A Feasibility Pump Algorithm Embedded in an Annealing Framework

By Nicolas Pradignac, Maliheh Aramon, & Helmut G. Katzgraber

The feasibility pump algorithm is an efficient primal heuristic for finding feasible solutions to mixed-integer programming problems. The algorithm suffers mainly from fast convergence to local optima. In this paper, we investigate the effect of an alternative approach to circumvent this challenge by designing a two-stage approach that embeds the feasibility pump heuristic into an annealing framework. The algorithm dynamically breaks the discrete decision variables into two subsets based on the fractionality information obtained from prior runs, and enforces integrality on each subset separately. The feasibility pump algorithm iterates between rounding a fractional solution to one that is integral and projecting an infeasible integral solution onto the solution space of the relaxed mixed-integer programming problem. These two components are used in a Monte Carlo search framework to initially promote diversification and focus on intensification later. The computational results obtained from solving 91 mixed-binary problems demonstrate the superiority of our new approach over Feasibility Pump 2.0.