A heuristic-based hybrid genetic-variable neighborhood search algorithm for task scheduling in heterogeneous multiprocessor system

Effective task scheduling, which is essential for achieving high performance in a heterogeneous multiprocessor system, remains a challenging problem despite extensive studies. In this article, a heuristic-based hybrid genetic-variable neighborhood search algorithm is proposed for the minimization of makespan in the heterogeneous multiprocessor scheduling problem. The proposed algorithm distinguishes itself from many existing genetic algorithm (GA) approaches in three aspects. First, it incorporates GA with the variable neighborhood search (VNS) algorithm, a local search metaheuristic, to exploit the intrinsic structure of the solutions for guiding the exploration process of GA. Second, two novel neighborhood structures are proposed, in which problem-specific knowledge concerned with load balancing and communication reduction is utilized respectively, to improve both the search quality and efficiency of VNS. Third, the proposed algorithm restricts the use of GA to evolve the task-processor mapping solutions, while taking advantage of an upward-ranking heuristic mostly used by traditional list scheduling approaches to determine the task sequence assignment in each processor. Empirical results on benchmark task graphs of several well-known parallel applications, which have been validated by the use of non-parametric statistical tests, show that the proposed algorithm significantly outperforms several related algorithms in terms of the schedule quality. Further experiments are carried out to reveal that the proposed algorithm is able to maintain high performance within a wide range of parameter settings.     

SOLVING THE OPEN SHOP SCHEDULING PROBLEM VIA A HYBRID GENETIC-VARIABLE NEIGHBORHOOD SEARCH ALGORITHM

In this article, a hybrid metaheuristic method for solving the open shop scheduling problem (OSSP) is proposed. The optimization criterion is the minimization of makespan and the solution method consists of four components: a randomized initial population generation, a heuristic solution included in the initial population acquired by a Nawaz-Enscore-Ham (NEH)-based heuristic for the flow shop scheduling problem, and two interconnected metaheuristic algorithms: a variable neighborhood search and a genetic algorithm. To our knowledge, this is the first hybrid application of genetic algorithm (GA) and variable neighborhood search (VNS) for the open shop scheduling problem. Computational experiments on benchmark data sets demonstrate that the proposed hybrid metaheuristic reaches a high quality solution in short computational times. Moreover, 12 new hard, large-scale open shop benchmark instances are proposed that simulate realistic industrial cases.     

S-shaped and V-shaped gaining-sharing knowledge-based algorithm for feature selection

In machine learning, searching for the optimal feature subset from the original datasets is a very challenging and prominent task. The metaheuristic algorithms are used in finding out the relevant, important features, that enhance the classification accuracy and save the resource time. Most of the algorithms have shown excellent performance in solving feature selection problems. A recently developed metaheuristic algorithm, gaining-sharing knowledge-based optimization algorithm (GSK), is considered for finding out the optimal feature subset. GSK algorithm was proposed over continuous search space; therefore, a total of eight S-shaped and V-shaped transfer functions are employed to solve the problems into binary search space. Additionally, a population reduction scheme is also employed with the transfer functions to enhance the performance of proposed approaches. It explores the search space efficiently and deletes the worst solutions from the search space, due to the updation of population size in every iteration. The proposed approaches are tested over twenty-one benchmark datasets from UCI repository. The obtained results are compared with state-of-the-art metaheuristic algorithms including binary differential evolution algorithm, binary particle swarm optimization, binary bat algorithm, binary grey wolf optimizer, binary ant lion optimizer, binary dragonfly algorithm, binary salp swarm algorithm. Among eight transfer functions, V₄ transfer function with population reduction on binary GSK algorithm outperforms other optimizers in terms of accuracy, fitness values and the minimal number of features. To investigate the results statistically, two non-parametric statistical tests are conducted that concludes the superiority of the proposed approach.

