An analysis of heuristic subsequences for offline hyper-heuristic learning

Abstract

A selection hyper-heuristic is used to minimise the objective functions of a wellknown set of benchmark problems. The resulting sequences of low level heuristic selections and objective function values are used to generate a database of heuristic selections. The sequences in the database are broken down into subsequences and the mathematical concept of a logarithmic return is used to discriminate between "effective" subsequences, which tend to decrease the objective value, and "disruptive" subsequences, which tend to increase the objective value. These subsequences are then employed in a sequenced based hyper-heuristic and evaluated on an unseen set of benchmark problems. Empirical results demonstrate that the "effective" subsequences perform significantly better than the "disruptive" subsequences across a number of problem domains with 99% confidence. The identification of subsequences of heuristic selections that can be shown to be effective across a number of problems or problem domains could have important implications for the design of future sequence based hyper-heuristics.

A Methodology to Determine the Subset of Heuristics for Hyperheuristics through Metalearning for Solving Graph Coloring and Capacitated Vehicle Routing Problems

“…We focused on offline learning hyperheuristics selection with perturbation heuristics, whose aim is to gather knowledge in the form of rules or programs, from training set instances. Usually, the offline selection hyperheuristics belong to machine learning methods, which are trained to create a tuned methodology for a problem domain [3]. Yates and Keedwell [19] demonstrated that subsequences of heuristics were found in the offline learning database that is effective for some problem domains.…”

“…Hyperheuristics can be classified according to their learning methods, such as no learning, online learning [2], and offline learning [3]. In the context of combinatorial optimization, hyperheuristics are defined as "heuristics to choose heuristics" [4], or as "an automated methodology for selecting or generation heuristics to solve computational search problems," [4].…”

“…According to Pillay in [2], the generality of a hyperheuristic can be seen from three levels: a generalization on instances of problems, generalization for a particular problem, and a generalization focused on different types of problems, the latter being high level. Some variations of hyperheuristics depend on the type of learning used (e.g., with online learning [2] and offline learning [3]) or the nature of the heuristics.…”

Analysing heuristic subsequences for offline hyper-heuristic learning

“…The number and implementation of the low level heuristics in each class differs between problem domains (see table 1). part of a sequence (or subsequence) of selections [5]. This study presents a novel statistical framework for the analysis of subsequences of heuristics based on the concept of logarithmic returns.…”

“…The paper [5] explores the impact of sequences of search operations on the performance of an optimiser through the use of log returns and a database of sequences. The study demonstrates that although the performance of individual perturbation operators is important, understanding their performance in sequence provides greater opportunity for performance improvements within and across operations research domains.…”