John H. Drake

An improved choice function heuristic selection for cross domain heuristic search

Hyper-heuristics are a class of high-level search technologies to solve computationally difficult problems which operate on a search space of low-level heuristics rather than solutions directly. A iterative selection hyper-heuristic framework based on single-point search relies on two key components, a heuristic selection method and a move acceptance criteria. The Choice Function is an elegant heuristic selection method which scores heuristics based on a combination of three different measures and applies the heuristic with the highest rank at each given step. Each measure is weighted appropriately to provide balance between intensification and diversification during the heuristic search process. Choosing the right parameter values to weight these measures is not a trivial process and a small number of methods have been proposed in the literature. In this study we describe a new method, inspired by reinforcement learning, which controls these parameters automatically. The proposed method is tested and compared to previous approaches over a standard benchmark across six problem domains.

Generation of VNS components with grammatical evolution for vehicle routing

The vehicle routing problem (VRP) is a family of problems whereby a fleet of vehicles must service the commodity demands of a set of geographically scattered customers from one or more depots, subject to a number of constraints. Early hyper-heuristic research focussed on selecting and applying a low-level heuristic at a given stage of an optimisation process. Recent trends have led to a number of approaches being developed to automatically generate heuristics for a number of combinatorial optimisation problems. Previous work on the VRP has shown that the application of hyper-heuristic approaches can yield successful results. In this paper we investigate the potential of grammatical evolution as a method to evolve the components of a variable neighbourhood search (VNS) framework. In particular two components are generated; constructive heuristics to create initial solutions and neighbourhood move operators to change the state of a given solution. The proposed method is tested on standard benchmark instances of two common VRP variants.

A genetic programming hyper-heuristic for the multidimensional knapsack problem

Purpose – Hyper-heuristics are a class of high-level search techniques which operate on a search space of heuristics rather than directly on a search space of solutions. The purpose of this paper is to investigate the suitability of using genetic programming as a hyper-heuristic methodology to generate constructive heuristics to solve the multidimensional 0-1 knapsack problem Design/methodology/approach – Early hyper-heuristics focused on selecting and applying a low-level heuristic at each stage of a search. Recent trends in hyper-heuristic research have led to a number of approaches being developed to automatically generate new heuristics from a set of heuristic components. A population of heuristics to rank knapsack items are trained on a subset of test problems and then applied to unseen instances. Findings – The results over a set of standard benchmarks show that genetic programming can be used to generate constructive heuristics which yield human-competitive results. Originality/value – In this work...

Late acceptance-based selection hyper-heuristics for cross-domain heuristic search

Hyper-heuristics are high-level search methodologies used to find solutions to difficult real-world optimisation problems. Hyper-heuristics differ from many traditional optimisation techniques as they operate on a search space of low-level heuristics, rather than directly on a search space of potential solutions. A traditional iterative selection hyper-heuristic relies on two core components, a method for selecting a heuristic to apply at a given point and a method to decide whether or not to accept the result of the heuristic application. Raising the level of generality at which search methods operate is a key goal in hyper-heuristic research. Many existing selection hyper-heuristics make use of complex acceptance criteria which require problem specific expertise in controlling the various parameters. Such hyper-heuristics are often not general enough to be successful in a variety of problem domains. Late Acceptance is a simple yet powerful local search method which has only a single parameter to control. The contributions of this paper are twofold. Firstly, we will test the effect of the set of low-level heuristics on the performance of a simple stochastic selection mechanism within a Late Acceptance hyper-heuristic framework. Secondly, we will introduce a new class of heuristic selection methods based on roulette wheel selection and combine them with Late Acceptance acceptance criteria. The performance of these hyper-heuristics will be compared to a number of methods from the literature over six benchmark problem domains.

A case study of controlling crossover in a selection hyper-heuristic framework using the multidimensional knapsack problem

Hyper-heuristics are high-level methodologies for solving complex problems that operate on a search space of heuristics. In a selection hyper-heuristic framework, a heuristic is chosen from an existing set of low-level heuristics and applied to the current solution to produce a new solution at each point in the search. The use of crossover low-level heuristics is possible in an increasing number of general-purpose hyper-heuristic tools such as HyFlex and Hyperion. However, little work has been undertaken to assess how best to utilise it. Since a single-point search hyper-heuristic operates on a single candidate solution, and two candidate solutions are required for crossover, a mechanism is required to control the choice of the other solution. The frameworks we propose maintain a list of potential solutions for use in crossover. We investigate the use of such lists at two conceptual levels. First, crossover is controlled at the hyper-heuristic level where no problem-specific information is required. Second, it is controlled at the problem domain level where problem-specific information is used to produce good-quality solutions to use in crossover. A number of selection hyper-heuristics are compared using these frameworks over three benchmark libraries with varying properties for an NP-hard optimisation problem: the multidimensional 0-1 knapsack problem. It is shown that allowing crossover to be managed at the domain level outperforms managing crossover at the hyper-heuristic level in this problem domain.

