Crossover control in selection hyper-heuristics: case studies using MKP and HyFlex

Hyper-heuristics are a class of high-level search methodologies which operate over a search space of heuristics rather than a search space of solutions. Hyper-heuristic research has set out to develop methods which are more general than traditional search and optimisation techniques. In recent years, focus has shifted considerably towards cross-domain heuristic search. The intention is to develop methods which are able to deliver an acceptable level of performance over a variety of different problem domains, given a set of low-level heuristics to work with. This thesis presents a body of work investigating the use of selection hyper-heuristics in a number of different problem domains. Specifically the use of crossover operators, prevalent in many evolutionary algorithms, is explored within the context of single-point search hyper-heuristics. A number of traditional selection hyper-heuristics are applied to instances of a well-known NP-hard combinatorial optimisation problem, the multidimensional knapsack problem. This domain is chosen as a benchmark for the variety of existing problem instances and solution methods available. The results suggest that selection hyper-heuristics are a viable method to solve some instances of this problem domain. Following this, a framework is defined to describe the conceptual level at which crossover low-level heuristics are managed in single-point selection hyper-heuristics. HyFlex is an existing software framework which supports the design of heuristic search methods over multiple problem domains, i.e. cross-domain optimisation. A traditional heuristic selection mechanism is modified in order to improve results in the context of cross-domain optimisation. Finally the effect of crossover use in cross-domain optimisation is explored

Sample Efficiency Matters: A Benchmark for Practical Molecular Optimization

Molecular optimization is a fundamental goal in the chemical sciences and is of central interest to drug and material design. In recent years, significant progress has been made in solving challenging problems across various aspects of computational molecular optimizations, emphasizing high validity, diversity, and, most recently, synthesizability. Despite this progress, many papers report results on trivial or self-designed tasks, bringing additional challenges to directly assessing the performance of new methods. Moreover, the sample efficiency of the optimization--the number of molecules evaluated by the oracle--is rarely discussed, despite being an essential consideration for realistic discovery applications. To fill this gap, we have created an open-source benchmark for practical molecular optimization, PMO, to facilitate the transparent and reproducible evaluation of algorithmic advances in molecular optimization. This paper thoroughly investigates the performance of 25 molecular design algorithms on 23 tasks with a particular focus on sample efficiency. Our results show that most "state-of-the-art" methods fail to outperform their predecessors under a limited oracle budget allowing 10K queries and that no existing algorithm can efficiently solve certain molecular optimization problems in this setting. We analyze the influence of the optimization algorithm choices, molecular assembly strategies, and oracle landscapes on the optimization performance to inform future algorithm development and benchmarking. PMO provides a standardized experimental setup to comprehensively evaluate and compare new molecule optimization methods with existing ones. All code can be found at https://github.com/wenhao-gao/mol_opt

An Investigation of Factors Influencing Algorithm Selection for High Dimensional Continuous Optimisation Problems

The problem of algorithm selection is of great importance to the optimisation community, with a number of publications present in the Body-of-Knowledge. This importance stems from the consequences of the No-Free-Lunch Theorem which states that there cannot exist a single algorithm capable of solving all possible problems. However, despite this importance, the algorithm selection problem has of yet failed to gain widespread attention . In particular, little to no work in this area has been carried out with a focus on large-scale optimisation; a field quickly gaining momentum in line with advancements and influence of big data processing. As such, it is not as yet clear as to what factors, if any, influence the selection of algorithms for very high-dimensional problems (> 1000) - and it is entirely possible that algorithms that may not work well in lower dimensions may in fact work well in much higher dimensional spaces and vice-versa. This work therefore aims to begin addressing this knowledge gap by investigating some of these influencing factors for some common metaheuristic variants. To this end, typical parameters native to several metaheuristic algorithms are firstly tuned using the state-of-the-art automatic parameter tuner, SMAC. Tuning produces separate parameter configurations of each metaheuristic for each of a set of continuous benchmark functions; specifically, for every algorithm-function pairing, configurations are found for each dimensionality of the function from a geometrically increasing scale (from 2 to 1500 dimensions). The nature of this tuning is therefore highly computationally expensive necessitating the use of SMAC. Using these sets of parameter configurations, a vast amount of performance data relating to the large-scale optimisation of our benchmark suite by each metaheuristic was subsequently generated. From the generated data and its analysis, several behaviours presented by the metaheuristics as applied to large-scale optimisation have been identified and discussed. Further, this thesis provides a concise review of the relevant literature for the consumption of other researchers looking to progress in this area in addition to the large volume of data produced, relevant to the large-scale optimisation of our benchmark suite by the applied set of common metaheuristics. All work presented in this thesis was funded by EPSRC grant: EP/J017515/1 through the DAASE project

