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.     

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.     

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.     

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.     

Decomposition-based multi-objective evolutionary algorithm for vehicle routing problem with stochastic demands

Vehicle routing problem with stochastic demands (VRPSD) is a famous and challenging optimization problem which is similar to many real world problems. To resemble the real world scenario, total traveling distance, total driver remuneration, the number of vehicles used and the difference between driver remuneration are considered and formulated in the multi-objective optimization perspective. This paper aims to solve multi-objective VRPSD under the constraints of available time window and vehicle capacity using decomposition-based multi-objective evolutionary algorithm (MOEA/D) with diversity-loss-based selection method incorporates with local search and multi-mode mutation heuristics. We have also compared the optimization performance of the decomposition-based approach with the domination-based approach to study the difference between these two well-known evolutionary multi-objective algorithm frameworks. The simulation results have showed that the decomposition-based approach with diversity-loss-based selection method is able to maintain diverse output solutions.     

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.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

基于自变量简约的大规模稀疏多目标优化

现有的大多数进化算法在求解大规模优化问题时性能会随决策变量维数的增长而下降。通常,多目标优化的Pareto有效解集是自变量空间的一个低维流形,该流形的维度远小于自变量空间的维度。鉴于此,提出一种基于自变量简约的多目标进化算法求解大规模稀疏多目标优化问题。该算法通过引入局部保持投影降维,保留原始自变量空间中的局部近邻关系,并设计一个归档集,将寻找到的非劣解存入其中进行训练,以提高投影的准确性。将该算法与四种流行的多目标进化算法在一系列测试问题和实际应用问题上进行了比较。实验结果表明,所提算法在解决稀疏多目标问题上具有较好的效果。因此,通过自变量简约能降低问题的求解难度,提高算法的搜索效率,在解决大规模稀疏多目标问题方面具有显著的优势。     

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 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 hyper-heuristic based framework for dynamic optimization problems

Most of the real world problems have dynamic characteristics, where one or more elements of the underlying model for a given problem including the objective, constraints or even environmental parameters may change over time. Hyper-heuristics are problem-independent meta-heuristic techniques that are automating the process of selecting and generating multiple low-level heuristics to solve static combinatorial optimization problems. In this paper, we present a novel hybrid strategy for applicability of hyper-heuristic techniques on dynamic environments by integrating them with the memory/search algorithm. The memory/search algorithm is an important evolutionary technique that have applied on various dynamic optimization problems. We validate performance of our method by considering both the dynamic generalized assignment problem and the moving peaks benchmark. The former problem is extended from the generalized assignment problem by changing resource consumptions, capacity constraints and costs of jobs over time; and the latter one is a well-known synthetic problem that generates and updates a multidimensional landscape consisting of several peaks. Experimental evaluation performed on various instances of the given two problems validates that our hyper-heuristic integrated framework significantly outperforms the memory/search algorithm.     

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。     

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.     

基于灰色综合关联分析的多目标优化方法

针对现有多目标优化方法存在的搜索性能弱、效率低等问题,提出一种基于灰色综合关联分析的多目标优化方法.该多目标优化方法采用单目标优化算法构建高质量的参考序列,计算参考序列与优化解的目标函数值序列之间的灰色综合关联度,定义基于灰色综合关联度的解支配关系准则,将灰色综合关联度作为多目标优化算法的适应度值.以带顺序相关调整时间的多目标流水车间调度问题作为应用对象,建立总生产成本、最大完工时间、平均流程时间及机器平均闲置时间的多目标函数优化模型.提出基于灰色关联分析的多目标烟花算法,对所建立的多目标优化模型进行优化求解.仿真实验表明,所提出多目标烟花算法的性能优于3种基于不同多目标优化方法的烟花算法及两种经典多目标算法,验证了所提出的多目标优化方法及多目标算法的可行性和有效性.     

A self-adaptive multi-objective harmony search algorithm based on harmony memory variance

Although harmony search (HS) algorithm has shown many advantages in solving global optimization problems, its parameters need to be set by users according to experience and problem characteristics. This causes great difficulties for novice users. In order to overcome this difficulty, a self-adaptive multi-objective harmony search (SAMOHS) algorithm based on harmony memory variance is proposed in this paper. In the SAMOHS algorithm, a modified self-adaptive bandwidth is employed, moreover, the self-adaptive parameter setting based on variation of harmony memory variance is proposed for harmony memory considering rate (HMCR) and pitch adjusting rate (PAR). To solve multi-objective optimization problems (MOPs), the proposed SAMOHS uses non-dominated sorting and truncating procedure to update harmony memory (HM). To demonstrate the effectiveness of the SAMOHS, it is tested with many benchmark problems and applied to solve a practical engineering optimization problem. The experimental results show that the SAMOHS is competitive in convergence performance and diversity performance, compared with other multi-objective evolutionary algorithms (MOEAs). In the experiment, the impact of harmony memory size (HMS) on the performance of SAMOHS is also analyzed.     

