Variable neighborhood formulation search approach for the multi-item capacitated lot-sizing problem with time windows and setup times

Abstract

In this paper we suggest a new variant of Variable neighborhood search designed for solving Mixed integer programming problems. We call it Variable neighborhood formulation search (VNFS), since both neighborhoods and formulations are changed during the search. VNS deals with integer variables, while an available (commercial) solver is responsible for continues variables and the objective function value. We address the multi-item capacitated lotsizing problem with production time windows and setup times, under the non-customer specific case. This problem is known to be NP-hard and can be formulated as a mixed 0-1 program. Neighborhoods are induced from the Hamming distance in 0-1 variables, while the objective function values in the corresponding neighborhoods are evaluated using different mathematical programming formulations of the problem. The computational experiments show that our approach is more effective and efficient when compared with the existing methods from the literature.

Packing a fixed number of identical circles in a circular container with circular prohibited areas

“…At a slightly more general level FSS can be regarded as a variant of variable neighbourhood search, for example see [1,11]. Recently Erromdhani et al [8] used the phrase variable neighbourhood formulation search to describe their approach for solving the multi-item capacitated lot-sizing problem with time windows and setup times. In their approach both formulations and neighbourhoods are changed during the search process.…”