An iterated local search for the multi-objective permutation flowshop scheduling problem with sequence-dependent setup times

Due to its simplicity yet powerful search ability, iterated local search (ILS) has been widely used to tackle a variety of single-objective combinatorial optimization problems. However, applying ILS to solve multi-objective combinatorial optimization problems is scanty. In this paper we design a multi-objective ILS (MOILS) to solve the multi-objective permutation flowshop scheduling problem with sequence-dependent setup times to minimize the makespan and total weighted tardiness of all jobs. In the MOILS, we design a Pareto-based variable depth search in the multi-objective local search phase. The search depth is dynamically adjusted during the search process of the MOILS to strike a balance between exploration and exploitation. We incorporate an external archive into the MOILS to store the non-dominated solutions and provide initial search points for the MOILS to escape from local optima traps. We compare the MOILS with several multi-objective evolutionary algorithms (MOEAs) shown to be effective for treating the multi-objective permutation flowshop scheduling problem in the literature. The computational results show that the proposed MOILS outperforms the MOEAs.     

Using iterated local search for solving the flow‐shop problem: Parallelization,parametrization, and randomization issues

Iterated local search (ILS) is a powerful framework for developing efficient algorithms for the permutation flow‐shop problem (PFSP). These algorithms are relatively simple to implement and use very few parameters, which facilitates the associated fine‐tuning process. Therefore, they constitute an attractive solution for real‐life applications. In this paper, we discuss some parallelization, parametrization, and randomization issues related to ILS‐based algorithms for solving the PFSP. In particular, the following research questions are analyzed: (a) Is it possible to simplify even more the parameter setting in an ILS framework without affecting performance? (b) How do parallelized versions of these algorithms behave as we simultaneously vary the number of different runs and the computation time? (c) For a parallelized version of these algorithms, is it worthwhile to randomize the initial solution so that different starting points are considered? (d) Are these algorithms affected by the use of a “good‐quality” pseudorandom number generator? In this paper, we introduce the new ILS‐ESP (where ESP is efficient, simple, and parallelizable) algorithm that is specifically designed to take advantage of parallel computing, allowing us to obtain competitive results in “real time” for all tested instances. The ILS‐ESP also uses “natural” parameters, which simplifies the calibration process. An extensive set of computational experiments has been carried out in order to answer the aforementioned research questions.     

带释放时间的并行机调度问题的ILS & SS算法

研究工件带释放时间的两类并行机最小化总完成时间的调度问题.针对问题提出了一种新的基于变深度环交换邻域结构的Iterated local search(ILS)算法.1)提出了变深度环交换邻域结构.2)基于变深度环交换和传统Swap的混合邻域,提出了带有两种kick策略的ILS算法.3)为了加强ILS逃出局部最优的能力,将Scatter search (SS)搜索方法引入了ILS算法中;算法将当前最好解和次好解进行分散处理,再从处理后的解开始继续迭代.为了验证算法的有效性,对两类并行机问题分别随机产生100组数据进行试验.实验结果表明:对于同构并行机问题,引入SS的ILS算法的计算结果与下界的平均偏差为0.99%,而没有引入SS的ILS算法的为1.06%;对于无关并行机问题,引入SS搜索方法后,ILS算法的计算结果 改进了6.06%,并明显优于多点下降算法.     

An iterative local search approach based on fitness landscapes analysis for the delay-constrained multicast routing problem

This paper presents the first fitness landscape analysis on the delay-constrained least-cost multicast routing problem (DCLC-MRP). Although the problem has attracted an increasing research attention over the past decade in telecommunications and operational research, little research has been conducted to analyze the features of its underlying landscape. Two of the most commonly used landscape analysis techniques, the fitness distance correlation analysis and the autocorrelation analysis, have been applied to analyze the global and local landscape features of DCLC-MRPs. A large amount of simulation experiments on a set of problem instances generated based on the benchmark Steiner tree problems in the OR-library reveals that the landscape of the DCLC-MRP is highly instance dependent with different landscape features. Different delay bounds also affect the distribution of solutions in the search space. The autocorrelation analysis on the benchmark instances of different sizes and delay bounds shows the impact of different local search heuristics and neighborhood structures on the fitness distance landscapes of the DCLC-MRP. The delay bound constraint in the DCLC-MRP has shown a great influence on the underlying landscape characteristic of the problem. Based on the fitness landscape analysis, an iterative local search (ILS) approach is proposed in this paper for the first time to tackle the DCLC-MRP. Computational results demonstrate the effectiveness of the proposed ILS algorithm for the problem in comparison with other algorithms in the literature.     

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.     

