Open AccessVariable and single neighbourhood diving for MIP feasibility
Author(s) -
Jasmina Lazić,
Raca Todosijević,
Saïd Hanafi,
Nenad Mladenović
Publication year - 2016
Publication title -
yugoslav journal of operations research
Language(s) - English
Resource type - Journals
eISSN - 1820-743X
pISSN - 0354-0243
DOI - 10.2298/yjor140417027l
Subject(s) - neighbourhood (mathematics) , heuristics , mathematical optimization , solver , variable (mathematics) , integer programming , computer science , mathematics , algorithm , mathematical analysis
In this paper, we propose two new diving heuristics for finding a feasible solution for a mixed integer programming problem, called variable neighbourhood (VN) diving and single neighbourhood (SN) diving, respectively. They perform systematic hard variable fixing (i.e. diving) by exploiting the information obtained from a series of LP relaxations in order to generate a sequence of subproblems. Pseudo cuts are added during the search process to avoid revisiting the same search space areas. VN diving is based on the variable neighbourhood decomposition search framework. Conversely, SN diving explores only a single neighbourhood in each iteration: if a feasible solution is not found, then the next reference solution is chosen using the feasibility pump principle and the search history. Moreover, we prove that the two proposed algorithms converge in a finite number of iterations (i.e. either return a feasible solution of the input problem, or prove its infeasibility). We show that our proposed algorithms significantly outperform the CPLEX 12.4 MIP solver and the recent variants of feasibility pump regarding the solution quality