Bidirectional best-fit heuristic considering compound placement for two dimensional orthogonal rectangular strip packing

The two dimensional orthogonal rectangular strip packing problem is a common NP-hard optimisation problem whereby a set of rectangular shapes must be placed on a fixed width stock sheet with infinite length in such a way that wastage is minimised and material utilisation is maximised. The bidirectional best-fit heuristic is a deterministic approach which has previously been shown to outperform existing heuristic methods as well as many metaheuristics from the literature. Here, we propose a modification to the original bidirectional best-fit heuristic whereby combinations of pairs of rectangles are considered generating improved results over standard benchmark sets.

Modified choice function heuristic selection for the multidimensional knapsack problem

Hyper-heuristics are a class of high-level search methods used to solve computationally difficult problems, which operate on a search space of low-level heuristics rather than solutions directly. Previous work has shown that selection hyper-heuristics are able to solve many combinatorial optimisation problems, including the multidimensional 0-1 knapsack problem (MKP). The traditional framework for iterative selection hyper-heuristics relies on two key components, a heuristic selection method and a move acceptance criterion. Existing work has shown that a hyper-heuristic using Modified Choice Function heuristic selection can be effective at solving problems in multiple problem domains. Late Acceptance Strategy is a hill climbing metaheuristic strategy often used as a move acceptance criteria in selection hyper-heuristics. This work compares a Modified Choice Function - Late Acceptance Strategy hyper-heuristic to an existing selection hyper-heuristic method from the literature which has previously performed well on standard MKP benchmarks.

A Modified Choice Function hyper-heuristic controlling unary and binary operators

Hyper-heuristics are a class of high-level search methodologies which operate on a search space of low-level heuristics or components, rather than on solutions directly. Traditional iterative selection hyper-heuristics rely on two key components, a heuristic selection method and a move acceptance criterion. Choice Function heuristic selection scores heuristics based on a combination of three measures, selecting the heuristic with the highest score. Modified Choice Function heuristic selection is a variant of the Choice Function which emphasises intensification over diversification within the heuristic search process. Previous work has shown that improved results are possible in some problem domains when using Modified Choice Function heuristic selection over the classic Choice Function, however in most of these cases crossover low-level heuristics (operators) are omitted. In this paper, we introduce crossover low-level heuristics into a Modified Choice Function selection hyper-heuristic and present results over six problem domains. It is observed that although on average there is an increase in performance when using crossover low-level heuristics, the benefit of using crossover can vary on a per-domain or per-instance basis.

A Comparison of Acceptance Criteria for the Daily Car-Pooling Problem

Previous work on the Daily Car-Pooling problem includes an algorithm that consists of greedy assignment alternating with random perturbation. In this study, we examine the effect of varying the move acceptance policy, specifically Late-acceptance criteria with and without reheating. Late acceptance-based move acceptance criteria were chosen because there is strong empirical evidence in the literature indicating their superiority. Late-acceptance compares the objective values of the current solution with one which was obtained at a fixed number of steps prior to the current step during the search process in order to make an acceptance decision. We observe that the Late-acceptance criteria also achieve superior results in over 75 % of cases for the Daily Car-Pooling problem, the majority of these results being statistically significant.

Two Frameworks for Cross-Domain Heuristic and Parameter Selection Using Harmony Search

Harmony Search is a metaheuristic technique for optimizing problems involving sets of continuous or discrete variables, inspired by musicians searching for harmony between instruments in a performance. Here we investigate two frameworks, using Harmony Search to select a mixture of continuous and discrete variables forming the components of a Memetic Algorithm for cross-domain heuristic search. The first is a single-point based framework which maintains a single solution, updating the harmony memory based on performance from a fixed starting position. The second is a population-based method which co-evolves a set of solutions to a problem alongside a set of harmony vectors. This work examines the behaviour of each framework over thirty problem instances taken from six different, real-world problem domains. The results suggest that population co-evolution performs better in a time-constrained scenario, however both approaches are ultimately constrained by the underlying metaphors.