An evolutionary tabu search for cell image segmentation

Many engineering problems can be formulated as optimization problems. It has become more and more important to develop an efficient global optimization technique for solving these problems. In this paper, we propose an evolutionary tabu search (ETS) for cell image segmentation. The advantages of genetic algorithms (GA) and TS algorithms are incorporated into the proposed method. More precisely, we incorporate "the survival of the fittest" from evolutionary algorithms into TS. The method has been applied to the segmentation of several kinds of cell images. The experimental results show that the new algorithm is a practical and effective one for global optimization; it can yield good, near-optimal solutions and has better convergence and robustness than other global optimization approaches.     

Local search based metaheuristics for the robust vehicle routing problem with discrete scenarios

The Capacitated Vehicle Routing Problem (CVRP) is extended here to handle uncertain arc costs without resorting to probability distributions, giving the Robust VRP (RVRP). The unique set of arc costs in the CVRP is replaced by a set of discrete scenarios. A scenario is for instance the travel time observed on each arc at a given traffic hour. The goal is to build a set of routes using the lexicographic min–max criterion: the worst cost over all scenarios is minimized but ties are broken using the other scenarios, from the worst to the best. This version of robust CVRP has never been studied before. A Mixed Integer Linear Program (MILP), two greedy heuristics, a local search and four metaheuristics are proposed: a Greedy Randomized Adaptive Search Procedure, an Iterated Local Search (ILS), a Multi-Start ILS (MS-ILS), and an MS-ILS based on Giant Tours (MS-ILS-GT) converted into feasible routes via a lexicographic splitting procedure. The greedy heuristics provide the other algorithms with good initial solutions. Tests on small instances (10–20 customers, 2–3 vehicles, 10–30 scenarios) show that the four metaheuristics retrieve all optima found by the MILP. On larger cases with 50–100 customers, 5–20 vehicles and 10–20 scenarios, MS-ILS-GT dominates the other approaches. As our algorithms share the same components (initial heuristic, local search), the positive contribution of using the giant tour approach is confirmed on the RVRP.     

A Multi-Objective Integer Melody Search Algorithm

There are a number of algorithms for the solution of continuous optimization problems. However, many practical design optimization problems use integer design variables instead of continuous. These types of problems cannot be handled by using continuous design variables-based algorithms. In this paper, we present a multi-objective integer melody search optimization algorithm (MO-IMS) for solving multi-objective integer optimization problems, which take design variables as integers. The proposed algorithm is a modified version of single-objective melody search (MS) algorithm, which is an innovative optimization algorithm, inspired by basic concepts applied in harmony search (HS) algorithm. Results show that MO-IMS has better performance in solving multi-objective integer problems than the existing multi-objective integer harmony search algorithm (MO-IHS). Performance of proposed algorithm is evaluated by using various performance metrics on test functions. The simulation results show that the proposed MO-IMS can be a better technique for solving multi-objective problems having integer decision variables.     

MAGMA: a multiagent architecture for metaheuristics

In this work, we introduce a multiagent architecture called the MultiAGent Metaheuristic Architecture (MAGMA) conceived as a conceptual and practical framework for metaheuristic algorithms. Metaheuristics can be seen as the result of the interaction among different kinds of agents: The basic architecture contains three levels, each hosting one or more agents. Level-0 agents build solutions, level-1 agents improve solutions, and level-2 agents provide the high level strategy. In this framework, classical metaheuristic algorithms can be smoothly accommodated and extended. The basic three level architecture can be enhanced with the introduction of a fourth level of agents (level-3 agents) coordinating lower level agents. With this additional level, MAGMA can also describe, in a uniform way, cooperative search and, in general, any combination of metaheuristics. We describe the entire architecture, the structure of agents in each level in terms of tuples, and the structure of their coordination as a labeled transition system. We propose this perspective with the aim to achieve a better and clearer understanding of metaheuristics, obtain hybrid algorithms, suggest guidelines for a software engineering-oriented implementation and for didactic purposes. Some specializations of the general architecture will be provided in order to show that existing metaheuristics [e.g., greedy randomized adaptive procedure (GRASP), ant colony optimization (ACO), iterated local search (ILS), memetic algorithms (MAs)] can be easily described in our framework. We describe cooperative search and large neighborhood search (LNS) in the proposed framework exploiting level-3 agents. We show also that a simple hybrid algorithm, called guided restart ILS, can be easily conceived as a combination of existing components in our framework.     

