From the Publisher:
This book explores the meta-heuristics approach called tabu search, which is dramatically changing our ability to solve a hostof problems that stretch over the realms of resource planning,telecommunications, VLSI design, financial analysis, scheduling, spaceplanning, energy distribution, molecular engineering, logistics,pattern classification, flexible manufacturing, waste management,mineral exploration, biomedical analysis, environmental conservationand scores of other problems. The major ideas of tabu search arepresented with examples that show their relevance to multipleapplications. Numerous illustrations and diagrams are used to clarifyprinciples that deserve emphasis, and that have not always been wellunderstood or applied. The book's goal is to provide ''hands-on' knowledge and insight alike, rather than to focus exclusively eitheron computational recipes or on abstract themes. This book is designedto be useful and accessible to researchers and practitioners inmanagement science, industrial engineering, economics, and computerscience. It can appropriately be used as a textbook in a masterscourse or in a doctoral seminar. Because of its emphasis on presentingideas through illustrations and diagrams, and on identifyingassociated practical applications, it can also be used as asupplementary text in upper division undergraduate courses. 

Finally, there are many more applications of tabu search than canpossibly be covered in a single book, and new ones are emerging everyday. The book's goal is to provide a grounding in the essential ideasof tabu search that will allow readers to create successfulapplications of their own. Along with the essentialideas,understanding of advanced issues is provided, enabling researchers togo beyond today's developments and create the methods of tomorrow.

Tabu Search

Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial interpolation 5. Divided differences 6. The uniform convergence of polynomial approximations 7. The theory of minimax approximation 8. The exchange algorithm 9. The convergence of the exchange algorithm 10. Rational approximation by the exchange algorithm 11. Least squares approximation 12. Properties of orthogonal polynomials 13. Approximation of periodic functions 14. The theory of best L1 approximation 15. An example of L1 approximation and the discrete case 16. The order of convergence of polynomial approximations 17. The uniform boundedness theorem 18. Interpolation by piecewise polynomials 19. B-splines 20. Convergence properties of spline approximations 21. Knot positions and the calculation of spline approximations 22. The Peano kernel theorem 23. Natural and perfect splines 24. Optimal interpolation Appendices Index.

Approximation theory and methods, by M. J. D. Powell. Pp 339. £25 (hardcover), £8·50 (paperback). 1981. ISBN 0-521-22472-1/29514-9 (Cambridge University Press)

The computational complexity of VLSI digital filters using fixed point binary multiplier coefficients is normally dominated by the number of adders used in the implementation of the multipliers. It has been shown that using multiplier blocks to exploit redundancy across the coefficients results in significant reductions in complexity over methods using canonic signed-digit (CSD) representation, which in turn are less complex than standard binary representation. Three new algorithms for the design of multiplier blocks are described: an efficient modification to an existing algorithm, a new algorithm giving better results, and a hybrid of these two which trades off performance against computation time. Significant savings in filter implementation cost over existing techniques result in all three cases. For a given wordlength, it was found that a threshold set size exists above which the multiplier block is extremely likely to be optimal. In this region, design computation time is substantially reduced. >

Use of minimum-adder multiplier blocks in FIR digital filters

If each delay element of a linear phase low-pass digital filter is replaced by M delay elements, an (M + 1) -band filter is produced. The transition-width of this (M + 1) -band filter is 1/M that of the prototype low-pass filter. A complementary filter can be obtained by subtracting the output of the (M + 1) -band filter from a suitably delayed version of the input. The complementary filter is an (M + 1) -band filter whose passbands and stopbands are the stopbands and passbands, respectively, of the original (M + 1) -band filter. If the frequency responses of the original ( M + 1) -band filter and its complementary filter are properly masked and recombined, narrow transition-band filter can be obtained. This technique can be used to design sharp low-pass, high-pass, bandpass, and bandstop filters with arbitrary passband bandwidth.

Frequency-response masking approach for the synthesis of sharp linear phase digital filters

FIR digital filters with discrete coefficient values selected from the powers-of-two coefficient space are designed using the methods of integer programming. The frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients. Both the weighted minimax and the weighted least square error criteria are considered. Using a weighted least square error criterion, it is shown that it is possible to predict the improvement that can be expected when integer quadratic programming is used instead of simple coefficient rounding.

FIR filter design over a discrete powers-of-two coefficient space

The application of a general-purpose integer-programming computer program to the design of optimal finite wordlength FIR digital filters is described. Examples of two optimal low-pass FIR finite wordlength filters are given and the results are compared with the results obtained by rounding the infinite wordlength coefficients. An analysis of the approach based on the results of more than 50 design cases is presented and the problem of optimal wordlength choice is discussed.

Design of optimal finite wordlength FIR digital filters using integer programming techniques

We give a theorem which shows that there is a lower bound on the Chebyshev approximation error for linear-phase direct-form FIR digital filters, when the coefficients are constrained to be b-bit numbers. We then investigate the tradeoff between filter-length N and coefficient word-length b, using the product Nb as a complexity measure, for both the usual direct form and the sharpening structures of Kaiser and Hamming. The sharpening structures usually provide no overall gain in Nb product, but achieve a given performance with a smaller value of b.

Filter-length word-length tradeoffs in FIR digital filter design

The problem of the optimal allocation of components to a printed circuit board assembly line will several non-identical placement machines in series is considered. The objective is to achieve the highest throughput by minimizing the production cycle time of the assembly line. This problem can be formulated as a minimax approximation integer programming problem that belongs to the family of scheduling problems. The difficulty lies in the fact that this problem is proven to be NP-complete. All known algorithms are exponential and work only if the number of variables is reasonably small. This particular problem, however, has properties that allow the development of a very efficient type of branch-and-bound-based optimal algorithm that works for problems with a practically useful number of variables. Detailed description of the algorithm is given together with examples that demonstrate its effectiveness.

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Optimal algorithm for minimizing production cycle time of a printed circuit board assembly line

In many practical situations, it is necessary to represent the coefficients of a finite impulse response (FIR) digital filter by a finite number of bits. This not only degrades the filter frequency response but also introduces a theoretical limit on the performance of the filter. Derivation of a lower bound on filter degradation is the purpose of this paper. We consider a general case of a length N filter with a discrete set of allowable coefficients. A theorem that gives the lower bound on the increase in minimax approximation error that is caused by the finite wordlength restriction is presented. Its extension and application to filter design cases is demonstrated. The importance of this bound is not only theoretical. Its practical effectiveness is shown in the algorithm for optimal finite wordlength FIR filter design where it significantly reduces the amount of computation.

Dušan M. Kodek

Papers

Design of optimal finite wordlength FIR digital filters using integer programming techniques

Filter-length word-length tradeoffs in FIR digital filter design

Optimal algorithm for minimizing production cycle time of a printed circuit board assembly line

Performance limit of finite wordlength FIR digital filters

Using asymmetric windows in automatic speech recognition