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.     

Choice function based hyper-heuristics for multi-objective optimization

A selection hyper-heuristic is a high level search methodology which operates over a fixed set of low level heuristics. During the iterative search process, a heuristic is selected and applied to a candidate solution in hand, producing a new solution which is then accepted or rejected at each step. Selection hyper-heuristics have been increasingly, and successfully, applied to single-objective optimization problems, while work on multi-objective selection hyper-heuristics is limited. This work presents one of the initial studies on selection hyper-heuristics combining a choice function heuristic selection methodology with great deluge and late acceptance as non-deterministic move acceptance methods for multi-objective optimization. A well-known hypervolume metric is integrated into the move acceptance methods to enable the approaches to deal with multi-objective problems. The performance of the proposed hyper-heuristics is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, they are applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the non-deterministic move acceptance, particularly great deluge when used as a component of a choice function based selection hyper-heuristic.     

Iterated local search using an add and delete hyper-heuristic for university course timetabling

Hyper-heuristics are (meta-)heuristics that operate at a higher level to choose or generate a set of low-level (meta-)heuristics in an attempt of solve difficult optimization problems. Iterated local search (ILS) is a well-known approach for discrete optimization, combining perturbation and hill-climbing within an iterative framework. In this study, we introduce an ILS approach, strengthened by a hyper-heuristic which generates heuristics based on a fixed number of add and delete operations. The performance of the proposed hyper-heuristic is tested across two different problem domains using real world benchmark of course timetabling instances from the second International Timetabling Competition Tracks 2 and 3. The results show that mixing add and delete operations within an ILS framework yields an effective hyper-heuristic approach.     

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.     

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 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.     

Case-based heuristic selection for timetabling problems

This paper presents a case-based heuristic selection approach for automated university course and exam timetabling. The method described in this paper is motivated by the goal of developing timetabling systems that are fundamentally more general than the current state of the art. Heuristics that worked well in previous similar situations are memorized in a case base and are retrieved for solving the problem in hand. Knowledge discovery techniques are employed in two distinct scenarios. Firstly, we model the problem and the problem solving situations along with specific heuristics for those problems. Secondly, we refine the case base and discard cases which prove to be non-useful in solving new problems. Experimental results are presented and analyzed. It is shown that case based reasoning can act effectively as an intelligent approach to learn which heuristics work well for particular timetabling situations. We conclude by outlining and discussing potential research issues in this critical area of knowledge discovery for different difficult timetabling problems.     

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.     

Integrating neural networks and logistic regression to underpin hyper-heuristic search

A hyper-heuristic often represents a heuristic search method that operates over a space of heuristic rules. It can be thought of as a high level search methodology to choose lower level heuristics. Nearly 200 papers on hyper-heuristics have recently appeared in the literature. A common theme in this body of literature is an attempt to solve the problems in hand in the following way: at each decision point, first employ the chosen heuristic(s) to generate a solution, then calculate the objective value of the solution by taking into account all the constraints involved. However, empirical studies from our previous research have revealed that, under many circumstances, there is no need to carry out this costly 2-stage determination and evaluation at all times. This is because many problems in the real world are highly constrained with the characteristic that the regions of feasible solutions are rather scattered and small. Motivated by this observation and with the aim of making the hyper-heuristic search more efficient and more effective, this paper investigates two fundamentally different data mining techniques, namely artificial neural networks and binary logistic regression. By learning from examples, these techniques are able to find global patterns hidden in large data sets and achieve the goal of appropriately classifying the data. With the trained classification rules or estimated parameters, the performance (i.e. the worth of acceptance or rejection) of a resulting solution during the hyper-heuristic search can be predicted without the need to undertake the computationally expensive 2-stage of determination and calculation. We evaluate our approaches on the solutions (i.e. the sequences of heuristic rules) generated by a graph-based hyper-heuristic proposed for exam timetabling problems. Time complexity analysis demonstrates that the neural network and the logistic regression method can speed up the search significantly. We believe that our work sheds light on the development of more advanced knowledge-based decision support systems.     

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.     

Hyper-heuristics with low level parameter adaptation

Recent years have witnessed the great success of hyper-heuristics applying to numerous real-world applications. Hyper-heuristics raise the generality of search methodologies by manipulating a set of low level heuristics (LLHs) to solve problems, and aim to automate the algorithm design process. However, those LLHs are usually parameterized, which may contradict the domain independent motivation of hyper-heuristics. In this paper, we show how to automatically maintain low level parameters (LLPs) using a hyper-heuristic with LLP adaptation (AD-HH), and exemplify the feasibility of AD-HH by adaptively maintaining the LLPs for two hyper-heuristic models. Furthermore, aiming at tackling the search space expansion due to the LLP adaptation, we apply a heuristic space reduction (SAR) mechanism to improve the AD-HH framework. The integration of the LLP adaptation and the SAR mechanism is able to explore the heuristic space more effectively and efficiently. To evaluate the performance of the proposed algorithms, we choose the p-median problem as a case study. The empirical results show that with the adaptation of the LLPs and the SAR mechanism, the proposed algorithms are able to achieve competitive results over the three heterogeneous classes of benchmark instances.     

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.     

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.     

