The Reverse Elimination Method (REM) is a dynamic strategy for managing the tabu list. It is based on logical interdependencies between the solutions encountered during recent iterations of the search. REM provides both a necessary and sufficient condition to prevent cycling. The purpose of this paper is first to incorporate in REM a chronological order rule when cycling is unavoidable, thereby assuring the finite convergence of Tabu Search. Secondly, we correct a generalization of REM, the so-called REM-t method proposed by Glover (1990) where t is an integer parameter which controls the number of tabu attributes. A suitable adjustment of this parameter t can be designed in order to create a balance between diversification and intensification. In this paper, new dynamic rules for controlling the adjustment of the parameter t, are proposed. Finally, to illustrate the differences between the variants proposed for managing the tabu list, we test some of them on the 0–1 multidimensional knapsack problem.

For a given partial solution,the partial inverse problem is to modify the coefficientssuch that there is a full solution containing the partial solution, while the full solution becomes optimal under new coefficients, and the total modification is minimum.In this paper, we show that the partial inverseassignment problem and the partial inverse minimum cut problem are NP-hard ifthere are bound constraints on the changes of coefficients.

We study a continuous version of the capacity and flow assignment problem(CFA) where the design cost is combined with an average delay measureto yield a non convex objective function coupled with multicommodity flowconstraints. A separable convexification of each arc cost function is proposedto obtain approximate feasible solutions within easily computable gaps fromoptimality. On the other hand, DC (difference of convex functions) programming can be usedto compute accurate upper bounds and reduce the gap.The technique is shown to be effective when topology is assumedfixed and capacity expansion on some arcs is considered.

A method to infer X-trees (valued trees having X as set of leaves) from incomplete distance arrays (where some entries are uncertain or unknown) is described. It allows us to build an unrooted tree using only 2n-3 distance values between the n elements of X, if they fulfill some explicit conditions. This construction is based on the mapping between X-tree and a weighted generalized 2-tree spanning X.

The simple plant location problem (SPLP) is considered and a genetic algorithm is proposed to solve this problem. By using the developed algorithm it is possible to solve SPLP with more than 1000 facility sites and customers. Computational results are presented and compared to dual based algorithms.