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

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

Design Of Perturbative Hyper-Heuristics For Combinatorial Optimisation

Combinatorial optimisation is an area which seeks to identify optimal solution(s) from a discrete solution search space. Approaches for solving combinatorial optimisation problems can be separated into two main sub-classes, i.e. exact and approximation algorithms. Exact algorithm is a sub-class of techniques that is able to guarantee global optimality. However, exact algorithms are not feasible for solving complex problem due to its high computational overhead. Approximation algorithm is a sub-class of techniques which is able to provide sub-optimal solution(s) with reasonable computational cost. In order to explore the solution search space of a combinatorial optimisation problem, an approximation algorithm performs perturbations on the existing solutions by adopting a single or multiple perturbative Low-Level Heuristic(s) (LLHs). The use of a single LLH leads to poor performance when the particular heuristic is incompetent in solving the problem. Thus, the use of multiple LLHs is more desirable as the weaknesses of one heuristic can be compensated by the strengths of another. When there are multiple LLHs, a hyper-heuristic can be integrated to determine the choice of heuristics for a particular problem or situation. Hyper-heuristic automates the selection of LLHs through a high-level heuristic that consists of two key components, i.e. a heuristic selection method and a move acceptance method. The capability of a high-level heuristic is highly problem dependent as the landscape properties of a problem are unique among others. The high-level heuristics in the existing hyper-heuristics are designed by manually matching different combinations of high-level heuristic components

Solving Travelling Thief Problems using Coordination Based Methods

A travelling thief problem (TTP) is a proxy to real-life problems such as postal collection. TTP comprises an entanglement of a travelling salesman problem (TSP) and a knapsack problem (KP) since items of KP are scattered over cities of TSP, and a thief has to visit cities to collect items. In TTP, city selection and item selection decisions need close coordination since the thief's travelling speed depends on the knapsack's weight and the order of visiting cities affects the order of item collection. Existing TTP solvers deal with city selection and item selection separately, keeping decisions for one type unchanged while dealing with the other type. This separation essentially means very poor coordination between two types of decision. In this paper, we first show that a simple local search based coordination approach does not work in TTP. Then, to address the aforementioned problems, we propose a human designed coordination heuristic that makes changes to collection plans during exploration of cyclic tours. We further propose another human designed coordination heuristic that explicitly exploits the cyclic tours in item selections during collection plan exploration. Lastly, we propose a machine learning based coordination heuristic that captures characteristics of the two human designed coordination heuristics. Our proposed coordination based approaches help our TTP solver significantly outperform existing state-of-the-art TTP solvers on a set of benchmark problems. Our solver is named Cooperation Coordination (CoCo) and its source code is available from https://github.com/majid75/CoCoComment: expanded and revised version of arXiv:1911.0312

Grammar-based generation of variable-selection heuristics for constraint satisfaction problems

We propose a grammar-based genetic programming framework that generates variable-selection heuristics for solving constraint satisfaction problems. This approach can be considered as a generation hyper-heuristic. A grammar to express heuristics is extracted from successful human-designed variable-selection heuristics. The search is performed on the derivation sequences of this grammar using a strongly typed genetic programming framework. The approach brings two innovations to grammar-based hyper-heuristics in this domain: the incorporation of if-then-else rules to the function set, and the implementation of overloaded functions capable of handling different input dimensionality. Moreover, the heuristic search space is explored using not only evolutionary search, but also two alternative simpler strategies, namely, iterated local search and parallel hill climbing. We tested our approach on synthetic and real-world instances. The newly generated heuristics have an improved performance when compared against human-designed heuristics. Our results suggest that the constrained search space imposed by the proposed grammar is the main factor in the generation of good heuristics. However, to generate more general heuristics, the composition of the training set and the search methodology played an important role. We found that increasing the variability of the training set improved the generality of the evolved heuristics, and the evolutionary search strategy produced slightly better results

