The General Combinatorial Optimization Problem: Towards Automated Algorithm Design

This paper defines a new combinatorial optimisation problem, namely General Combinatorial Optimisation Problem (GCOP), whose decision variables are a set of parametric algorithmic components, i.e. algorithm design decisions. The solutions of GCOP, i.e. compositions of algorithmic components, thus represent different generic search algorithms. The objective of GCOP is to find the optimal algorithmic compositions for solving the given optimisation problems. Solving the GCOP is thus equivalent to automatically designing the best algorithms for optimisation problems. Despite recent advances, the evolutionary computation and optimisation research communities are yet to embrace formal standards that underpin automated algorithm design. In this position paper, we establish GCOP as a new standard to define different search algorithms within one unified model. We demonstrate the new GCOP model to standardise various search algorithms as well as selection hyper-heuristics. A taxonomy is defined to distinguish several widely used terminologies in automated algorithm design, namely automated algorithm composition, configuration and selection. We would like to encourage a new line of exciting research directions addressing several challenging research issues including algorithm generality, algorithm reusability, and automated algorithm design

A learning automata based multiobjective hyper-heuristic

Metaheuristics, being tailored to each particular domain by experts, have been successfully applied to many computationally hard optimisation problems. However, once implemented, their application to a new problem domain or a slight change in the problem description would often require additional expert intervention. There is a growing number of studies on reusable cross-domain search methodologies, such as, selection hyper-heuristics, which are applicable to problem instances from various domains, requiring minimal expert intervention or even none. This study introduces a new learning automata based selection hyper-heuristic controlling a set of multiobjective metaheuristics. The approach operates above three well-known multiobjective evolutionary algorithms and mixes them, exploiting the strengths of each algorithm. The performance and behaviour of two variants of the proposed selection hyper-heuristic, each utilising a different initialisation scheme are investigated across a range of unconstrained multiobjective mathematical benchmark functions from two different sets and the realworld problem of vehicle crashworthiness. The empirical results illustrate the effectiveness of our approach for cross-domain search, regardless of the initialisation scheme, on those problems when compared to each individual multiobjective algorithm. Moreover, both variants perform signicantly better than some previously proposed selection hyper-heuristics for multiobjective optimisation, thus signicantly enhancing the opportunities for improved multiobjective optimisation

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

Multi-objective evolutionary algorithms and hyper-heuristics for wind farm layout optimisation

Wind farm layout optimisation is a challenging real-world problem which requires the discovery of trade-off solutions considering a variety of conflicting criteria, such as minimisation of the land area usage and maximisation of energy production. However, due to the complexity of handling multiple objectives simultaneously, many approaches proposed in the literature often focus on the optimisation of a single objective when deciding the locations for a set of wind turbines spread across a given region. In this study, we tackle a multi-objective wind farm layout optimisation problem. Different from the previously proposed approaches, we are applying a high-level search method, known as selection hyper-heuristic to solve this problem. Selection hyper-heuristics mix and control a predefined set of low-level (meta)heuristics which operate on solutions. We test nine different selection hyper-heuristics including an online learning hyper-heuristic on a multi-objective wind farm layout optimisation problem. Our hyper-heuristic approaches manage three well-known multi-objective evolutionary algorithms as low-level metaheuristics. The empirical results indicate the success and potential of selection hyper-heuristics for solving this computationally difficult problem. We additionally explore other objectives in wind farm layout optimisation problems to gain a better understanding of the conflicting nature of those objectives

Making and breaking power laws in evolutionary algorithm population dynamics

Deepening our understanding of the characteristics and behaviors of population-based search algorithms remains an important ongoing challenge in Evolutionary Computation. To date however, most studies of Evolutionary Algorithms have only been able to take place within tightly restricted experimental conditions. For instance, many analytical methods can only be applied to canonical algorithmic forms or can only evaluate evolution over simple test functions. Analysis of EA behavior under more complex conditions is needed to broaden our understanding of this population-based search process. This paper presents an approach to analyzing EA behavior that can be applied to a diverse range of algorithm designs and environmental conditions. The approach is based on evaluating an individual’s impact on population dynamics using metrics derived from genealogical graphs.\ud From experiments conducted over a broad range of conditions, some important conclusions are drawn in this study. First, it is determined that very few individuals in an EA population have a significant influence on future population dynamics with the impact size fitting a power law distribution. The power law distribution indicates there is a non-negligible probability that single individuals will dominate the entire population, irrespective of population size. Two EA design features are however found to cause strong changes to this aspect of EA behavior: i) the population topology and ii) the introduction of completely new individuals. If the EA population topology has a long path length or if new (i.e. historically uncoupled) individuals are continually inserted into the population, then power law deviations are observed for large impact sizes. It is concluded that such EA designs can not be dominated by a small number of individuals and hence should theoretically be capable of exhibiting higher degrees of parallel search behavior

