Peter J. M. van Laarhoven

Genetic Local Search Algorithms for the Travelling Salesman Problem

We briefly review previous attempts to generate near-optimal solutions of the Traveling Salesman Problem by applying Genetic Algorithms. Following the lines of Johnson [1990] we discuss some possibilities for speeding up classical Local Search algorithms by casting them into a genetic frame. In an experimental study two such approaches, viz. Genetic Local Search with 2-Opt neighbourhoods and Lin-Kernighan neighbourhoods, respectively, are compared with the corresponding classical multi-start Local Search algorithms, as well as with Simulated Annealing and Threshold Accepting, using 2-Opt neighbourhoods. As to be expected a genetic organization of Local Search algorithms can considerably improve upon performance though the genetic components alone can hardly counterbalance a poor choice of the neighbourhoods.

A quantitative analysis of the simulated annealing algorithm: A case study for the traveling salesman problem

A quantitative study is presented of the typical behavior of the simulated annealing algorithm based on a cooling schedule presented previously by the authors. The study is based on the analysis of numerical results obtained by systematically applying the algorithm to a 100-city traveling salesman problem. The expectation and the variance of the cost are analyzed as a function of the control parameter of the cooling schedule. A semiempirical average-case performance analysis is presented from which estimates are obtained on the expectation of the average final result obtained by the simulated annealing algorithm as a function of the distance parameter, which determines the decrement of the control parameter.

Simulated annealing: A pedestrian review of the theory and some applications

Simulated annealing is a combinatorial optimization method based on randomization techniques. The method originates from the analogy between the annealing of solids, as described by the theory of statistical physics, and the optimization of large combinatorial problems. Here we review the basic theory of simulated annealing and recite a number of applications of the method. The theoretical review includes concepts of the theory of homogeneous and inhomogeneous Markov chains, an analysis of the asymptotic convergence of the algorithm, and a discussion of the finite-time behaviour. The list of applications includes combinatorial optimization problems related to VLSI design, image processing, code design and artificial intelligence.

Some miscellaneous topics

In this chapter, parallel implementations of the simulated annealing algorithm on multi-processor architectures (section 8.1) are described as well as an extension of the algorithm to problems with continuous variables (section 8.2).

On the computational of Lauricella functions of the fourth kind

Abstract An identity is proved which simplifies the computation of Lauricella functions of the fourth kind. An application to a problem in mathematical statistics is briefly discussed.

PHIPLA--A New Algorithm for Logic Minimization

PHIPLA, a new algorithm for logic minimization, is presented. The algorithm sets out to find optimal sum-of-products representations for a set of Boolean functions, thus contributing to area minimization of the Programmable Logic Array corresponding to the set of functions. The results of a comparative study of PHIPLA and two other algorithms, SPAM and PRESTOL-II, are presented. From these results it is concluded that PHIPLA generates representations which are competitive with those generated by SPAM and PRESTOL-II, whilst the algorithm is extremely fast for small problems (up to 12 variables).

Combinatorial Optimization Problems in PCB Assembly

We analyze combinatorial optimization problems arising in a component insertion line for printed circuit board mounting. Such a line consists of a number of fully automated placement machines, connected by an automated, carrierless conveyor system. Each machine has a placement device, consisting of an arm equipped with three placement heads. Each head may pick and place certain component types; there is some freedom in the choice of equipment for each head. Components are supplied to each machine by tape feeders (each containing components of only one type) which are placed at certain feeder positions along the machine.

Simulated Annealing: Theory of the Past, Practice of the Future?

Simulated annealing is a general approach for approximately solving large combinatorial optimization problems. In this paper we first give a mathematical description of the algorithm and discuss its behaviour from both a theoretical and a practical point of view. We illustrate the practical use of the algorithm by discussing the application to a number of combinatorial optimization problems. In addition, we cite applications in such diverse areas as design of integrated circuits, image processing, code design and neural network theory, and discuss computational experience with the algorithm.

Performance of the simulated annealing algorithm

The performance analysis of an approximation algorithm concentrates on the following two quantities: the quality of the final solution obtained by the algorithm, i.e. the difference in cost value between the final solution and a globally minimal configuration; the running time required by the algorithm.

Asymptotic convergence results

Essential to the convergence proof for the homogeneous algorithm is the fact that, under certain conditions, the stationary distribution of a homogeneous Markov chain exists. The stationary distribution is defined as the vector q whose i-th component is given by [FELL50]