Jasmina Lazić

Variable neighbourhood decomposition search for 0-1 mixed integer programs

In this paper we propose a new hybrid heuristic for solving 0-1 mixed integer programs based on the principle of variable neighbourhood decomposition search. It combines variable neighbourhood search with a general-purpose CPLEX MIP solver. We perform systematic hard variable fixing (or diving) following the variable neighbourhood search rules. The variables to be fixed are chosen according to their distance from the corresponding linear relaxation solution values. If there is an improvement, variable neighbourhood descent branching is performed as the local search in the whole solution space. Numerical experiments have proven that exploiting boundary effects in this way considerably improves solution quality. With our approach, we have managed to improve the best known published results for 8 out of 29 instances from a well-known class of very difficult MIP problems. Moreover, computational results show that our method outperforms the CPLEX MIP solver, as well as three other recent most successful MIP solution methods.

New hybrid matheuristics for solving the multidimensional knapsack problem

In this paper we propose new hybrid methods for solving the multidimensional knapsack problem. They can be viewed as matheuristics that combine mathematical programming with the variable neighbourhood decomposition search heuristic. In each iteration a relaxation of the problem is solved to guide the generation of the neighbourhoods. Then the problem is enriched with a pseudo-cut to produce a sequence of not only lower, but also upper bounds of the problem, so that integrality gap is reduced. The results obtained on two sets of the large scale multidimensional knapsack problem instances are comparable with the current state-of-the-art heuristics. Moreover, a few best known results are reported for some large, long-studied instances.

Variable Neighbourhood Pump Heuristic for 0-1 Mixed Integer Programming Feasibility

Abstract In this paper we propose a new method for finding an initial feasible solution for Mixed integer programs. We call it “Variable neighborhood pump”, since it combines ideas of Variable neighborhood branching and Feasibility pump heuristics. The proposed heuristic was tested on an established set of 83 benchmark problems proven to be difficult to solve to feasibility. The results are compared with those of IBM ILOG CPLEX 11.1, which already includes standard feasibility pump as a primal heuristic. With our approach we managed to obtain better initial objective function values than CPLEX on 63 test instances, within similar average computational time.

Routing of barge container ships by mixed-integer programming heuristics

Abstract We investigate the optimization of transport routes of barge container ships with the objective to maximize the profit of a shipping company. This problem consists of determining the upstream and downstream calling sequence and the number of loaded and empty containers transported between any two ports. We present a mixed integer linear programming (MILP) formulation for this problem. The problem is tackled by the commercial CPLEX MIP solver and improved variants of the existing MIP heuristics: Local Branching, Variable Neighborhood Branching and Variable Neighborhood Decomposition Search. It appears that our implementation of Variable Neighborhood Branching outperforms CPLEX MIP solver both regarding the solution quality and the computational time. All other studied heuristics provide results competitive with CPLEX MIP solver within a significantly shorter amount of time. Moreover, we present a detailed case study transportation analysis which illustrates how the proposed approach can be used by managers of barge shipping companies to make appropriate decisions and solve real life problems.

Hybrid Variable Neighbourhood Decomposition Search for 0-1 Mixed Integer Programming Problem

Abstract In this paper we propose new hybrid heuristics for the 0-1 mixed integer programming problem, based on the variable neighbourhood decomposition search principle and on exploiting information obtained from a series of relaxations. In the case of a maximization problem, we add iteratively pseudo-cuts to the problem in order to produce a sequence of lower and upper bounds of the problem, so that integrality gap is reduced. We validate our approaches on the well-known 0-1 multidimensional knapsack problem, in which the general-purpose CPLEX MIP solver is used as a black box for solving subproblems generated during the search process. The results obtained with these methods are comparable with the current state-of-the-art heuristics on a set of large scale instances.

