Hybrid Variants for Iterative Flattening Search

Abstract

Iterative Flattening Search (IFS) [1] is an iterative improvement heuristic schema for makespan minimization in scheduling problems. Given an initial solution, IFS iteratively interleaves a relaxation-step, which randomly retracts some search decisions, and an incremental solving step (or flattening-step) to recompute a new solution. The process continues until a stop condition is met and the best solution found is returned. In two subsequent works the performance of the original IFS procedure has been improved through refinements of the basic search schema. [2] proposes a simple and effective extension of IFS, which iterates the relaxation step multiple times. The resulting algorithm found many new upper bounds for the reference benchmark of Multi Capacity Job Shop Scheduling (mcjssp) problems and produced solutions within 1% of the best upper bounds on average. Additional optimal solutions and improvements were obtained in [3]: this approach follows the IFS schema using different engines for the flattening and relaxation steps. In this paper we combine basic ‘component’ strategies to obtain hybrid variants (until now, no attempt has been made in this direction) and perform a detailed experimental evaluation of their performance. Specifically, we examine the utility of: (1) operating with different relaxation strategies; (2) using different searching strategies to built a new solution. We present a two-step experimental evaluation: (a) an extensive explorative evaluation with a spectrum of parameter combination; (b) a time-intensive evaluation of the best IFS combinations emerged from the previous. The experimental results shed light on weaknesses and strengths of the different variants improving the current understanding of this family of meta-heuristics.