Multi-objective optimisation with a sequence-based selection hyper-heuristic

Hyper-heuristics have been used widely to solve optimisation problems, often single-objective and discrete in nature. Herein, we extend a recently-proposed selection hyper-heuristic to the multiobjective domain and with it optimise continuous problems. The MOSSHH algorithm operates as a hidden Markov model, using transition probabilities to determine which low-level heuristic or sequence of heuristics should be applied next. By incorporating dominance into the transition probability update rule, and an elite archive of solutions, MOSSHH generates solutions to multi-objective problems that are competitive with bespoke multi-objective algorithms. When applied to test problems, it is able to find good approximations to the true Pareto front, and yields information about the type of low-level heuristics that it uses to solve the problem

Markov Chain Selection Hyper-heuristic for the Optimisation of Constrained Magic Squares

UKCI 2015: UK Workshop on Computational Intelligence, University of Exeter, UK, 7-9 September 2015A square matrix of size n × n, containing each of the numbers (1, . . . , n2) in which every row, column and both diagonals has the same total is referred to as a magic square. The problem can be formulated as an optimisation problem where the task is to minimise the deviation from the magic square constraints and is tackled here by using hyper-heuristics. Hyper-heuristics have recently attracted the attention of the artificial intelligence, operations research, engineering and computer science communities where the aim is to design and develop high level strategies as general solvers which are applicable to a range of different problem domains. There are two main types of hyper-heuristics in the literature: methodologies to select and to generate heuristics and both types of approaches search the space of heuristics rather than solutions. In this study, we describe a Markov chain selection hyper-heuristic as an effective solution methodology for optimising constrained magic squares. The empirical results show that the proposed hyper-heuristic is able to outperform the current state-of-the-art method

Multi-objective Optimisation of a Water Distribution Network with a Sequence-based Selection Hyper-heuristic

This is the author accepted manuscript. The final version is available from the publisher.Multi-objective hyper-heuristics are fast becoming an efficient way of optimising complex problems. The water distribution network design problem is an example of such a problem, and this work employs a recent hyper-heuristic that generates sequences of low-level heuristics to solve the multi-objective water distribution design problem. The results presented are comparable to those generated by state-of-the-art metaheuristics, as well as a single-objective version of the algorithm from the literature. The information revealed from analysing the sequences generated to solve the problem reveal important information about the nature of the problem space that is not available from the metaheuristics, and the entire Pareto front can be explored in a single run as opposed to the multiple runs needed with the original single-objective algorithm

Heuristic sequence selection for inventory routing problem

In this paper, an improved sequence-based selection hyper-heuristic method for the Air Liquide inventory routing problem, the subject of the ROADEF/EURO 2016 challenge, is described. The organizers of the challenge have proposed a real-world problem of inventory routing as a difficult combinatorial optimization problem. An exact method often fails to find a feasible solution to such problems. On the other hand, heuristics may be able to find a good quality solution that is significantly better than those produced by an expert human planner. There is a growing interest toward self-configuring automated general-purpose reusable heuristic approaches for combinatorial optimization. Hyper-heuristics have emerged as such methodologies. This paper investigates a new breed of hyper-heuristics based on the principles of sequence analysis to solve the inventory routing problem. The primary point of this work is that it shows the usefulness of the improved sequence-based selection hyper-heuristic, and in particular demonstrates the advantages of using a data science technique of hidden Markov model for the heuristic selection

Analysing heuristic subsequences for offline hyper-heuristic learning

This is the author accepted manuscript. The final version is available from ACM via the DOI in this recordThe paper explores the impact of sequences of search operationson the performance of an optimiser through the use of log returnsand a database of sequences. The study demonstrates that althoughthe performance of individual perturbation operators is important,understanding their performance in sequence provides greater op-portunity for performance improvements within and across opera-tions research domains

Offline Learning for Selection Hyper-heuristics with Elman Networks

This is the author accepted manuscript. The final version is available from the publisher via the link in this record.Offline selection hyper-heuristics are machine learning methods that are trained on heuristic selections to create an algorithm that is tuned for a particular problem domain. In this work, a simple selection hyper-heuristic is executed on a number of computationally hard benchmark optimisation problems, and the resulting sequences of low level heuristic selections and objective function values are used to construct an offline learning database. An Elman network is trained on sequences of heuristic selections chosen from the offline database and the network’s ability to learn and generalise from these sequences is evaluated. The networks are trained using a leave-one-out cross validation methodology and the sequences of heuristic selections they produce are tested on benchmark problems drawn from the HyFlex set. The results demonstrate that the Elman network is capable of intra-domain learning and generalisation with 99% confidence and produces better results than the training sequences in many cases. When the network was trained using an interdomain training set, the Elman network did not exhibit generalisation indicating that inter-domain generalisation is a harder problem and that strategies learned on one domain cannot necessarily be transferred to another

