Fitting of Tabu Search to Optimize Functions of Continuous Variables

Abstract

SUMMARYTabu Search (TS) is a stochastic global optimization procedure which proved efficient to solve various combinatorial optimization problems. However, very few works deal with its application to global minimization of functions depending on continuous variables. The aim of this paper is to propose an adaptation of TS to the optimization of continuous functions, and to study the influence of the main algorithm parameters on the convergence towards the optimum. In particular, the application of TS to function optimization involves the definition of the current solution neighbourhood and the management of the tabu list. The efficiency of TS applied to continuous global optimization has been tested in detail by using classical multimodal functions for which minima are known.1997 by John Wiley & Sons, Ltd.

A simulation optimisation approach for inventory management decision support based on incomplete information

“…However, the algorithm of Hu is rather far from original tabu search. Siarry and Berthiau (1997) propose an adaptation of tabu search to the optimisation of continuous functions where the purpose is to keep as close as possible to original simple tabu search. As neighbourhood of the current solution, they perform a partition of the space around the current solution using a set of concentric balls.…”

“…The tabu list contains m balls, corresponding to the immediate neighbourhoods of the m last retained solutions. Chelouah and Siarry (2000) improve the algorithm of Siarry and Berthiau (1997) and propose an Enhanced Continuous Tabu Search for the global optimisation of continuous functions. They replace the balls by hyperrectangles for the partition of the current solution neighbourhood and add diversification and intensification concepts to the algorithm.…”

“…They replace the balls by hyperrectangles for the partition of the current solution neighbourhood and add diversification and intensification concepts to the algorithm. The method we propose here is based on (Siarry and Berthiau 1997) and (Chelouah and Siarry 2000). In Figure 6.2, a general flowchart of the TS algorithm is shown.…”

Global optimization approaches to an aircraft routing problem

“…The algorithm is based on ideas described in [12] and [2]; and it resembles the one outlined in the previous section both in its use of tabu search ideas and its reliance on randomly generated points.…”

“…In general, on iteration k it begins with a diversification phase. This can involve either a set of hyperspheres with radii h 1 h 2 h η centred upon x´k µ (as in [12]) or else a set of concentric hyper-rectangles about x´k µ (as in [2] If in fact f´x ¼ j µ f´x´k µ µ then x´k µ is considered to be "promising" since our sampling of neighbouring points suggests it could be close to a local minimum. It is therefore added to a "promising list" -provided it is not within a certain distance d p of an existing member of the list.…”