Linking Search Space Structure, Run-Time Dynamics, and Problem Difficulty: A Step Toward Demystifying Tabu Search

Abstract

Tabu search is one of the most effective heuristics for locating high-quality solutions to a diverse array of NP-hard combinatorial optimization problems. Despite the widespread success of tabu search, researchers have a poor understanding of many key theoretical aspects of this algorithm, including models of the high-level run-time dynamics and identification of those search space features that influence problem difficulty. We consider these questions in the context of the job-shop scheduling problem (JSP), a domain where tabu search algorithms have been shown to be remarkably effective. Previously, we demonstrated that the mean distance between random local optima and the nearest optimal solution is highly correlated with problem difficulty for a well-known tabu search algorithm for the JSP introduced by Taillard. In this paper, we discuss various shortcomings of this measure and develop a new model of problem difficulty that corrects these deficiencies. We show that Taillard's algorithm can be modeled with high fidelity as a simple variant of a straightforward random walk. The random walk model accounts for nearly all of the variability in the cost required to locate both optimal and sub-optimal solutions to random JSPs, and provides an explanation for differences in the difficulty of random versus structured JSPs. Finally, we discuss and empirically substantiate two novel predictions regarding tabu search algorithm behavior. First, the method for constructing the initial solution is highly unlikely to impact the performance of tabu search. Second, tabu tenure should be selected to be as small as possible while simultaneously avoiding search stagnation; values larger than necessary lead to significant degradations in performance.

Data-driven local optima network characterization of QAPLIB instances

“…The amount of instance hardness variability explained by these LON models is very high by static cost model standards [31], being up to 85%.…”

“…In the present work about QAP, Taillard's Robust Tabu Search (RoTS) [24] is a natural candidate, as its results are still state-of-the art on some problem instances. Moreover, even if Tabu Search appears to effectively restrict its search around local optima and close-by solutions [31], its search dynamics are not explicitly bounded to kick-moves and LON structure as in the Iterated Local Search case. For this reason also, the RoTS is a good choice to test the relevance of the LON study.…”

New hard benchmark for flowshop scheduling problems minimising makespan

“…However, and as pointed out in Reeves (2007), the fitness landscape is not an invariant of the problem instance, i.e., it depends on the algorithm that is being used in the optimisation. For example, Watson et al (2005) study the search space topology linked to taboo search algorithms for the job shop problem. Marmion et al (2011b) study the concept of neutrality of the flowshop fitness landscape.…”

A hybrid MIP-based large neighborhood search heuristic for solving the machine reassignment problem

“…We can hypothesize that combining ideas of the three algorithms in the instance-specific approach may outperform these algorithms applied separately. Taking one step further would include conducting a fitness landscape analysis (Watson et al 2005), which could shed new light on the search space characteristics that make certain instances particularly hard to solve. This could potentially explain the differences in algorithm performances and help design more robust approaches.…”