Showing papers on "Metaheuristic published in 1983"

Problem complexity and method efficiency in optimization

Abstract: (1984). Problem Complexity and Method Efficiency in Optimization. Journal of the Operational Research Society: Vol. 35, No. 5, pp. 455-455.

Global optimization by controlled random search

Abstract: The paper describes a new version, known as CRS2, of the author's controlled random search procedure for global optimization (CRS). The new procedure is simpler and requires less computer storage than the original version, yet it has a comparable performance. The results of comparative trials of the two procedures, using a set of standard test problems, are given. These test problems are examples of unconstrained optimization. The controlled random search procedure can also be effective in the presence of constraints. The technique of constrained optimization using CRS is illustrated by means of examples taken from the field of electrical engineering.

Optimization : Theory and Algorithms

Abstract: This book is concerned with tangent cones, duality formulas, a generalized concept of conjugation, and the notion of maxi-minimizing sequence for a saddle-point problem, and deals more with algorithms in optimization. It focuses on the multiple exchange algorithm in convex programming.

Multiextremal optimization problems

Abstract: The first researchers in the field of applied optimization have not paid much attention to the problem of multiextremality; they have merely ignored it. However, it was only by luck that they came across uniextremal problems: the problem of the design of the minimal weight column, which was first solved by N. Clausen by means of the calculus of variations,’ and the problem of the lightest circular arch under uniform pressure solved by L. R. Jorgensen, who used the differential calculus.’ The same is true with respect to the first inventory problems, which were resolved at the beginning of this century. Linear programming problems are not generally uniextremal; rather, they may have an infinite number of solutions with the same value of the objective function. (The first engineering application was made by J. Foulkes.’) But the first researchers in optimal engineering design who used nonlinear programming did not mention the local extrema The wide scope of multiextremality in structural design was given in Reference 6. It was shown that the problem of the structural design of flexural bar structures could often be multiextremal. It is especially important when nonlinear programming is applied, since the techniques mostly provide us with only the necessary optimality conditions. As was shown in References 6 and 7, the majority of the optimum design problems are multiextremal. In fact, uniextremal problems are a rather narrow set inside the general set of the optimum design problems. And there are many examples where neglect of multiextremality has brought to closest local extremal point instead of the global one. The multiextremality is an essential property of a problem; it seems naive to deal with it using substitutions, however sophisticated. Economic problems contain more uncertainties than engineering problems; this sometimes justifies ignoring multiextremality. This problem makes any quantification of economic problems doubtful and prevents any formal analysis. However, most economic problems of optimization are multiextremal. We belive that optimum design techniques have to be developed to allow for multiextremality. The probability of achieving the global extremum among several millions of !ocal ones-some of which have a larger gravitational area than the global one-is very small. On the other hand, there is a good chance of finding the closest local extremum of no significance. In the next section, we shall show that some optimum design problems are basically multiextremal; in the section following we shall discuss some ways of overcoming this obstacle.