Constructing constrained-version of magic squares using selection hyper-heuristics

A square matrix of distinct numbers in which every row, column and both diagonals have the same total is referred to as a magic square. Constructing a magic square of a given order is considered a difficult computational problem, particularly when additional constraints are imposed. Hyper-heuristics are emerging high-level search methodologies that explore the space of heuristics for solving a given problem. In this study, we present a range of effective selection hyper-heuristics mixing perturbative low-level heuristics for constructing the constrained version of magic squares. The results show that selection hyper-heuristics, even the non-learning ones deliver an outstanding performance, beating the best-known heuristic solution on average

A reinforcement learning hyper-heuristic for the optimisation of flight connections

Many combinatorial computational problems have been effectively solved by means of hyper-heuristics. In this study, we focus on a problem proposed by Kiwi.com and solve this problem by implementing a Reinforcement Learning (RL) hyperheuristic algorithm. Kiwi.com proposed a real-world NP-hard minimisation problem associated with air travelling services. The problem shares some characteristics with several TSP variants, such as time-dependence and time-windows that make the problem more complex in comparison to the classical TSP. In this work, we evaluate our proposed RL method on kiwi.com problem and compare its results statistically with common random-based hyper-heuristic approaches. The empirical results show that RL method achieves the best performance between the tested selection hyper-heuristics. Another significant achievement of RL is that better solutions were found compared to the best known solutions in several problem instances

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

Ensemble move acceptance in selection hyper-heuristics

Selection hyper-heuristics are high level search methodologies which control a set of low level heuristics while solving a given problem. Move acceptance is a crucial component of selection hyper-heuristics, deciding whether to accept or reject a new solution at each step during the search process. This study investigates group decision making strategies as ensemble methods exploiting the strengths of multiple move acceptance methods for improved performance. The empirical results indicate the success of the proposed methods across six combinatorial optimisation problems from a benchmark as well as an examination timetabling problem

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

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

HySST: hyper-heuristic search strategies and timetabling

9th International Conference on the Practice and Theory of Automated Timetabling, Son, Norway, 28-31 August 201

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

A greedy gradient-simulated annealing hyper-heuristic for a curriculum-based course timetabling problem

Copyright © 2012 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.12th UK Workshop on Computational Intelligence (UKCI), Edinburgh, Scotland, 5-7 September 2012The course timetabling problem is a well known constraint optimization problem which has been of interest to researchers as well as practitioners. Due to the NP-hard nature of the problem, the traditional exact approaches might fail to find a solution even for a given instance. Hyper-heuristics which search the space of heuristics for high quality solutions are alternative methods that have been increasingly used in solving such problems. In this study, a curriculum based course timetabling problem at Yeditepe University is described. An improvement oriented heuristic selection strategy combined with a simulated annealing move acceptance as a hyper-heuristic utilizing a set of low level constraint oriented neighbourhood heuristics is investigated for solving this problem. The proposed hyper-heuristic was initially developed to handle a variety of problems in a particular domain with different properties considering the nature of the low level heuristics. On the other hand, a goal of hyper-heuristic development is to build methods which are general. Hence, the proposed hyper-heuristic is applied to six other problem domains and its performance is compared to different state-of-the-art hyper-heuristics to test its level of generality. The empirical results show that the proposed method is sufficiently general and powerful

Solving urban transit route design problem using selection hyper-heuristics

The urban transit routing problem (UTRP) focuses on finding efficient travelling routes for vehicles in a public transportation system. It is one of the most significant problems faced by transit planners and city authorities throughout the world. This problem belongs to the class of difficult combinatorial problems, whose optimal solution is hard to find with the complexity that arises from the large search space, and the number of constraints imposed in constructing the solution. Hyper-heuristics have emerged as general-purpose search techniques that explore the space of low level heuristics to improve a given solution under an iterative framework. In this work, we evaluate the performance of a set of selection hyper-heuristics on the route design problem of bus networks, with the goal of minimising the passengers’ travel time, and the operator’s costs. Each selection hyper-heuristic is empirically tested on a set of benchmark instances and statistically compared to the other selection hyper-heuristics to determine the best approach. A sequence-based selection method combined with the great deluge acceptance method achieved the best performance, succeeding in finding improved results in much faster run times over the current best known solutions