A generation perturbative hyper-heuristic for combinatorial optimization problems

Dissertation (MSc (Computer Science))--University of Pretoria, 2020.Perturbative heuristics or move operators are problem dependent operators commonly used by search techniques to solve computationally hard problems such as combinatorial optimization problems. These operators are generally derived manually by problem domain experts but this process is extremely challenging and time consuming. Hence, some initiatives aimed at automating the derivation process using search methodologies such as hyper-heuristics have been proposed in recent years. However, most of the proposed hyper-heuristic approaches generate new perturbative heuristics by recombining already existing and human-derived perturbative heuristics or components with various move acceptance criteria instead of generating the heuristics from scratch. As a result, these approaches cannot be easily applied to other problem domains where the human-derived heuristics are not available. In addition, the few hyper-heuristic approaches that have been proposed to generate perturbative heuristics from scratch are either designed for a single problem domain or applicable only to specific types of problems such as those that can be represented as graphs. The research presented in this dissertation addresses these issues by proposing a novel approach that can be used to automatically generate perturbative heuristics for any combinatorial optimization problem. In the proposed approach, perturbative heuristics are defined in terms of a set of basic operations (e.g. move and swap) and components of the solution (e.g. exam, period and room for the examination timetabling problem). Grammatical evolution, a well-known Evolutionary Algorithm, is used to combine the basic operations and components of the solution into perturbative heuristics. The generality of the proposed approach is tested by applying it to benchmark sets from three different problem domains, namely examination timetabling, vehicle routing and Boolean satisfiability. In addition, the performance of the perturbative heuristics generated by the proposed approach on the benchmark sets is compared to that of the commonly-used human-derived perturbative heuristics as well as the perturbative heuristics generated by other hyper-heuristic approaches in the literature. The experimental results show that the perturbative heuristics evolved by the proposed approach, specifically the grammatical evolution extended approach, outperformed the human-derived perturbative heuristics on all benchmark sets from the three problem domains. When compared to existing hyper-heuristic approaches, the proposed approach obtained solutions that were superior to those obtained by most hyper-heuristic approaches on the examination timetabling problem and only slightly inferior to those obtained by the best performing hyper-heuristic approaches on the vehicle routing and Boolean satisfiability problems. This performance of the proposed approach can be attributed to the fact that the generated perturbative heuristics were applied as is with no optimization as is commonly done with most hyper-heuristic approaches. Overall, the experimental results demonstrated success in developing an approach that can be used to automatically generate perturbative heuristics from scratch. Future work will consider incorporating optimization techniques during problem solving as well as performing a fitness landscape analysis in order to further improve the quality of solutions and have a better understanding of the proposed approach.SELF/ NRF MastersComputer ScienceMSc (Computer Science)Unrestricte

The automatic design of hyper-heuristic framework with gene expression programming for combinatorial optimization problems

Hyper-heuristic approaches aim to automate heuristic design in order to solve multiple problems instead of designing tailor-made methodologies for individual problems. Hyper-heuristics accomplish this through a high level heuristic (heuristic selection mechanism and an acceptance criterion). This automates heuristic selection, deciding whether to accept or reject the returned solution. The fact that different problems or even instances, have different landscape structures and complexity, the design of efficient high level heuristics can have a dramatic impact on hyper-heuristic performance. In this work, instead of using human knowledge to design the high level heuristic, we propose a gene expression programming algorithm to automatically generate, during the instance solving process, the high level heuristic of the hyper-heuristic framework. The generated heuristic takes information (such as the quality of the generated solution and the improvement made) from the current problem state as input and decides which low level heuristic should be selected and the acceptance or rejection of the resultant solution. The benefit of this framework is the ability to generate, for each instance, different high level heuristics during the problem solving process. Furthermore, in order to maintain solution diversity, we utilize a memory mechanism which contains a population of both high quality and diverse solutions that is updated during the problem solving process. The generality of the proposed hyper-heuristic is validated against six well known combinatorial optimization problem, with very different landscapes, provided by the HyFlex software. Empirical results comparing the proposed hyper-heuristic with state of the art hyper-heuristics, conclude that the proposed hyper-heuristic generalizes well across all domains and achieves competitive, if not superior, results for several instances on all domains