A graph coloring constructive hyper-heuristic for examination timetabling problems

In this work we investigate a new graph coloring constructive hyper-heuristic for solving examination timetabling problems. We utilize the hierarchical hybridizations of four low level graph coloring heuristics, these being largest degree, saturation degree, largest colored degree and largest enrollment. These are hybridized to produce four ordered lists. For each list, the difficulty index of scheduling the first exam is calculated by considering its order in all lists to obtain a combined evaluation of its difficulty. The most difficult exam to be scheduled is scheduled first (i.e. the one with the minimum difficulty index). To improve the effectiveness of timeslot selection, a?roulette wheel selection mechanism is included in the algorithm to probabilistically select an appropriate timeslot for the chosen exam. We test our proposed approach on the most widely used un-capacitated Carter benchmarks and also on the recently introduced examination timetable dataset from the 2007 International Timetabling Competition. Compared against other methodologies, our results demonstrate that the graph coloring constructive hyper-heuristic produces good results and outperforms other approaches on some of the benchmark instances.     

混合流水车间插单重调度的超启发式遗传算法

针对带有紧急订单的混合流水车间插单重调度问题,提出了一种双层编码的超启发式遗传算法。针对混合流水车间具有的订单排序和机器选择的双决策特征,在算法低层设计双层编码方案,在个体中表示订单排序和机器选择两类信息,对应一个唯一调度解,进而提出了12种排序和选择启发式对个体进行迭代优化;在算法高层采用自适应遗传算法,用来确定订单排序启发式和机器选择启发式的操作组合以及各组合执行的次序,并设计了自适应变异算子来优化算法的有效性。大规模数据实验的结果表明,所提算法具有很好的求解质量和求解效率。     

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.     

A unified hyper-heuristic framework for solving bin packing problems

One- and two-dimensional packing and cutting problems occur in many commercial contexts, and it is often important to be able to get good-quality solutions quickly. Fairly simple deterministic heuristics are often used for this purpose, but such heuristics typically find excellent solutions for some problems and only mediocre ones for others. Trying several different heuristics on a problem adds to the cost. This paper describes a hyper-heuristic methodology that can generate a fast, deterministic algorithm capable of producing results comparable to that of using the best problem-specific heuristic, and sometimes even better, but without the cost of trying all the heuristics. The generated algorithm handles both one- and two-dimensional problems, including two-dimensional problems that involve irregular concave polygons. The approach is validated using a large set of 1417 such problems, including a new benchmark set of 480 problems that include concave polygons.     

Quantifying Heuristics in the Ordinal Optimization Framework

Finding the optimal design for a discrete event dynamic system (DEDS) is in general difficult due to the large search space and the simulation-based performance evaluation. Various heuristics have been developed to find good designs. An important question is how to quantify the goodness of the heuristic designs. Inspired by the Ordinal Optimization, which has become an important tool for optimizing DEDS, we provide a method which can quantify the goodness of the design. By comparing with a set of designs that are uniformly sampled, we measure the ordinal performances of heuristic designs, i.e., we quantify the ranks of all (or some of) the heuristic designs among all the designs in the entire search space. The mathematical tool we use is the Hypothesis Testing, and the probability of making Type II error in the quantification is controlled to be under a very low level. The method can be used both when the performances of the designs can be accurately evaluated and when such performances are estimated by a crude but computationally easy model. The method can quantify both heuristics that output a single design and that output a set of designs. The method is demonstrated through numerical examples.     

Timetabling through Constrained Heuristic Search and Genetic Algorithms

Hybrid genetic algorithms are presented that use constrained heuristic search and genetic techniques for the timetabling problem (TP). The TP is an NP-hard problem for which a general polynomial time deterministic algorithm is not known. The paper describes the classification of constraints and the constraint ordering to obtain the minimization of backtracking and the maximization of parallelism. The school timetabling problem is discussed in detail as a case study. The genetic algorithm approach is particularly well suited to this kind of problem, since there exists an easy way to assess a good timetable, but not a well structured automatic technique for constructing it. So, a population of timetables is created that evolves toward the best solution. The evaluation function and the genetic operators are well separated from the domain-specific parts, such as the knowledge of the problem and the heuristics, i.e. from the timetable builder. The present paper illustrates an approach based on the hybridization of constrained heuristic search with novel genetic algorithm techniques. It compares favourably with known programs to solve decision problems under logic constraints. The cost of the new algorithm and the quality of the solutions obtained in significant experiments are reported.     

Hybrid genetic algorithms for timetabling

Hybrid genetic algorithms are presented that use optimization heuristics and genetic techniques to outperform all existing programs for the timetabling problem. The timetabling problem is very hard (NP-complete) and a general polynomial time deterministic algorithm is not known. An artificial intelligence approach, in a logic programming environment, may be useful for such a problem. The decomposition and classification of constraints and the constraint ordering to obtain the minimization of the backtracking and the maximization of the parallelism are illustrated. The school timetabling problem is discussed in detail as a case study. The genetic algorithm approach is particularly well suited for this kind of problem, since there exists an easy way to assess a good timetable but not a well-structured automatic technique for constructing it. So, a population of timetables is created that evolves toward the best solutions. The evaluation function and the genetic operators are well separated from the domain-specific parts, such as the problem knowledge and the heuristics, i.e., from the timetable builder. A fundamental issue and a general problem in the decision process and automated reasoning is how to efficiently obtain logic decisions under disjunctive constraints. Logic constraint satisfaction problems are in general NP-hard and a general deterministic polynomial time algorithm is not known. The present article illustrates an approach based on the hybridization of constrained heuristic search with novel genetic algorithm techniques. It compares favorably with the best-known programs to solve decisions problems under logic constraints. Complexity of the new algorithms and results of significant experiments are reported. © 1996 John Wiley & Sons, Inc.