Hyper-parameter Optimisation by Restrained Stochastic Hill Climbing

Abstract. Machine learning practitioners often refer to hyper-parameter optimisation (HPO) as an art form and a skill that requires intuition and experience; Neuroevolution (NE) typically employs a combination of manual and evolutionary approaches for HPO. This paper explores the integration of a stochastic hill climbing approach for HPO within a NE algorithm. We empirically show that HPO by restrained stochastic hill climbing (HORSHC) is more effective than manual and pure evolutionary HPO. Empirical evidence is derived from a comparison of: (1) a NE algorithm that solely optimises hyper-parameters through evolution and (2) a number of derived algorithms with random search optimisation integration for optimising the hyper-parameters of a Neural Network. Through statistical analysis of the experimental results it has been revealed that random initialisation of hyper-parameters does not significantly affect the final performance of the Neural Networks evolved. However, HORSHC, a novel optimisation approach proposed in this paper has been proven to significantly out-perform the NE control algorithm. HORSHC presents itself as a solution that is computationally comparable in terms of both time and complexity as well as outperforming the control algorithm

Crossover control in selection hyper-heuristics: case studies using MKP and HyFlex

Hyper-heuristics are a class of high-level search methodologies which operate over a search space of heuristics rather than a search space of solutions. Hyper-heuristic research has set out to develop methods which are more general than traditional search and optimisation techniques. In recent years, focus has shifted considerably towards cross-domain heuristic search. The intention is to develop methods which are able to deliver an acceptable level of performance over a variety of different problem domains, given a set of low-level heuristics to work with. This thesis presents a body of work investigating the use of selection hyper-heuristics in a number of different problem domains. Specifically the use of crossover operators, prevalent in many evolutionary algorithms, is explored within the context of single-point search hyper-heuristics. A number of traditional selection hyper-heuristics are applied to instances of a well-known NP-hard combinatorial optimisation problem, the multidimensional knapsack problem. This domain is chosen as a benchmark for the variety of existing problem instances and solution methods available. The results suggest that selection hyper-heuristics are a viable method to solve some instances of this problem domain. Following this, a framework is defined to describe the conceptual level at which crossover low-level heuristics are managed in single-point selection hyper-heuristics. HyFlex is an existing software framework which supports the design of heuristic search methods over multiple problem domains, i.e. cross-domain optimisation. A traditional heuristic selection mechanism is modified in order to improve results in the context of cross-domain optimisation. Finally the effect of crossover use in cross-domain optimisation is explored

Simple low cost causal discovery using mutual information and domain knowledge

PhDThis thesis examines causal discovery within datasets, in particular observational datasets where normal experimental manipulation is not possible. A number of machine learning techniques are examined in relation to their use of knowledge and the insights they can provide regarding the situation under study. Their use of prior knowledge and the causal knowledge produced by the learners are examined. Current causal learning algorithms are discussed in terms of their strengths and limitations. The main contribution of the thesis is a new causal learner LUMIN that operates with a polynomial time complexity in both the number of variables and records examined. It makes no prior assumptions about the form of the relationships and is capable of making extensive use of available domain information. This learner is compared to a number of current learning algorithms and it is shown to be competitive with them

An Autonomous Driver of a TORCS Racing Car

Tato práce popisuje simulátor TORCS a optimalizační algoritmy, jenž jsou využívány při tvorbě autonomních řidičů pro tento simulátor. Hlavním cílem je navržení nového autonomního řidiče, který se bude schopen s použitím přírodou inspirovaných optimalizačních technik vyrovnat již dříve navrženým řešením. Chování implementovaného řešení lze rozdělit do dvou hlavních částí, které jsou využívány v různých rozdílných etapách závodu. Zahřívací kolo je využito pro vytvoření modelu trati, ze kterého je posléze získána optimální trajektorie pomocí genetického algoritmu. Této trajektorie je potom využíváno v samotné kvalifikaci či závodě pro zajetí co nejrychlejšího kola. Z důvodu složitosti problému optimalizace celé trajektorie je nutno tuto trajektorii rozdělit na menší úseky nazývané segmenty, přičemž každý z nich je potom optimalizován odděleně. Jednotlivé optimalizované segmenty jsou následně spojeny dohromady, aby opět utvořily trajektorii pro celou trať. Protože některé přechody mezi segmenty mohou být nesouvislé, je zde znovu aplikován genetický algoritmus pro jejich vyhlazení. Během závodu je tato trajektorie následována, přičemž se z ní odvíjí i maximální možná rychlost v daném úseku. V práci jsme ukázali, že vzorkování trati s následnou optimalizací pomocí genetického algoritmu trvá pouze zlomek času vyhrazeného pro zahřívací kolo. Nejen díky tomuto se řešení jeví jako vhodné pro závody autonomních řidičů a může být dále rozšířeno.This work describes the TORCS simulator and optimization algorithms used in the field of autonomous driving competitions. The main purpose of this work is to design a new controller solution based on genetic algorithms. The controller's behavior can be divided into two main parts which are exploited during the distinct stages of the competition. The warm-up stage serves for the track model sampling and the race line optimization. The race stage logic then benefits from the data obtained in the warm-up stage. The track optimization is done by a Genetic algorithm while the track is divided into several segments optimized separately. A genetic algorithm is applied once again to the track trajectory to smooth out gaps caused by the segment composition. In this work was shown that the track sampling and race line optimization by a genetic algorithm can be done during the warm-up stage. This makes the controller suitable for an autonomous driver competitions.

