课程表问题的一种模拟退火超启发式算法

课程表问题是经典的组合优化问题,属于NP-hard问题.长期以来人们一直都在寻求快速高效的近似算法,以便在合理的计算时间内准确解决大规模课程安排问题,并提出许多有效且实用的启发式和元启发式算法.在此基础上提出了一种基于多个图染色启发式规则的模拟退火超启发式算法.在超启发式算法的框架中,用模拟退火算法作为高层搜索算法,多个图染色启发式规则为底层的构造算法.与现有的方法相比,该算法具有很好的通用性,可以很容易推广到考试时间表、会议安排.旅行商问题、背包问题等应用领域.实验表明,该算法是可行有效的,且无一例时间、空间冲突.     

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.     

Parallel hyper heuristic algorithm based on reinforcement learning for the corridor allocation problem and parallel row ordering problem

Hyper heuristics is a relatively new optimisation algorithm. Numerous studies have reported that hyper heuristics are well applied in combinatorial optimisation problems. As a classic combinatorial optimisation problem, the row layout problem has not been publicly reported on applying hyper heuristics to its various sub-problems. To fill this gap, this study proposes a parallel hyper-heuristic approach based on reinforcement learning for corridor allocation problems and parallel row ordering problems. For the proposed algorithm, an outer layer parallel computing framework was constructed based on the encoding of the problem. The simulated annealing, tabu search, and variable neighbourhood algorithms were used in the algorithm as low-level heuristic operations, and Q-learning in reinforcement learning was used as a high-level strategy. A state space containing sequences and fitness values was designed. The algorithm performance was then evaluated for benchmark instances of the corridor allocation problem (37 groups) and parallel row ordering problem (80 groups). The results showed that, in most cases, the proposed algorithm provided a better solution than the best-known solutions in the literature. Finally, the meta-heuristic algorithm applied to three low-level heuristic operations is taken as three independent algorithms and compared with the proposed hyper-heuristic algorithm on four groups of parallel row ordering problem instances. The effectiveness of Q-learning in selection is illustrated by analysing the comparison results of the four algorithms and the number of calls of the three low-level heuristic operations in the proposed method.     

超启发算法研究进展综述

超启发算法是一类新兴的优化方法,通过机器学习、算法选择、算法生成等技术求解组合优化等问题,具备跨问题领域求解的能力。针对超启发算法研究进展进行综述和讨论。首先,梳理超启发算法的定义、结构、特点和分类;其次,归纳选择式超启发算法和生成式超启发算法的研究进展及相关技术,包括选择低层启发式算法采用的学习方法,迭代计算中的移动接受策略,低层启发式算法的生成方法;最后,讨论现有超启发算法研究中存在的不足及未来的研究方向。     

A hyper-heuristic approach to aircraft structural design optimization

The conceptual design of an aircraft is a challenging problem in which optimization can be of great importance to the quality of design generated. Mass optimization of the structural design of an aircraft aims to produce an airframe of minimal mass whilst maintaining satisfactory strength under various loading conditions due to flight and ground manoeuvres. Hyper-heuristic optimization is an evolving field of research wherein the optimization process is continuously adapted in order to provide greater improvements in the quality of the solution generated. The relative infancy of hyper-heuristic optimization has resulted in limited application within the field of aerospace design. This paper describes a framework for the mass optimization of the structural layout of an aircraft at the conceptual level of design employing a novel hyper-heuristic approach. This hyper-heuristic approach encourages solution space exploration, thus reducing the likelihood of premature convergence, and improves the feasibility of and convergence upon the best solution found. A case study is presented to illustrate the effects of hyper-heuristics on the problem for a large commercial aircraft. Resulting solutions were generated of considerably lighter mass than the baseline aircraft. A further improvement in solution quality was found with the use of the hyper-heuristics compared to that obtained without, albeit with a penalty on computation time.     

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.     