Using metaheuristic algorithms for parameter estimation in generalized Mallows models

This paper deals with the problem of parameter estimation in the generalized Mallows model (GMM) by using both local and global search metaheuristic (MH) algorithms. The task we undertake is to learn parameters for defining the GMM from a dataset of complete rankings/permutations. Several approaches can be found in the literature, some of which are based on greedy search and branch and bound search. The greedy approach has the disadvantage of usually becoming trapped in local optima, while the branch and bound approach, basically A^* search, usually comes down to approximate search because of memory requirements, losing in this way its guaranteed optimality. Here, we carry out a comparative study of several MH algorithms (iterated local search (ILS) methods, variable neighborhood search (VNS) methods, genetic algorithms (GAs) and estimation of distribution algorithms (EDAs)) and a tailored algorithm A^* to address parameter estimation in GMMs. We use 22 real datasets of different complexity, all but one of which were created by the authors by preprocessing real raw data. We provide a complete analysis of the experiments in terms of accuracy, number of iterations and CPU time requirements.     

Scatter search for mixed blocking flowshop scheduling

Empty or limited storage capacities between machines introduce various types of blocking constraint in the industries with flowshop environment. While large applications demand flowshop scheduling with a mix of different types of blocking, research in this area mainly focuses on using only one kind of blocking in a given problem instance. In this paper, using makespan as a criterion, we study permutation flowshops with zero capacity buffers operating under mixed blocking conditions. We present a very effective scatter search (SS) algorithm for this. At the initialisation phase of SS, we use a modified version of the well-known Nawaz, Enscore and Ham (NEH) heuristic. For the improvement method in SS, we use an Iterated Local Search (ILS) algorithm that adopts a greedy job selection and a powerful NEH-based perturbation procedure. Moreover, in the reference set update phase of SS, with small probabilities, we accept worse solutions so as to increase the search diversity. On standard benchmark problems of varying sizes, our algorithm very significantly outperforms well-known existing algorithms in terms of both the solution quality and the computing time. Moreover, our algorithm has found new upper bounds for 314 out of 360 benchmark problem instances.     

基于增强型kick策略的ILS算法求解一类聚类问题

提出一种新型的基于环交换邻域的迭代局部搜索算（ILS）．用于求解一类聚类问题,算法的主要特点是：1）基于环交换的邻域结构;环交换邻域与传统的Swap和Insert邻域相比,算法在一次迭代中允许多个点同时移动;2）针对聚类问题提出了增强型的kick移动策略：根据每组内点的密度分布摄动聚类中心,对给定的解重新聚类,实验结果表明,基于环交换的迭代局部搜索算法对求解该类聚类问题是有效的．     

Search Algorithms for Regression Test Case Prioritization

Regression testing is an expensive, but important, process. Unfortunately, there may be insufficient resources to allow for the reexecution of all test cases during regression testing. In this situation, test case prioritization techniques aim to improve the effectiveness of regression testing by ordering the test cases so that the most beneficial are executed first. Previous work on regression test case prioritization has focused on greedy algorithms. However, it is known that these algorithms may produce suboptimal results because they may construct results that denote only local minima within the search space. By contrast, metaheuristic and evolutionary search algorithms aim to avoid such problems. This paper presents results from an empirical study of the application of several greedy, metaheuristic, and evolutionary search algorithms to six programs, ranging from 374 to 11,148 lines of code for three choices of fitness metric. The paper addresses the problems of choice of fitness metric, characterization of landscape modality, and determination of the most suitable search technique to apply. The empirical results replicate previous results concerning greedy algorithms. They shed light on the nature of the regression testing search space, indicating that it is multimodal. The results also show that genetic algorithms perform well, although greedy approaches are surprisingly effective, given the multimodal nature of the landscape     

基于局部搜索的反向学习竞争粒子群优化算法

为提升粒子群优化算法在复杂优化问题,特别是高维优化问题上的优化性能,提出一种基于Solis&Wets局部搜索的反向学习竞争粒子群优化算法(solis and wets-opposition based learning competitive particle swarm optimizer with local search, SW-OBLCSO). SW-OBLCSO算法采用竞争学习和反向学习两种学习机制,并设计了基于个体的局部搜索算子.利用10个常用基准测试函数和12个带有偏移旋转的复杂测试函数,在不同维度情况下将SW-OBLCSO算法与多种优化算法进行对比.实验结果表明,所提出算法在收敛速度和全局搜索能力上表现出突出的性能.对模糊认知图(fuzzy cognitive maps)学习问题的测试表明, SW-OBLCSO算法在处理实际问题时同样具有出色的性能.     