Grammatical evolution hyper-heuristic for combinatorial optimization problems

Designing generic problem solvers that perform well across a diverse set of problems is a challenging task. In this work, we propose a hyper-heuristic framework to automatically generate an effective and generic solution method by utilizing grammatical evolution. In the proposed framework, grammatical evolution is used as an online solver builder, which takes several heuristic components (e.g., different acceptance criteria and different neighborhood structures) as inputs and evolves templates of perturbation heuristics. The evolved templates are improvement heuristics, which represent a complete search method to solve the problem at hand. To test the generality and the performance of the proposed method, we consider two well-known combinatorial optimization problems: exam timetabling (Carter and ITC 2007 instances) and the capacitated vehicle routing problem (Christofides and Golden instances). We demonstrate that the proposed method is competitive, if not superior, when compared to state-of-the-art hyper-heuristics, as well as bespoke methods for these different problem domains. In order to further improve the performance of the proposed framework we utilize an adaptive memory mechanism, which contains a collection of both high quality and diverse solutions and is updated during the problem solving process. Experimental results show that the grammatical evolution hyper-heuristic, with an adaptive memory, performs better than the grammatical evolution hyper-heuristic without a memory. The improved framework also outperforms some bespoke methodologies, which have reported best known results for some instances in both problem domains

Assessing hyper-heuristic performance

Limited attention has been paid to assessing the generality performance of hyper-heuristics. The performance of hyper-heuristics has been predominately assessed in terms of optimality which is not ideal as the aim of hyper-heuristics is not to be competitive with state of the art approaches but rather to raise the level of generality, i.e. the ability of a technique to produce good results for different problem instances or problems rather than the best results for some instances and poor results for others. Furthermore from existing literature in this area it is evident that different hyper-heuristics aim to achieve different levels of generality and need to be assessed as such. To cater for this the paper firstly presents a new taxonomy of four different levels of generality that can be attained by a hyper-heuristic based on a survey of the literature. The paper then proposes a performance measure to assess the performance of different types of hyper-heuristics at the four levels of generality in terms of generality rather than optimality. Three case studies from the literature are used to demonstrate the application of the generality performance measure. The paper concludes by examining how the generality measure can be combined with measures of other performance criteria, such as optimality, to assess hyper-heuristic performance on more than one criterion

Hyper‐Heuristics and Metaheuristics for Selected Bio‐Inspired Combinatorial Optimization Problems

Many decision and optimization problems arising in bioinformatics field are time demanding, and several algorithms are designed to solve these problems or to improve their current best solution approach. Modeling and implementing a new heuristic algorithm may be time‐consuming but has strong motivations: on the one hand, even a small improvement of the new solution may be worth the long time spent on the construction of a new method; on the other hand, there are problems for which good‐enough solutions are acceptable which could be achieved at a much lower computational cost. In the first case, specially designed heuristics or metaheuristics are needed, while the latter hyper‐heuristics can be proposed. The paper will describe both approaches in different domain problems

Evolved parameterized selection for evolutionary algorithms

Selection functions enable Evolutionary Algorithms (EAs) to apply selection pressure to a population of individuals, by regulating the probability that an individual\u27s genes survive, typically based on fitness. Various conventional fitness based selection functions exist, each providing a unique method of selecting individuals based on their fitness, fitness ranking within the population, and/or various other factors. However, the full space of selection algorithms is only limited by max algorithm size, and each possible selection algorithm is optimal for some EA configuration applied to a particular problem class. Therefore, improved performance is likely to be obtained by tuning an EA\u27s selection algorithm to the problem at hand, rather than employing a conventional selection function. This thesis details an investigation of the extent to which performance can be improved by tuning the selection algorithm. We do this by employing a Hyper-heuristic to explore the space of algorithms which determine the methods used to select individuals from the population. We show, with both a conventional EA and a Covariance Matrix Adaptation Evolutionary Strategy, the increase in performance obtained with a tuned selection algorithm, versus conventional selection functions. Specifically, we measure performance on instances from several benchmark problem classes, including separate testing instances to show generalization of the improved performance. This thesis consists of work that was presented at the Genetic and Evolutionary Computation Conference (GECCO) in 2018, as well as work that will be submitted to GECCO in 2019 --Abstract, page iii

