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7. Rossum, D., Constraint based audio interpolators, IEEE ASSP Workshop on Applications of Signal<br />

Processing to Audio and Acoustics (Mohonk), 1993.<br />

8. Zhang, M., Tan, K. C., and Er, M. H., Three-dimensional synthesis based on head-related transfer<br />

functions, Journal of the Audio Engineering Society, 46, 836, 1998.<br />

9. Audio Codec ’97 Revision 2.2, Intel Corporation, San Jose, CA, 2000.<br />

10. IEC-958 Digital Audio Interface, International Electrotechnical Commission, 1989.<br />

39.4 Modern Approximation Iterative Algorithms and Their<br />

Applications in Computer Engineering<br />

Sadiq M. Sait and Habib Youssef<br />

Introduction<br />

This chapter section discusses one class of combinatorial optimization algorithms: approximation iterative<br />

algorithms. We shall limit ourselves to four of these algorithms, which are, in order of their popularity<br />

among the engineering community: (1) simulated annealing (SA), (2) genetic algorithm (GA), (3) tabu<br />

search (TS), and (4) simulated evolution (SimE).<br />

GA and SimE are evolutionary algorithms, a term used to refer to any probabilistic algorithm whose<br />

design is inspired by evolutionary mechanisms found in biological species. Evolutionary algorithms, SA<br />

and TS have been found very effective and robust in solving numerous problems from a wide range of<br />

application domains. Furthermore, they are even suitable for ill-posed problems where some of the<br />

parameters are not known beforehand. These properties are lacking in all traditional optimization techniques.<br />

The four algorithms share the following properties:<br />

1. They are approximation algorithms, i.e., they do not guarantee finding an optimal solution. Actually,<br />

they are blind, in that they do not know when they reached an optimal solution. Therefore, they<br />

must be told when to stop.<br />

2. They are neighborhood search algorithms, which start from one suboptimal solution (or a population<br />

of solutions) and perform a partial search of the solution space for better solutions.<br />

3. They are all “general.” They are not problem-specific and, practically, they can be tailored to solve<br />

any combinatorial optimization problem.<br />

4. They all strive to exploit domain specific heuristic knowledge to bias the search toward “good”<br />

solution subspace. The quality of subspace searched depends to a large extent on the amount of<br />

heuristic knowledge used.<br />

5. They are easy to implement. All that is required is to have a suitable solution representation, a<br />

cost function, and a mechanism to traverse the search space.<br />

6. They have hill climbing property, i.e., they occasionally accept uphill (bad) moves.<br />

The goal in this chapter section is to briefly introduce these four powerful algorithms. It is organized<br />

into nine sections. In the next four subsections, an intuitive discussion of each of the four iterative<br />

algorithms is provided. The remaining sections briefly address convergence aspects of the heuristics, their<br />

parallel implementation, and examples of applications. The final subsection concludes the chapter section<br />

with a comparison among the heuristics and a glimpse at the notion of hybrids. This chapter section<br />

does not provide a full account of any of this important class of heuristics. For more details, readers<br />

should consult the numerous references cited in the body of this work.<br />

Simulated Annealing<br />

Simulated Annealing (SA) is one of the most well-developed and widely used iterative techniques for solving<br />

optimization problems. It is a general adaptive heuristic and belongs to the class of nondeterministic<br />

algorithms [1]. It has been applied to several combinatorial optimization problems from various fields<br />

© 2002 by CRC Press LLC

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