Learning heuristic selection using a time delay neural network for open vehicle routing

A selection hyper-heuristic is a search method that controls a prefixed set of low-level heuristics for solving a given computationally difficult problem. This study investigates a learning-via demonstrations approach generating a selection hyper-heuristic for Open Vehicle Routing Problem (OVRP). As a chosen ‘expert’ hyper-heuristic is run on a small set of training problem instances, data is collected to learn from the expert regarding how to decide which low-level heuristic to select and apply to the solution in hand during the search process. In this study, a Time Delay Neural Network (TDNN) is used to extract hidden patterns within the collected data in the form of a classifier ,i.e an ‘apprentice’ hyper-heuristic, which is then used to solve the ‘unseen’ problem instances. Firstly, the parameters of TDNN are tuned using Taguchi orthogonal array as a design of experiments method. Then the influence of extending and enriching the information collected from the expert and fed into TDNN is explored on the behaviour of the generated apprentice hyper-heuristic. The empirical results show that the use of distance between solutions as an additional information collected from the expert generates an apprentice which outperforms the expert algorithm on a benchmark of OVRP instances

A multi-objective hyper-heuristic based on choice function

Hyper-heuristics are emerging methodologies that perform a search over the space of heuristics in an attempt to solve difficult computational optimization problems. We present a learning selection choice function based hyper-heuristic to solve multi-objective optimization problems. This high level approach controls and combines the strengths of three well-known multi-objective evolutionary algorithms (i.e. NSGAII, SPEA2 and MOGA), utilizing them as the low level heuristics. The performance of the proposed learning hyper-heuristic is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, the proposed hyper-heuristic is applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the hyper-heuristic approach when compared to the performance of each low level heuristic run on its own, as well as being compared to other approaches including an adaptive multi-method search, namely AMALGAM

Hybridizations within a graph based hyper-heuristic framework for university timetabling problems

A significant body of recent literature has explored various research directions in hyper-heuristics (which can be thought as heuristics to choose heuristics). In this paper, we extend our previous work to construct a unified graph-based hyper-heuristic (GHH) framework, under which a number of local search-based algorithms (as the high level heuristics) are studied to search upon sequences of low-level graph colouring heuristics. To gain an in-depth understanding on this new framework, we address some fundamental issues concerning neighbourhood structures and characteristics of the two search spaces (namely, the search spaces of the heuristics and the actual solutions). Furthermore, we investigate efficient hybridizations in GHH with local search methods and address issues concerning the exploration of the high-level search and the exploitation ability of the local search. These, to our knowledge, represent entirely novel directions in hyper-heuristics. The efficient hybrid GHH obtained competitive results compared with the best published results for both benchmark course and exam timetabling problems, demonstrating its efficiency and generality across different problem domains. Possible extensions upon this simple, yet general, GHH framework are also discussed

A genetic programming hyper-heuristic approach for evolving 2-D strip packing heuristics

We present a genetic programming (GP) system to evolve reusable heuristics for the 2-D strip packing problem. The evolved heuristics are constructive, and decide both which piece to pack next and where to place that piece, given the current partial solution. This paper contributes to a growing research area that represents a paradigm shift in search methodologies. Instead of using evolutionary computation to search a space of solutions, we employ it to search a space of heuristics for the problem. A key motivation is to investigate methods to automate the heuristic design process. It has been stated in the literature that humans are very good at identifying good building blocks for solution methods. However, the task of intelligently searching through all of the potential combinations of these components is better suited to a computer. With such tools at their disposal, heuristic designers are then free to commit more of their time to the creative process of determining good components, while the computer takes on some of the design process by intelligently combining these components. This paper shows that a GP hyper-heuristic can be employed to automatically generate human competitive heuristics in a very-well studied problem domain