Sequence analysis-based hyper-heuristics for water distribution network optimisation

Hyper-heuristics operate at the level above traditional (meta-)heuristics that 'optimise the optimiser'. These algorithms can combine low level heuristics to create bespoke algorithms for particular classes of problems. The low level heuristics can be mutation operators or hill climbing algorithms and can include industry expertise. This paper investigates the use of a new hyper-heuristic based on sequence analysis in the biosciences, to develop new optimisers that can outperform conventional evolutionary approaches. It demonstrates that the new algorithms develop high quality solutions on benchmark water distribution network optimisation problems efficiently, and can yield important information about the problem search space

Tackling a VRP challenge to redistribute scarce equipment within time windows using metaheuristic algorithms

This paper reports on the results of the VeRoLog Solver Challenge 2016–2017: the third solver challenge facilitated by VeRoLog, the EURO Working Group on Vehicle Routing and Logistics Optimization. The authors are the winners of second and third places, combined with members of the challenge organizing committee. The problem central to the challenge was a rich VRP: expensive and, therefore, scarce equipment was to be redistributed over customer locations within time windows. The difficulty was in creating combinations of pickups and deliveries that reduce the amount of equipment needed to execute the schedule, as well as the lengths of the routes and the number of vehicles used. This paper gives a description of the solution methods of the above-mentioned participants. The second place method involves sequences of 22 low level heuristics: each of these heuristics is associated with a transition probability to move to another low level heuristic. A randomly drawn sequence of these heuristics is applied to an initial solution, after which the probabilities are updated depending on whether or not this sequence improved the objective value, hence increasing the chance of selecting the sequences that generate improved solutions. The third place method decomposes the problem into two independent parts: first, it schedules the delivery days for all requests using a genetic algorithm. Each schedule in the genetic algorithm is evaluated by estimating its cost using a deterministic routing algorithm that constructs feasible routes for each day. After spending 80 percent of time in this phase, the last 20 percent of the computation time is spent on Variable Neighborhood Descent to further improve the routes found by the deterministic routing algorithm. This article finishes with an in-depth comparison of the results of the two approaches

A Hidden Markov Model Approach to the Problem of Heuristic Selection in Hyper-Heuristics with a Case Study in High School Timetabling Problems

Operations research is a well-established field that uses computational systems to support decisions in business and public life. Good solutions to operations research problems can make a large difference to the efficient running of businesses and organisations and so the field often searches for new methods to improve these solutions. The high school timetabling problem is an example of an operations research problem and is a challenging task which requires assigning events and resources to time slots subject to a set of constraints. In this article, a new sequence-based selection hyper-heuristic is presented that produces excellent results on a suite of high school timetabling problems. In this study, we present an easy-to-implement, easy-to-maintain, and effective sequence-based selection hyper-heuristic to solve high school timetabling problems using a benchmark of unified real-world instances collected from different countries. We show that with sequence-based methods, it is possible to discover new best known solutions for a number of the problems in the timetabling domain. Through this investigation, the usefulness of sequence-based selection hyper-heuristics has been demonstrated and the capability of these methods has been shown to exceed the state of the art

Public Transport Network Optimisation in PTV Visum using Selection Hyper-Heuristics

Despite the progress in the field of automatic public transport route opti-misation in recent years, there exists a clear gap between the development of opti-misation algorithms and their applications in real-world planning processes. In this study, we bridge this gap by developing an interface between the Urban Transit Routing Problem (UTRP) and the professional transport modelling software PTV Visum. The interface manages the differences in data requirements between the two models and allows the optimisation of public transport lines in Visum network models. This is demonstrated with the application of Selection Hyper-heuristics on two network models representing real world urban areas. The optimisation objectives include the passengers' average travel time and operators' costs. Furthermore, we show how our approach can be combined with a mode choice model to optimise the use of public transport in relation to other modes. This feature is applied in a special optimisation experiment to reduce the number of private vehicles on a selected set of links in the network. The results demonstrate the successful implementation of our interface and the applied optimisation methods for a multi-modal public transport network