Accelerating Benders method using covering cut bundle generation

TLDR

Various techniques have been proposed to accelerate the classical Benders decomposition algorithm, mainly by reducing iterations or restricting the solution space. This article proposes a new strategy for Benders algorithm and applies it to two case studies to evaluate its efficiency. The strategy, called covering cut bundle (CCB) generation, implements multiple constraints generation in a novel way for mixed‑integer problems in crude‑oil scheduling and multi‑product batch plant scheduling. In both case studies, CCB significantly reduces Benders iterations and improves resolution times.

Abstract

Abstract Over the years, various techniques have been proposed to speed up the classical Benders decomposition algorithm. The work presented in the literature has focused mainly on either reducing the number of iterations of the algorithm or on restricting the solution space of the decomposed problems. In this article, a new strategy for Benders algorithm is proposed and applied to two case studies in order to evaluate its efficiency. This strategy, referred to as covering cut bundle (CCB) generation, is shown to implement in a novel way the multiple constraints generation idea. The CCB generation is applied to mixed integer problems arising from two types of applications: the scheduling of crude oil and the scheduling problem for multi‐product, multi‐purpose batch plants. In both cases, CCB significantly decreases the number of iterations of the Benders method, leading to improved resolution times.