An iterated multi-stage selection hyper-heuristic

There is a growing interest towards the design of reusable general purpose search methods that are applicable to different problems instead of tailored solutions to a single particular problem. Hyper-heuristics have emerged as such high level methods that explore the space formed by a set of heuristics (move operators) or heuristic components for solving computationally hard problems. A selection hyper-heuristic mixes and controls a predefined set of low level heuristics with the goal of improving an initially generated solution by choosing and applying an appropriate heuristic to a solution in hand and deciding whether to accept or reject the new solution at each step under an iterative framework. Designing an adaptive control mechanism for the heuristic selection and combining it with a suitable acceptance method is a major challenge, because both components can influence the overall performance of a selection hyper-heuristic. In this study, we describe a novel iterated multi-stage hyper-heuristic approach which cycles through two interacting hyper-heuristics and operates based on the principle that not all low level heuristics for a problem domain would be useful at any point of the search process. The empirical results on a hyper-heuristic benchmark indicate the success of the proposed selection hyper-heuristic across six problem domains beating the state-of-the-art approach

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

Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimization

Combinatorial optimization has found applications in numerous fields, from aerospace to transportation planning and economics. The goal is to find an optimal solution among a finite set of possibilities. The well-known challenge one faces with combinatorial optimization is the state-space explosion problem: the number of possibilities grows exponentially with the problem size, which makes solving intractable for large problems. In the last years, deep reinforcement learning (DRL) has shown its promise for designing good heuristics dedicated to solve NP-hard combinatorial optimization problems. However, current approaches have two shortcomings: (1) they mainly focus on the standard travelling salesman problem and they cannot be easily extended to other problems, and (2) they only provide an approximate solution with no systematic ways to improve it or to prove optimality. In another context, constraint programming (CP) is a generic tool to solve combinatorial optimization problems. Based on a complete search procedure, it will always find the optimal solution if we allow an execution time large enough. A critical design choice, that makes CP non-trivial to use in practice, is the branching decision, directing how the search space is explored. In this work, we propose a general and hybrid approach, based on DRL and CP, for solving combinatorial optimization problems. The core of our approach is based on a dynamic programming formulation, that acts as a bridge between both techniques. We experimentally show that our solver is efficient to solve two challenging problems: the traveling salesman problem with time windows, and the 4-moments portfolio optimization problem. Results obtained show that the framework introduced outperforms the stand-alone RL and CP solutions, while being competitive with industrial solvers

A greedy gradient-simulated annealing selection hyper-heuristic

Educational timetabling problem is a challenging real world problem which has been of interest to many researchers and practitioners. There are many variants of this problem which mainly require scheduling of events and resources under various constraints. In this study, a curriculum based course timetabling problem at Yeditepe University is described and an iterative selection hyper-heuristic is presented as a solution method. A selection hyper-heuristic as a high level methodology operates on the space formed by a fixed set of low level heuristics which operate directly on the space of solutions. The move acceptance and heuristic selection methods are the main components of a selection hyper-heuristic. The proposed hyper-heuristic in this study combines a simulated annealing move acceptance method with a learning heuristic selection method and manages a set of low level constraint oriented heuristics. A key goal in hyper-heuristic research is to build low cost methods which are general and can be reused on unseen problem instances as well as other problem domains desirably with no additional human expert intervention. Hence, the proposed method is additionally applied to a high school timetabling problem, as well as six other problem domains from a hyper-heuristic benchmark to test its level of generality. The empirical results show that our easy-to-implement hyper-heuristic is effective in solving the Yeditepe course timetabling problem. Moreover, being sufficiently general, it delivers a reasonable performance across different problem domains

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

A stochastic local search algorithm with adaptive acceptance for high-school timetabling

Automating high school timetabling is a challenging task. This problem is a well known hard computational problem which has been of interest to practitioners as well as researchers. High schools need to timetable their regular activities once per year, or even more frequently. The exact solvers might fail to find a solution for a given instance of the problem. A selection hyper-heuristic can be defined as an easy-to-implement, easy-to-maintain and effective 'heuristic to choose heuristics' to solve such computationally hard problems. This paper describes the approach of the team hyper-heuristic search strategies and timetabling (HySST) to high school timetabling which competed in all three rounds of the third international timetabling competition. HySST generated the best new solutions for three given instances in Round 1 and gained the second place in Rounds 2 and 3. It achieved this by using a fairly standard stochastic search method but significantly enhanced by a selection hyper-heuristic with an adaptive acceptance mechanism. © 2014 Springer Science+Business Media New York

A comparative study of evolutionary approaches to the bi-objective dynamic Travelling Thief Problem

