quote belongs to M.W Padberg and M. Grotschel, Chap. 9., "Polyhedral computations", from the book The Traveling Salesman Problem: A Guided tour of Combinatorial Optimization [124]. It is interesting to compare the number of configurations of real-world problems in combinatorial optimization with those large numbers arising in Cosmol...

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...

The Facility Layout Problem (FLP) concerns minimising total traffic cost between facilities in a particular location under given conditions including facility size and traffic between each pair of them. Because of its NP-completeness, many suboptimal methods, which look for reasonably good solutions, have been suggested. Although many papers exist which compare the performance of these methods with each other, the work is limited in the following ways: benchmark tests were done only on FLPs consisting of identical facilities; most of the algorithms being compared relied on deterministic approaches. Genetic Algorithms (GAs), which use a stochastic approach, have been used with some success for a number of NP-complete problems, typically finding good answers but not necessarily the best. However, a range of other approaches, from traditional operations research to simulated annealing, are possible. Moreover, a GA itself can be varied in many ways. So, in this research project, not only t...

In this paper we have proposed a semi-heuristic optimization algorithm for designing optimal plant layouts in process-focused manufacturing/service facilities. Our proposed algorithm marries the well-known CRAFT (Computerized Relative Allocation of Facilities Technique) with the Hungarian assignment algorithm. Being a semi-heuristic search, our algorithm is likely to be more efficient in terms of computer CPU engagement time as it tends to converge on the global optimum faster than the traditional CRAFT algorithm- a pure heuristic. We also present a numerical illustration of our algorithm. Key Words Facilities layout planning, load matrix, CRAFT, Hungarian assignment algorithm