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 di±cult 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

Exploiting the Power of mip Solvers in maxsat

Abstract. maxsat is an optimization version of satisfiability. Since many practical problems involve optimization, there are a wide range of potential applications for effective maxsat solvers. In this paper we present an extensive empirical evaluation of a number of maxsat solvers. In addition to traditional maxsat solvers, we also evaluate the use of a state-of-the-art Mixed Integer Program (mip) solver, cplex, for solving maxsat. mip solvers are the most popular technology for solving opti-mization problems and are also theoretically more powerful than sat solvers. In fact, we show that cplex is quite effective on a range of maxsat instances. Based on these observations we extend a previously developed hybrid approach for solving maxsat, that utilizes both a sat solver and a mip solver. Our extensions aim to take better advantage of the power of the mip solver. The resulting improved hybrid solver is shown to be quite effective.

An (MI)LP-based Primal Heuristic for 3-Architecture Connected Facility Location in Urban Access Network Design

We investigate the 3-architecture Connected Facility Location Problem arising in the design of urban telecommunication access networks. We propose an original optimization model for the problem that includes additional variables and constraints to take into account wireless signal coverage. Since the problem can prove challenging even for modern state-of-the art optimization solvers, we propose to solve it by an original primal heuristic which combines a probabilistic fixing procedure, guided by peculiar Linear Programming relaxations, with an exact MIP heuristic, based on a very large neighborhood search. Computational experiments on a set of realistic instances show that our heuristic can find solutions associated with much lower optimality gaps than a state-of-the-art solver.Comment: This is the authors' final version of the paper published in: Squillero G., Burelli P. (eds), EvoApplications 2016: Applications of Evolutionary Computation, LNCS 9597, pp. 283-298, 2016. DOI: 10.1007/978-3-319-31204-0_19. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-31204-0_1

Towards the fast and robust optimal design of Wireless Body Area Networks

Wireless body area networks are wireless sensor networks whose adoption has recently emerged and spread in important healthcare applications, such as the remote monitoring of health conditions of patients. A major issue associated with the deployment of such networks is represented by energy consumption: in general, the batteries of the sensors cannot be easily replaced and recharged, so containing the usage of energy by a rational design of the network and of the routing is crucial. Another issue is represented by traffic uncertainty: body sensors may produce data at a variable rate that is not exactly known in advance, for example because the generation of data is event-driven. Neglecting traffic uncertainty may lead to wrong design and routing decisions, which may compromise the functionality of the network and have very bad effects on the health of the patients. In order to address these issues, in this work we propose the first robust optimization model for jointly optimizing the topology and the routing in body area networks under traffic uncertainty. Since the problem may result challenging even for a state-of-the-art optimization solver, we propose an original optimization algorithm that exploits suitable linear relaxations to guide a randomized fixing of the variables, supported by an exact large variable neighborhood search. Experiments on realistic instances indicate that our algorithm performs better than a state-of-the-art solver, fast producing solutions associated with improved optimality gaps.Comment: Authors' manuscript version of the paper that was published in Applied Soft Computin

Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition

In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer formulation, we derive its linear counterparts and show that they could be stronger than existing linear formulations. We also develop a variant of Jensen's inequality that extends the one for stochastic program. To solve this challenging problem, we present a variant of Benders decomposition method in bilinear form, which actually provides an easy-to-use algorithm framework for further improvements, along with a few enhancement strategies based on structural properties or Jensen's inequality. Computational study shows that the presented Benders decomposition method, jointly with appropriate enhancement techniques, outperforms a commercial solver by an order of magnitude on solving chance constrained program or detecting its infeasibility

On alternative mixed integer programming formulations and LP-based heuristics for lot-sizing with setup times

We address the multi-item, capacitated lot-sizing problem (CLSP) encountered in environments where demand is dynamic and to be met on time. Items compete for a limited capacity resource, which requires a setup for each lot of items to be produced causing unproductive time but no direct costs. The problem belongs to a class of problems that are difcult to solve. Even the feasibility problem becomes combinatorial when setup times are considered. This difculty in reaching optimality and the practical relevance of CLSP make it important to design and analyse heuristics to nd good solutions that can be implemented in practice. We consider certain mixed integer programming formulations of the problem and develop heuristics including a curtailed branch and bound, for rounding the setup variables in the LP solution of the tighter formulations. We report our computational results for a class of instances taken from literature

Mixed integer programming in production planning with backlogging and setup carryover : modeling and algorithms

This paper proposes a mixed integer programming formulation for modeling the capacitated multi-level lot sizing problem with both backlogging and setup carryover. Based on the model formulation, a progressive time-oriented decomposition heuristic framework is then proposed, where improvement and construction heuristics are effectively combined, therefore efficiently avoiding the weaknesses associated with the one-time decisions made by other classical time-oriented decomposition algorithms. Computational results show that the proposed optimization framework provides competitive solutions within a reasonable time