An evolutionary-based hyper-heuristic approach for the Jawbreaker puzzle

In this paper a hyper-heuristic algorithm is designed and developed for its application to the Jawbreaker puzzle. Jawbreaker is an addictive game consisting in a matrix of colored balls, that must be cleared by popping sets of balls of the same color. This puzzle is perfect to be solved by applying hyper-heuristics algorithms, since many different low-level heuristics are available, and they can be applied in a sequential fashion to solve the puzzle. We detail a set of low-level heuristics and a global search procedure (evolutionary algorithm) that conforms to a robust hyper-heuristic, able to solve very difficult instances of the Jawbreaker puzzle. We test the proposed hyper-heuristic approach in Jawbreaker puzzles of different size and difficulty, with excellent results.     

A new hyper-heuristic as a general problem solver: an implementation in HyFlex

This study provides a new hyper-heuristic design using a learning-based heuristic selection mechanism together with an adaptive move acceptance criterion. The selection process was supported by an online heuristic subset selection strategy. In addition, a pairwise heuristic hybridization method was designed. The motivation behind building an intelligent selection hyper-heuristic using these adaptive hyper-heuristic sub-mechanisms is to facilitate generality. Therefore, the designed hyper-heuristic was tested on a number of problem domains defined in a high-level framework, i.e., HyFlex. The framework provides a set of problems with a number of instances as well as a group of low-level heuristics. Thus, it can be considered a good environment to measure the generality level of selection hyper-heuristics. The computational results demonstrated the generic performance of the proposed strategy in comparison with other tested hyper-heuristics composed of the sub-mechanisms from the literature. Moreover, the performance and behavior analysis conducted for the hyper-heuristic clearly showed its adaptive characteristics under different search conditions. The principles comprising the here presented algorithm were at the heart of the algorithm that won the first international cross-domain heuristic search competition.     

Grammatical evolution as a hyper-heuristic to evolve deterministic real-valued optimization algorithms

Hyper-heuristic methodologies have been extensively and successfully used to generate combinatorial optimization heuristics. On the other hand, there have been almost no attempts to build a hyper-heuristic to evolve an algorithm for solving real-valued optimization problems. In our previous research, we succeeded to evolve a Nelder–Mead-like real function minimization heuristic using genetic programming and the primitives extracted from the original Nelder–Mead algorithm. The resulting heuristic was better than the original Nelder–Mead method in the number of solved test problems but it was slower in that it needed considerably more cost function evaluations to solve the problems also solved by the original method. In this paper we exploit grammatical evolution as a hyper-heuristic to evolve heuristics that outperform the original Nelder–Mead method in all aspects. However, the main goal of the paper is not to build yet another real function optimization algorithm but to shed some light on the influence of different factors on the behavior of the evolution process as well as on the quality of the obtained heuristics. In particular, we investigate through extensive evolution runs the influence of the shape and dimensionality of the training function, and the impact of the size limit set to the evolving algorithms. At the end of this research we succeeded to evolve a number of heuristics that solved more test problems and in fewer cost function evaluations than the original Nelder–Mead method. Our solvers are also highly competitive with the improvements made to the original method based on rigorous mathematical convergence proofs found in the literature. Even more importantly, we identified some directions in which to continue the work in order to be able to construct a productive hyper-heuristic capable of evolving real function optimization heuristics that would outperform a human designer in all aspects.     

Teaching meta-heuristics within virtual learning environments

Modern education of operations research and management science (OR/MS) can greatly benefit from interactive learning methods in order to build and develop modeling and problem‐solving skills. In this paper we consider the teaching of meta‐heuristics as an important part of OR/MS with significant recent interest. We discuss possibilities of supporting the teaching of meta‐heuristics such as simulated annealing or tabu search through interactive learning. The paper also presents a survey of some relevant issues within VORMS (Virtual Operations Research/Management Science), a project currently undertaken at six universities within Germany, and provides a presentation of the advances regarding the teaching of meta‐heuristics within this project. Further ideas refer to incorporating hotframe, a heuristic optimization framework, into the virtual learning environment.     

