Heuristics with Performance Guarantees for the Minimum Number of Matches Problem in Heat Recovery Network Design

TL;DR

This paper introduces heuristic algorithms with performance guarantees for solving the NP-hard minimum number of matches problem in heat recovery network design, improving solution quality and computational efficiency.

Contribution

It develops new heuristic methods based on relaxation rounding, water filling, and greedy packing, with proven performance guarantees, for the first time in this context.

Findings

Heuristic methods outperform traditional approaches on benchmark instances.

The new formulation avoids big-M parameters, simplifying the problem.

Numerical results show significant improvements in solution quality.

Abstract

Heat exchanger network synthesis exploits excess heat by integrating process hot and cold streams and improves energy efficiency by reducing utility usage. Determining provably good solutions to the minimum number of matches is a bottleneck of designing a heat recovery network using the sequential method. This subproblem is an NP-hard mixed-integer linear program exhibiting combinatorial explosion in the possible hot and cold stream configurations. We explore this challenging optimization problem from a graph theoretic perspective and correlate it with other special optimization problems such as cost flow network and packing problems. In the case of a single temperature interval, we develop a new optimization formulation without problematic big-M parameters. We develop heuristic methods with performance guarantees using three approaches: (i) relaxation rounding, (ii) water filling, and (iii) greedy packing. Numerical results from a collection of 51 instances substantiate the strength of the methods.