# A feasibility pump algorithm embedded in an annealing framework

## TL;DR

This paper introduces an innovative two-stage annealing framework embedding the feasibility pump heuristic to improve solution quality and avoid local optima in mixed-integer programming problems.

## Contribution

It proposes a novel annealing-based approach that dynamically partitions variables and combines diversification and intensification for better feasibility solutions.

## Key findings

- Outperforms Feasibility Pump 2.0 on 91 mixed-binary problems.
- Enhances convergence to feasible solutions by avoiding local optima.
- Demonstrates the effectiveness of the annealing framework in mixed-integer programming.

## Abstract

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.