Multi-stage hyper-heuristics for optimisation problems

There is a growing interest towards self configuring/tuning automated general-purpose reusable heuristic approaches for combinatorial optimisation, such as, hyper-heuristics. Hyper-heuristics are search methodologies which explore the space of heuristics rather than the solutions to solve a broad range of hard computational problems without requiring any expert intervention. There are two common types of hyper-heuristics in the literature: selection and generation methodologies. This work focuses on the former type of hyper-heuristics. Almost all selection hyper-heuristics perform a single point based iterative search over the space of heuristics by selecting and applying a suitable heuristic to the solution in hand at each decision point. Then the newly generated solution is either accepted or rejected using an acceptance method. This improvement process is repeated starting from an initial solution until a set of termination criteria is satisfied. The number of studies on the design of hyper-heuristic methodologies has been rapidly increasing and currently, we already have a variety of approaches, each with their own strengths and weaknesses. It has been observed that different hyper-heuristics perform differently on a given subset of problem instances and more importantly, a hyper-heuristic performs differently as the set of low level heuristics vary. This thesis introduces a general "multi-stage" hyper-heuristic framework enabling the use and exploitation of multiple selection hyper-heuristics at different stages during the search process. The goal is designing an approach utilising multiple hyper-heuristics for a more effective and efficient overall performance when compared to the performance of each constituent selection hyper-heuristic. The level of generality that a hyper-heuristic can achieve has always been of interest to the hyper-heuristic researchers. Hence, a variety of multi-stage hyper-heuristics based on the framework are not only applied to the real-world combinatorial optimisation problems of high school timetabling, multi-mode resource-constrained multi-project scheduling and construction of magic squares, but also tested on the well known hyper-heuristic benchmark of CHeSC 2011. The empirical results show that the multi-stage hyper-heuristics designed based on the proposed framework are still inherently general, easy-to-implement, adaptive and reusable. They can be extremely effective solvers considering their success in the competitions of ITC 2011 and MISTA 2013. Moreover, a particular multi-stage hyper-heuristic outperformed the state-of-the-art selection hyper-heuristic from CHeSC 2011

An Algorithm for Evolving Protocol Constraints

Centre for Intelligent Systems and their ApplicationsWe present an investigation into the design of an evolutionary mechanism for multiagent protocol constraint optimisation. Starting with a review of common population based mechanisms we discuss the properties of the mechanisms used by these search methods. We derive a novel algorithm for optimisation of vectors of real numbers and empirically validate the efficacy of the design by comparing against well known results from the literature. We discuss the application of an optimiser to a novel problem and remark upon the relevance of the no free lunch theorem. We show the relative performance of the optimiser is strong and publish details of a new best result for the Keane optimisation problem. We apply the final algorithm to the multi-agent protocol optimisation problem and show the design process was successful

Multi-stage hyper-heuristics for optimisation problems

There is a growing interest towards self configuring/tuning automated general-purpose reusable heuristic approaches for combinatorial optimisation, such as, hyper-heuristics. Hyper-heuristics are search methodologies which explore the space of heuristics rather than the solutions to solve a broad range of hard computational problems without requiring any expert intervention. There are two common types of hyper-heuristics in the literature: selection and generation methodologies. This work focuses on the former type of hyper-heuristics. Almost all selection hyper-heuristics perform a single point based iterative search over the space of heuristics by selecting and applying a suitable heuristic to the solution in hand at each decision point. Then the newly generated solution is either accepted or rejected using an acceptance method. This improvement process is repeated starting from an initial solution until a set of termination criteria is satisfied. The number of studies on the design of hyper-heuristic methodologies has been rapidly increasing and currently, we already have a variety of approaches, each with their own strengths and weaknesses. It has been observed that different hyper-heuristics perform differently on a given subset of problem instances and more importantly, a hyper-heuristic performs differently as the set of low level heuristics vary. This thesis introduces a general "multi-stage" hyper-heuristic framework enabling the use and exploitation of multiple selection hyper-heuristics at different stages during the search process. The goal is designing an approach utilising multiple hyper-heuristics for a more effective and efficient overall performance when compared to the performance of each constituent selection hyper-heuristic. The level of generality that a hyper-heuristic can achieve has always been of interest to the hyper-heuristic researchers. Hence, a variety of multi-stage hyper-heuristics based on the framework are not only applied to the real-world combinatorial optimisation problems of high school timetabling, multi-mode resource-constrained multi-project scheduling and construction of magic squares, but also tested on the well known hyper-heuristic benchmark of CHeSC 2011. The empirical results show that the multi-stage hyper-heuristics designed based on the proposed framework are still inherently general, easy-to-implement, adaptive and reusable. They can be extremely effective solvers considering their success in the competitions of ITC 2011 and MISTA 2013. Moreover, a particular multi-stage hyper-heuristic outperformed the state-of-the-art selection hyper-heuristic from CHeSC 2011