Dynamic evolutionary multi-objective optimization is a thriving research area. Recent contributions span the development of specialized algorithms and the construction of challenging benchmark problems. Here, we continue these research directions through the development and analysis of a new bi-objective problem, the dynamic Travelling Thief Problem (TTP), including three modes of dynamic change: city locations, item profit values, and item availability. The interconnected problem components embedded in the dynamic problem dictate that the effective tracking of good trade-off solutions that satisfy both objectives throughout dynamic events is non-trivial. Consequently, we examine the relative contribution to the non-dominated set from a variety of population seeding strategies, including exact solvers and greedy algorithms for the knapsack and tour components, and random techniques. We introduce this responsive seeding extension within an evolutionary algorithm framework. The efficacy of alternative seeding mechanisms is evaluated across a range of exemplary problem instances using ranking-based and quantitative statistical comparisons, which combines performance measurements taken throughout the optimization. Our detailed experiments show that the different dynamic TTP instances present varying difficulty to the seeding methods tested. We posit the dynamic TTP as a suitable benchmark capable of generating problem instances with different controllable characteristics aligning with many real-world problems

A Hybrid Tabu/Scatter Search Algorithm for Simulation-Based Optimization of Multi-Objective Runway Operations Scheduling

As air traffic continues to increase, air traffic flow management is becoming more challenging to effectively and efficiently utilize airport capacity without compromising safety, environmental and economic requirements. Since runways are often the primary limiting factor in airport capacity, runway operations scheduling emerge as an important problem to be solved to alleviate flight delays and air traffic congestion while reducing unnecessary fuel consumption and negative environmental impacts. However, even a moderately sized real-life runway operations scheduling problem tends to be too complex to be solved by analytical methods, where all mathematical models for this problem belong to the complexity class of NP-Hard in a strong sense due to combinatorial nature of the problem. Therefore, it is only possible to solve practical runway operations scheduling problem by making a large number of simplifications and assumptions in a deterministic context. As a result, most analytical models proposed in the literature suffer from too much abstraction, avoid uncertainties and, in turn, have little applicability in practice. On the other hand, simulation-based methods have the capability to characterize complex and stochastic real-life runway operations in detail, and to cope with several constraints and stakeholders’ preferences, which are commonly considered as important factors in practice. This dissertation proposes a simulation-based optimization (SbO) approach for multi-objective runway operations scheduling problem. The SbO approach utilizes a discrete-event simulation model for accounting for uncertain conditions, and an optimization component for finding the best known Pareto set of solutions. This approach explicitly considers uncertainty to decrease the real operational cost of the runway operations as well as fairness among aircraft as part of the optimization process. Due to the problem’s large, complex and unstructured search space, a hybrid Tabu/Scatter Search algorithm is developed to find solutions by using an elitist strategy to preserve non-dominated solutions, a dynamic update mechanism to produce high-quality solutions and a rebuilding strategy to promote solution diversity. The proposed algorithm is applied to bi-objective (i.e., maximizing runway utilization and fairness) runway operations schedule optimization as the optimization component of the SbO framework, where the developed simulation model acts as an external function evaluator. To the best of our knowledge, this is the first SbO approach that explicitly considers uncertainties in the development of schedules for runway operations as well as considers fairness as a secondary objective. In addition, computational experiments are conducted using real-life datasets for a major US airport to demonstrate that the proposed approach is effective and computationally tractable in a practical sense. In the experimental design, statistical design of experiments method is employed to analyze the impacts of parameters on the simulation as well as on the optimization component’s performance, and to identify the appropriate parameter levels. The results show that the implementation of the proposed SbO approach provides operational benefits when compared to First-Come-First-Served (FCFS) and deterministic approaches without compromising schedule fairness. It is also shown that proposed algorithm is capable of generating a set of solutions that represent the inherent trade-offs between the objectives that are considered. The proposed decision-making algorithm might be used as part of decision support tools to aid air traffic controllers in solving the real-life runway operations scheduling problem

Performance of selection hyper-heuristics on the extended HyFlex domains

Selection hyper-heuristics perform search over the space of heuristics by mixing and controlling a predefined set of low level heuristics for solving computationally hard combinatorial optimisation problems. Being reusable methods, they are expected to be applicable to multiple problem domains, hence performing well in cross-domain search. HyFlex is a general purpose heuristic search API which separates the high level search control from the domain details enabling rapid development and performance comparison of heuristic search methods, particularly hyper-heuristics. In this study, the performance of six previously proposed selection hyper-heuristics are evaluated on three recently introduced extended HyFlex problem domains, namely 0–1 Knapsack, Quadratic Assignment and Max-Cut. The empirical results indicate the strong generalising capability of two adaptive selection hyper-heuristics which perform well across the ‘unseen’ problems in addition to the six standard HyFlex problem domains