基于分解的高维多目标改进进化算法

针对基于参考向量的高维多目标进化算法中随机选择父代个体会降低算法的收敛速度,以及部分参考向量分配个体的缺失会减弱种群多样性的问题,提出了一种基于分解的高维多目标改进优化算法（IMaOEA/D）。首先,在分解策略框架下,当一个参考向量至少分配了2个个体时,对该参考向量分配的个体根据其到理想点的距离选择父代个体来繁殖子代,从而提高搜索速度。然后,针对未能分配到至少2个个体的参考向量,则从所有个体中选择沿该参考向量和理想点距离最小的点,使得该参考向量至少有2个个体与其相关。同时,确保环境选择后每个参考向量有一个个体与其相关,从而保证种群的多样性。在10个和15个目标的MaF测试问题集上将所提算法与其他4个基于分解的高维多目标优化算法进行了测试对比,实验结果表明所提算法对于高维多目标优化问题具有较好的寻优能力,且该算法在30个测试问题中的14个测试问题上得到的优化结果均优于其他4个对比算法,特别是对于退化问题具有一定的寻优优势。     

Finite element based hybrid evolutionary optimization approach to solving rigid pavement inversion problem

This paper focuses on the development of a new backcalculation method for concrete road structures based on a hybrid evolutionary global optimization algorithm, namely shuffled complex evolution (SCE). Evolutionary optimization algorithms are ideally suited for intrinsically multi-modal, non-convex, and discontinuous real-world problems such as pavement backcalculation because of their ability to explore very large and complex search spaces and locate the globally optimal solution using a parallel search mechanism as opposed to a point-by-point search mechanism employed by traditional optimization algorithms. SCE, a type of evolutionary optimization algorithms based on the tradeoff of exploration and exploitation, has proved to be an efficient method for many global optimization problems and in some cases it does not suffer the difficulties encountered by other evolutionary computation techniques. The SCE optimization approach is hybridized with a neural networks surrogate finite-element based forward pavement response model to enable rapid computation of global or near-global pavement layer moduli solutions. The proposed rigid pavement backcalculation model is evaluated using field non-destructive test data acquired from a full-scale airport pavement test facility.     

Adaptive augmented Lagrangian methods: algorithms and practical numerical experience

In this paper, we consider augmented Lagrangian (AL) algorithms for solving large-scale nonlinear optimization problems that execute adaptive strategies for updating the penalty parameter. Our work is motivated by the recently proposed adaptive AL trust region method by Curtis et al. [An adaptive augmented Lagrangian method for large-scale constrained optimization, Math. Program. 152 (2015), pp. 201–245.]. The first focal point of this paper is a new variant of the approach that employs a line search rather than a trust region strategy, where a critical algorithmic feature for the line search strategy is the use of convexified piecewise quadratic models of the AL function for computing the search directions. We prove global convergence guarantees for our line search algorithm that are on par with those for the previously proposed trust region method. A second focal point of this paper is the practical performance of the line search and trust region algorithm variants in Matlab software, as well as that of an adaptive penalty parameter updating strategy incorporated into the Lancelot software. We test these methods on problems from the CUTEst and COPS collections, as well as on challenging test problems related to optimal power flow. Our numerical experience suggests that the adaptive algorithms outperform traditional AL methods in terms of efficiency and reliability. As with traditional AL algorithms, the adaptive methods are matrix-free and thus represent a viable option for solving large-scale problems.     

On an evolutionary approach for constrained optimization problem solving

Over the last few decades, many different evolutionary algorithms have been introduced for solving constrained optimization problems. However, due to the variability of problem characteristics, no single algorithm performs consistently over a range of problems. In this paper, instead of introducing another such algorithm, we propose an evolutionary framework that utilizes existing knowledge to make logical changes for better performance. The algorithmic aspects considered here are: the way of using search operators, dealing with feasibility, setting parameters, and refining solutions. The combined impact of such modifications is significant as has been shown by solving two sets of test problems: (i) a set of 24 test problems that were used for the CEC2006 constrained optimization competition and (ii) a second set of 36 test instances introduced for the CEC2010 constrained optimization competition. The results demonstrate that the proposed algorithm shows better performance in comparison to the state-of-the-art algorithms.     

Two hybrid differential evolution algorithms for engineering design optimization

This paper presents two hybrid differential evolution algorithms for optimizing engineering design problems. One hybrid algorithm enhances a basic differential evolution algorithm with a local search operator, i.e., random walk with direction exploitation, to strengthen the exploitation ability, while the other adding a second metaheuristic, i.e., harmony search, to cooperate with the differential evolution algorithm so as to produce the desirable synergetic effect. For comparison, the differential evolution algorithm that the two hybrids are based on is also implemented. All algorithms incorporate a generalized method to handle discrete variables and Deb's parameterless penalty method for handling constraints. Fourteen engineering design problems selected from different engineering fields are used for testing. The test results show that: (i) both hybrid algorithms overall outperform the differential evolution algorithms; (ii) among the two hybrid algorithms, the cooperative hybrid overall outperforms the other hybrid with local search; and (iii) the performance of proposed hybrid algorithms can be further improved with some effort of tuning the relevant parameters.     

Memetic algorithm with Preferential Local Search using adaptive weights for multi-objective optimization problems

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.