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The feasibility pump algorithm is an efficient primal heuristic for findingfeasible solutions to mixed-integer programming problems. The algorithm suffersmainly from fast convergence to local optima. In this paper, we investigate theeffect of an alternative approach to circumvent this challenge by designing atwo-stage approach that embeds the feasibility pump heuristic into an annealingframework. The algorithm dynamically breaks the discrete decision variablesinto two subsets based on the fractionality information obtained from priorruns, and enforces integrality on each subset separately. The feasibility pumpalgorithm iterates between rounding a fractional solution to one that isintegral and projecting an infeasible integral solution onto the solution spaceof the relaxed mixed-integer programming problem. These two components are usedin a Monte Carlo search framework to initially promote diversification andfocus on intensification later. The computational results obtained from solving91 mixed-binary problems demonstrate the superiority of our new approach overFeasibility Pump 2.0.

A feasibility pump algorithm embedded in an annealing framework