Mathematical Perspectives on Neural Networks

By Paul Smolensky; Michael C. Mozer et al. | Go to book overview

6 Deterministic and Randomized Local Search

Emile H. L. Aarts Philips Research Laboratories Eindhoven University of Technology

Jan H. M. Korst Philips Research Laboratories

Patrick J. Zwietering Eindhoven University of Technology


1. INTRODUCTION

Local search is concerned with the design and analysis of a special class of algorithms that can find approximate solutions for hard combinatorial optimiza­tion problems. Solving a combinatorial optimization problem amounts to finding an optimal solution among a finite or countably infinite number of alternative solutions. Here, optimality is related to some cost criterion that provides a quan­titative measure of the quality of each solution. This area of discrete mathe­matics is of great practical use and has attracted much attention over the years. For extensive and detailed introductions in the field the reader is referred to the books by Aarts and Lenstra, Nemhauser and Wolsey ( 1988), Papadimitriou and Steiglitz ( 1982), and Schrijver ( 1986). An annotated bibliography of the field is given by O'hEigeartaigh, Lenstra, and Rinnooy Kan ( 1985). Many combinatorial optimization problems belong to the class of NP-hard problems; see Garey and Johnson ( 1979). It is generally believed that these problems cannot be solved to optimality within polynomially bounded computation times. This property has led to a variety of solution methods, which can be distinguished using the following criteria:

Optimization versus approximation. Optimization algorithms find optimal so­lutions, at the risk of large, possibly impracticable amounts of computation time. Approximation algorithms, often called heuristic algorithms, find solutions that are not necessarily optimal within acceptable running times.

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