Hybridizing a multi-objective simulated annealing algorithm with a multi-objective evolutionary algorithm to solve a multi-objective project scheduling problem

In this paper, a multi-objective project scheduling problem is addressed. This problem considers two conflicting, priority optimization objectives for project managers. One of these objectives is to minimize the project makespan. The other objective is to assign the most effective set of human resources to each project activity. To solve the problem, a multi-objective hybrid search and optimization algorithm is proposed. This algorithm is composed by a multi-objective simulated annealing algorithm and a multi-objective evolutionary algorithm. The multi-objective simulated annealing algorithm is integrated into the multi-objective evolutionary algorithm to improve the performance of the evolutionary-based search. To achieve this, the behavior of the multi-objective simulated annealing algorithm is self-adaptive to either an exploitation process or an exploration process depending on the state of the evolutionary-based search. The multi-objective hybrid algorithm generates a number of near non-dominated solutions so as to provide solutions with different trade-offs between the optimization objectives to project managers. The performance of the multi-objective hybrid algorithm is evaluated on nine different instance sets, and is compared with that of the only multi-objective algorithm previously proposed in the literature for solving the addressed problem. The performance comparison shows that the multi-objective hybrid algorithm significantly outperforms the previous multi-objective algorithm.     

C-PSA: Constrained Pareto simulated annealing for constrained multi-objective optimization

In recent years, evolutionary algorithms (EAs) have been extensively developed and utilized to solve multi-objective optimization problems. However, some previous studies have shown that for certain problems, an approach which allows for non-greedy or uphill moves (unlike EAs), can be more beneficial. One such approach is simulated annealing (SA). SA is a proven heuristic for solving numerical optimization problems. But owing to its point-to-point nature of search, limited efforts has been made to explore its potential for solving multi-objective problems. The focus of the presented work is to develop a simulated annealing algorithm for constrained multi-objective problems. The performance of the proposed algorithm is reported on a number of difficult constrained benchmark problems. A comparison with other established multi-objective optimization algorithms, such as infeasibility driven evolutionary algorithm (IDEA), Non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective Scatter search II (MOSS-II) has been included to highlight the benefits of the proposed approach.     

模糊时间窗VRP的动态规划和禁忌搜索混合算法

为优化具有模糊时间窗的车辆路径问题,以物流配送成本和顾客平均满意度为目标,建立了多目标数学规划模型。基于Pareto占优的理论给出了求解多目标优化问题的并行多目标禁忌搜索算法,算法中嵌入同时优化顾客满意度的动态规划方法,运用阶段划分,把原问题分解为关于紧路径的优化子问题。对模糊时间窗为线性分段函数形式和非线性凹函数形式的隶属度函数,分别提出了次梯度有限迭代算法和次梯度中值迭代算法来优化顾客的最优开始服务时间。通过Solomon的标准算例,与次梯度投影算法的比较验证了动态规划方法优化服务水平的有效性,与主流的NSGA-II算法的对比实验表明了该研究提出的多目标禁忌搜索算法的优越性。     

A self-organized speciation based multi-objective particle swarm optimizer for multimodal multi-objective problems

This paper proposes a self-organized speciation based multi-objective particle swarm optimizer (SS-MOPSO) to locate multiple Pareto optimal solutions for solving multimodal multi-objective problems. In the proposed method, the speciation strategy is used to form stable niches and these niches/subpopulations are optimized to search and maintain Pareto-optimal solutions in parallel. Moreover, a self-organized mechanism is proposed to improve the efficiency of the species formulation as well as the performance of the algorithm. To maintain the diversity of the solutions in both the decision and objective spaces, SS-MOPSO is incorporated with the non-dominated sorting scheme and special crowding distance techniques. The performance of SS-MOPSO is compared with a number of the state-of-the-art multi-objective optimization algorithms on fourteen test problems. Moreover, the proposed SS-MOSPO is also employed to solve a real-life problem. The experimental results suggest that the proposed algorithm is able to solve the multimodal multi-objective problems effectively and shows superior performance by finding more and better distributed Pareto solutions.     

Spiral water cycle algorithm for solving multi-objective optimization and truss optimization problems

This paper addresses multi-objective optimization and the truss optimization problem employing a novel meta-heuristic that is based on the real-world water cycle behavior in rivers, rainfalls, streams, etc. This meta-heuristic is called multi-objective water cycle algorithm (MOWCA) which is receiving great attention from researchers due to the good performance in handling optimization problems in different fields. Additionally, the hyperbolic spiral movement is integrated into the basic MOWCA to guide the agents throughout the search space. Consequently, under this hyperbolic spiral movement, the exploitation ability of the proposed MOSWCA is promoted. To assess the robustness and coherence of the MOSWCA, the performance of the proposed MOSWCA is analysed on some multi-objective optimisation benchmark functions; and three truss structure optimization problems. The results obtained by the MOSWCA of all test problems were compared with various multi-objective meta-heuristic algorithms reported in the literature. From the empirical results, it is evident that the suggested approach reaches an excellent performance when solving multi-objective optimization and the truss optimization problems.