Phased Genetic Programming for Application to the Traveling Salesman Problem

This is the author accepted manuscript. The final version is available from ACM via the DOI in this recordThe Traveling Salesman Problem (TSP) is a difficult permutation-based optimisation problem typically solved using heuristics or meta-heuristics which search the solution problem space. An alternative is to find sets of manipulations to a solution which lead to optimality. Hyper-heuristics search this space applying heuristics sequentially, similar to a program. Genetic Programming (GP) evolves programs typically for classification or regression problems. This paper hypothesizes that GP can be used to evolve heuristic programs to directly solve the TSP. However, evolving a full program to solve the TSP is likely difficult due to required length and complexity. Consequently, a phased GP method is proposed whereby after a phase of generations the best program is saved and executed. The subsequent generation phase restarts operating on this saved program output. A full program is evolved piecemeal. Experiments demonstrate that whilst pure GP cannot solve TSP instances when using simple operators, Phased-GP can obtain solutions within 4% of optimal for TSPs of several hundred cities. Moreover, Phased-GP operates up to nine times faster than pure GP.Innovate UKCity Scienc

Learning Optimisation Algorithms over Graphs

The paradigm of learning to optimise relies on the following principle: instead of designing an algorithm to solve a problem, we design an algorithm which will automate the design of such a solver. The initial idea was to alleviate the limitations stated by the No Free Lunch Theorem by producing an algorithm which efficiency is less dependent upon known instances of the problem to tackle. Hyper-heuristics constitute the main learning-to-optimise techniques. These rely on a high-level algorithm performing a search process into a space of low-level heuristics to tackle a given problem. Because the latter search space is problem-dependent, the vast majority of hyper-heuristics are designed to tackle a specific problem. Due to this lack of generality, existing works fully redesign hyper-heuristics when tackling a new problem, despite the fact that they may share a similar structure. In this dissertation, we tackle this challenge by proposing a generic way for learning to optimise any problem. To this end, this thesis introduces three main contributions: (i) an analysis of the formal functioning of learning-to-optimise techniques; (ii) a model of generic hyper-heuristic, named Algorithm Learner for Graph Optimisation problems (ALGO), constituting the central point of this work; (iii) a real-world use case where we use our generic hyper-heuristic to automate the design of behaviours within a swarm of drones. In the first part, we provide a formalism for optimisation and learning concepts, which we use to describe the large body of knowledge that combines two layers of optimisation and/or learning. We then put an emphasis on approaches using learning to improve an optimisation process, i.e., aiming at learning to optimise. In the second part, we present ALGO, our model of generic hyper-heuristic. We explain how we abstract from a given problem with a graph structure so that it can be used to tackle any optimisation problem. We also detail the steps to follow in order to use ALGO to tackle a given problem. We finally present the modularity of ALGO with inner components that a user can implement. The second part ends with a validation of our model, i.e., using ALGO to tackle a classical optimisation problem. In the third part, we use ALGO to tackle the problem of area surveillance with a swarm of drones. We demonstrate that ALGO constitutes a novel and efficient way to automate the design of such a distributed and multi-objective problem

Metaheuristic Design Patterns: New Perspectives for Larger-Scale Search Architectures

Design patterns capture the essentials of recurring best practice in an abstract form. Their merits are well established in domains as diverse as architecture and software development. They offer significant benefits, not least a common conceptual vocabulary for designers, enabling greater communication of high-level concerns and increased software reuse. Inspired by the success of software design patterns, this chapter seeks to promote the merits of a pattern-based method to the development of metaheuristic search software components. To achieve this, a catalog of patterns is presented, organized into the families of structural, behavioral, methodological and component-based patterns. As an alternative to the increasing specialization associated with individual metaheuristic search components, the authors encourage computer scientists to embrace the ‘cross cutting' benefits of a pattern-based perspective to optimization algorithms. Some ways in which the patterns might form the basis of further larger-scale metaheuristic component design automation are also discussed