Variable Neighbourhood Decomposition Search with Bounding for Multidimensional Knapsack Problem

Abstract In this paper we propose a new heuristic for solving multidimensional knapsack problem, based on the variable neighbourhood decomposition search principle. The set of neighbourhoods is generated by exploiting information obtained from a series of relaxations. In each iteration, we add new constraints to the problem in order to produce a sequence of lower and upper bounds around the optimal value, with the goal to reduce the gap between them. General-purpose CPLEX MIP solver is used as a black box for solving subproblems generated during the search process. With this approach, we have managed to obtain promising results on a set of large scale multidimensional knapsack problem instances. The results are comparable with the current state-of-the-art techniques for solving multidimensional knapsack problem.

Solving 0–1 Mixed Integer Programs with Variable Neighbourhood Decomposition Search

Abstract In this paper we propose a new heuristic for solving 0–1 mixed integer programs based on the variable neighbourhood decomposition search principle. It combines variable neighbourhood search with general-purpose CPLEX MIP solver. We perform systematic hard variables fixing (or diving) following the variable neighbourhood search rules. Variables to be fixed are chosen according to their distance from the corresponding linear relaxation solution values. If there is an improvement, variable neighbourhood descent branching is performed as the local search in the whole solution space. Numerical experiments have proven that by exploiting boundary effects in this way, solution quality can be considerably improved. With our approach, we have managed to improve the best known published results for 8 out of 29 instances from a well-known class of very difficult MIP problems. Moreover, computational results show that our method outperforms CPLEX MIP solver, as well as three other recent most successful MIP solution methods.

Benchmarking and Evaluating MATLAB Derivative-Free Optimisers for Single-Objective Applications

MATLAB® builds in a number of derivative-free optimisers (DFOs), conveniently providing tools beyond conventional optimisation means. However, with the increase of available DFOs and being compounded by the fact that DFOs are often problem dependent and parameter sensitive, it has become challenging to determine which one would be most suited to the application at hand, but there exist no comparisons on MATLAB DFOs so far. In order to help engineers use MATLAB for their applications without needing to learn DFOs in detail, this paper evaluates the performance of all seven DFOs in MATLAB and sets out an amalgamated benchmark of multiple benchmarks. The DFOs include four heuristic algorithms - simulated annealing, particle swarm optimization (PSO), the genetic algorithm (GA), and the genetic algorithm with elitism (GAe), and three direct-search algorithms - Nelder-Mead’s simplex search, pattern search (PS) and Powell’s conjugate search. The five benchmarks presented in this paper exceed those that have been reported in the literature. Four benchmark problems widely adopted in assessing evolutionary algorithms are employed. Under MATLAB’s default settings, it is found that the numerical optimisers Powell is the aggregative best on the unimodal Quadratic Problem, PSO on the lower dimensional Scaffer Problem, PS on the lower dimensional Composition Problem, while the extra-numerical genotype GAe is the best on the Varying Landscape Problem and on the other two higher dimensional problems. Overall, the GAe offers the highest performance, followed by PSO and Powell. The amalgamated benchmark quantifies the advantage and robustness of heuristic and population-based optimisers (GAe and PSO), especially on multimodal problems.

Combinatorial Formulation Guided Local Search for Inland Waterway Routing and Scheduling

We investigate the optimization of inland transport routes of barge container ships with the objective to maximize the profit of a shipping company. This problem consists of determining the upstream and downstream calling sequence and the number of loaded and empty containers transported between any two ports. We present Combinatorial as well as Mixed Integer Linear Programming (MILP) formulation for this problem. We propose to combine these two approaches with an aim to generate efficient heuristic to solve considered problem. The proposed mixed-formulation Local Search (MIX-LS) represents good basis for implementation of LS-based meta-heuristic methods and we presented Multi-start Local Search (MLS) within this framework. To compare the proposed approach with the state-ofthe-art Mixed Integer Programming (MIP) based heuristics we run all methods within a predefined time limit. It appears that pure local search is comparable with the MIPbased heuristic methods, while MLS outperforms all methods regarding both criteria: solution quality and running time.