A dynamic multiarmed bandit-gene expression programming hyper-heuristic for combinatorial optimization problems

Hyper-heuristics are search methodologies that aim to provide high-quality solutions across a wide variety of problem domains, rather than developing tailor-made methodologies for each problem instance/domain. A traditional hyper-heuristic framework has two levels, namely, the high level strategy (heuristic selection mechanism and the acceptance criterion) and low level heuristics (a set of problem specific heuristics). Due to the different landscape structures of different problem instances, the high level strategy plays an important role in the design of a hyper-heuristic framework. In this paper, we propose a new high level strategy for a hyper-heuristic framework. The proposed high-level strategy utilizes a dynamic multiarmed bandit-extreme value-based reward as an online heuristic selection mechanism to select the appropriate heuristic to be applied at each iteration. In addition, we propose a gene expression programming framework to automatically generate the acceptance criterion for each problem instance, instead of using human-designed criteria. Two well-known, and very different, combinatorial optimization problems, one static (exam timetabling) and one dynamic (dynamic vehicle routing) are used to demonstrate the generality of the proposed framework. Compared with state-of-the-art hyper-heuristics and other bespoke methods, empirical results demonstrate that the proposed framework is able to generalize well across both domains. We obtain competitive, if not better results, when compared to the best known results obtained from other methods that have been presented in the scientific literature. We also compare our approach against the recently released hyper-heuristic competition test suite. We again demonstrate the generality of our approach when we compare against other methods that have utilized the same six benchmark datasets from this test suite

A study of evoluntionary perturbative hyper-heuristics for the nurse rostering problem.

Master of Science in Computer Science. University of KwaZulu-Natal, Pietermaritzburg 2017.Hyper-heuristics are an emerging field of study for combinatorial optimization. The aim of a hyper-heuristic is to produce good results across a set of problems rather than producing the best results. There has been little investigation of hyper-heuristics for the nurse rostering problem. The majority of hyper-heuristics for the nurse rostering problem fit into a single type of hyper-heuristic, the selection perturbative hyper-heuristic. There is no work in using evolutionary algorithms employed as selection perturbative hyper-heuristics for the nurse rostering problem. There is also no work in using the generative perturbative type of hyper-heuristic for the nurse rostering problem. The first objective of this dissertation is to investigate the selection perturbative hyper-heuristic for the nurse rostering problem and the effectiveness of employing an evolutionary algorithm (SPHH). The second objective is to investigate a generative perturbative hyper-heuristic to evolve perturbation heuristics for the nurse rostering problem using genetic programming (GPHH). The third objective is to compare the performance of SPHH and GPHH. SPHH and GPHH were evaluated using the INRC2010 benchmark data set and the results obtained were compared to available results from literature. The INRC2010 benchmark set is comprised of sprint, medium and long instance types. SPHH and GPHH produced good results for the INRC2010 benchmark data set. GPHH and SPHH were found to have different strengths and weaknesses. SPHH found better results than GPHH for the medium instances. GPHH found better results than SPHH for the long instances. SPHH produced better average results. GPHH produced results that were closer to the best known results. These results suggest future research should investigate combining SPHH and GPHH to benefit from the strengths of both perturbative hyper-heuristics

The Automated Design of Probabilistic Selection Methods for Evolutionary Algorithms

Selection functions enable Evolutionary Algorithms (EAs) to apply selection pressure to a population of individuals, by regulating the probability that an individual\u27s genes survive, typically based on fitness. Various conventional fitness based selection methods exist, each providing a unique relationship between the fitnesses of individuals in a population and their chances of selection. However, the full space of selection algorithms is only limited by max algorithm size, and each possible selection algorithm is optimal for some EA configuration applied to a particular problem class. Therefore, improved performance may be expected by tuning an EA\u27s selection algorithm to the problem at hand, rather than employing a conventional selection method. The objective of this paper is to investigate the extent to which performance can be improved by tuning selection algorithms, employing a Hyper-heuristic to explore the space of search algorithms which encode the relationships between the fitnesses of individuals and their probability of selection. We show the improved performance obtained versus conventional selection functions on fixed instances from a benchmark problem class, including separate testing instances to show generalization of the improved performance