A Hyper-Heuristic Framework for Lifetime Maximization in Wireless Sensor Networks With A Mobile Sink

Maximizing the lifetime of wireless sensor networks(WSNs) is an important and challenging research problem. Properly scheduling the movements of mobile sinks to balance the energy consumption of wireless sensor network is one of the most effective approaches to prolong the lifetime of wireless sensor networks. However, the existing mobile sink scheduling methods either require a great amount of computational time or lack effectiveness in finding high-quality scheduling solutions. To address the above issues, this paper proposes a novel hyperheuristic framework, which can automatically construct high-level heuristics to schedule the sink movements and prolong the network lifetime. In the proposed framework, a set of low-level heuristics are defined as building blocks to construct high-level heuristics and a set of random networks with different features are designed for training. Further, a genetic programming algorithm is adopted to automatically evolve promising high-level heuristics based on the building blocks and the training networks. By using the genetic programming to evolve more effective heuristics and applying these heuristics in a greedy scheme, our proposed hyper-heuristic framework can prolong the network lifetime competitively with other methods, with small time consumption. A series of comprehensive experiments, including both static and dynamic networks,are designed. The simulation results have demonstrated that the proposed method can offer a very promising performance in terms of network lifetime and response time.     

A hybrid heuristic to solve the parallel machines job-shop scheduling problem

This paper presents an advanced software system for solving the flexible manufacturing systems (FMS) scheduling in a job-shop environment with routing flexibility, where the assignment of operations to identical parallel machines has to be managed, in addition to the traditional sequencing problem. Two of the most promising heuristics from nature for a wide class of combinatorial optimization problems, genetic algorithms (GA) and ant colony optimization (ACO), share data structures and co-evolve in parallel in order to improve the performance of the constituent algorithms. A modular approach is also adopted in order to obtain an easy scalable parallel evolutionary-ant colony framework. The performance of the proposed framework on properly designed benchmark problems is compared with effective GA and ACO approaches taken as algorithm components.     

Iterated local search heuristics for the Vehicle Routing Problem with Cross-Docking

This work addresses the Vehicle Routing Problem with Cross-Docking (VRPCD). The problem consists in defining a minimum cost set of routes for a fleet of vehicles that meets the demands of products for a set of suppliers and customers. The vehicles leave a single Cross-Dock (CD) towards the suppliers, pick up products and return to the CD, where products can be exchanged before being delivered to their customers. The vehicle routes must respect the vehicle capacity constraints, as well as the time window constraints. We adapted a constructive heuristic and six local search procedures from the literature of VRP, and made them efficient in the presence of the synchronization constraints of VRPCD. Besides, we propose three Iterated Local Search (Lourenço et al., 2010) heuristics for VRPCD. The first heuristic is a standard implementation of ILS, while the second extends the classic ILS framework by keeping a set of elite solutions, instead of a single current solution. The latter set is used in a restart procedure. As far as we can tell, this is the first ILS heuristic in the literature that keeps a population of current elite solutions. The third heuristic is an extension of the second that relies on an intensification procedure based on an Integer Programming formulation for the Set Partitioning problem. The latter allows a neighborhood with an exponential number of neighbors to be efficiently evaluated. We report computational results and comparisons with the best heuristics in the literature. Besides, we also present a new set with the largest instances in the literature of VRPCD, in order to demonstrate that the improvements we propose for the ILS metaheuristic are efficient even for large size instances. Results show that the best of our heuristics is competitive with the best heuristics in the literature of VRPCD. Besides, it improved the best solution known for half of the benchmark instances in the literature.     

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.     

A hybrid multi-population framework for dynamic environments combining online and offline learning

Population based incremental learning algorithms and selection hyper-heuristics are highly adaptive methods which can handle different types of dynamism that may occur while a given problem is being solved. In this study, we present an approach based on a multi-population framework hybridizing these methods to solve dynamic environment problems. A key feature of the hybrid approach is the utilization of offline and online learning methods at successive stages. The performance of our approach along with the influence of different heuristic selection methods used within the selection hyper-heuristic is investigated over a range of dynamic environments produced by a well known benchmark generator as well as a real world problem, referred to as the Unit Commitment Problem. The empirical results show that the proposed approach using a particular hyper-heuristic outperforms some of the best known approaches in literature on the dynamic environment problems dealt with.     

Adaptive selection of heuristics for assigning time slots and rooms in exam timetables

This paper presents an iterative adaptive approach which hybridises bin packing heuristics to assign exams to time slots and rooms. The approach combines a graph-colouring heuristic, to select an exam in every iteration, with bin-packing heuristics to automate the process of time slot and room allocation for exam timetabling problems. We start by analysing the quality of the solutions obtained by using one heuristic at a time. Depending on the individual performance of each heuristic, a random iterative hyper-heuristic is used to randomly hybridise the heuristics and produce a collection of heuristic sequences to construct solutions with different quality. Based on these sequences, we analyse the way in which the bin packing heuristics are automatically hybridised. It is observed that the performance of the heuristics used varies depending on the problem. Based on these observations, an iterative hybrid approach is developed to adaptively choose and hybridise the heuristics during solution construction. The overall aim here is to automate the heuristic design process, which draws upon an emerging research theme which is concerned with developing methods to design and adapt heuristics automatically. The approach is tested on the exam timetabling track of the second International Timetabling Competition, to evaluate its ability to generalise on instances with different features. The hyper-heuristic with low-level graph-colouring and bin-packing heuristics approach was found to generalise well over all the problem instances and performed comparably to the state of the art approaches.     

进化式超启发算法求解多车型低碳选址-路径问题

为了降低物流配送成本和减少CO$_2$排放量,提出一种综合考虑多车型和同时取送货的低碳选址-路径问题,并构建三维指数混合整数规划模型.针对所提问题,设计一种进化式超启发式求解算法,即在超启发式算法框架下,采用进化式策略作为高层学习策略,以实时准确地监控底层算子的性能信息并选择合适的底层算子,包括量子选择、蚂蚁策略、蛙跳机制以及自然竞争等.同时,挖掘算子性能信息以构建自适应接收机制,引导全局搜索,加快算法收敛速度.通过对不同规模实例的仿真实验与对比分析,验证了4种进化式超启发式算法在求解物流配送多车型同时取送货低碳选址-路径问题模型上的有效性与鲁棒性.     

An iterated local search algorithm for the permutation flowshop problem with total flowtime criterion

An ILS algorithm is proposed to solve the permutation flowshop sequencing problem with total flowtime criterion. The effects of different initial permutations and different perturbation strengths are studied. Comparisons are carried out with three constructive heuristics, three ant-colony algorithms and a particle swarm optimization algorithm. Experiments on benchmarks and a set of random instances show that the proposed algorithm is more effective. The presented ILS improves the best known permutations by a significant margin.     

Robust hyper-heuristic algorithms for the offline oriented/non-oriented 2D bin packing problems

The offline 2D bin packing problem (2DBPP) is an NP-hard combinatorial optimization problem in which objects with various width and length sizes are packed into minimized number of 2D bins. Various versions of this well-known industrial engineering problem can be faced frequently. Several heuristics have been proposed for the solution of 2DBPP but it has not been possible to find the exact solutions for large problem instances. Next fit, first fit, best fit, unified tabu search, genetic and memetic algorithms are some of the state-of-the-art methods successfully applied to this important problem. In this study, we propose a set of novel hyper-heuristic algorithms that select/combine the state-of-the-art heuristics and local search techniques for minimizing the number of 2D bins. The proposed algorithms introduce new crossover and mutation operators for the selection of the heuristics. Through the results of exhaustive experiments on a set of offline 2DBPP benchmark problem instances, we conclude that the proposed algorithms are robust with their ability to obtain high percentage of the optimal solutions.