     

Mapping stream programs onto multicore platforms by local search and genetic algorithm

This paper presents a number of novel metaheuristic approaches that can efficiently map stream graphs on multicores. A stream graph consists of a set of actors performing different functions communicating through edges. Orchestrating stream graphs on multicores can be formulated as an Integer Linear Programming (ILP) problem but ILP solver takes exponential time to provide an optimal solution. We propose metaheuristic algorithms to achieve near optimal solutions within a reasonable amount of time. We employ six different variants of the Hill-Climbing (HC) algorithm employing different tweak operators that produce excellent result extremely quickly. We also propose six different variants of Genetic Algorithm (GA) to examine how effective these variants can be in escaping the local optima. We finally combine HC and GA techniques (which is also known as ‘memetic algorithm’) to produce hybrid techniques that outperform the individual performance of HC and GA techniques. We compare our results with the results generated by the CPLEX optimization tool. Our best technique has achieved a geometric mean speedup of 7.42× across a range of StreamIt benchmarks on an eight-core processor.     

Extended artificial chromosomes genetic algorithm for permutation flowshop scheduling problems

In our previous researches, we proposed the artificial chromosomes with genetic algorithm (ACGA) which combines the concept of the Estimation of Distribution Algorithms (EDAs) with genetic algorithms (GAs). The probabilistic model used in the ACGA is the univariate probabilistic model. We showed that ACGA is effective in solving the scheduling problems. In this paper, a new probabilistic model is proposed to capture the variable linkages together with the univariate probabilistic model where most EDAs could use only one statistic information. This proposed algorithm is named extended artificial chromosomes with genetic algorithm (eACGA). We investigate the usefulness of the probabilistic models and to compare eACGA with several famous permutation-oriented EDAs on the benchmark instances of the permutation flowshop scheduling problems (PFSPs). eACGA yields better solution quality for makespan criterion when we use the average error ratio metric as their performance measures. In addition, eACGA is further integrated with well-known heuristic algorithms, such as NEH and variable neighborhood search (VNS) and it is denoted as eACGA_hybrid to solve the considered problems. No matter the solution quality and the computation efficiency, the experimental results indicate that eACGA_hybrid outperforms other known algorithms in literature. As a result, the proposed algorithms are very competitive in solving the PFSPs.     

Deriving operating policies for multi-objective reservoir systems: Application of Self-Learning Genetic Algorithm

Optimal multi-reservoir operation is a multi-objective problem in nature and some of its objectives are nonlinear, non-convex and multi-modal functions. There are a few areas of application of mathematical optimization models with a richer or more diverse history than in reservoir systems optimization. However, actual implementations remain limited or have not been sustained.Genetic Algorithms (GAs) are probabilistic search algorithms that are capable of solving a variety of complex multi-objective optimization problems, which may include non-linear, non-convex and multi-modal functions. GA is a population based global search method that can escape from local optima traps and find the global optima. However GAs have some drawbacks such as inaccuracy of the intensification process near the optimal set.In this paper, a new model called Self-Learning Genetic Algorithm (SLGA) is presented, which is an improved version of the SOM-Based Multi-Objective GA (SBMOGA) presented by Hakimi-Asiabar et al. (2009) [45]. The proposed model is used to derive optimal operating policies for a three-objective multi-reservoir system. SLGA is a new hybrid algorithm which uses Self-Organizing Map (SOM) and Variable Neighborhood Search (VNS) algorithms to add a memory to the GA and improve its local search accuracy. SOM is a neural network which is capable of learning and can improve the efficiency of data processing algorithms. The VNS algorithm can enhance the local search efficiency in the Evolutionary Algorithms (EAs).To evaluate the applicability and efficiency of the proposed methodology, it is used for developing optimal operating policies for the Karoon-Dez multi-reservoir system, which includes one-fifth of Iran's surface water resources. The objective functions of the problem are supplying water demands, generating hydropower energy and controlling water quality in downstream river.     

Variable neighborhood search for the cost constrained minimum label spanning tree and label constrained minimum spanning tree problems

Given an undirected graph whose edges are labeled or colored, edge weights indicating the cost of an edge, and a positive budget B, the goal of the cost constrained minimum label spanning tree (CCMLST) problem is to find a spanning tree that uses the minimum number of labels while ensuring its cost does not exceed B. The label constrained minimum spanning tree (LCMST) problem is closely related to the CCMLST problem. Here, we are given a threshold K on the number of labels. The goal is to find a minimum weight spanning tree that uses at most K distinct labels. Both of these problems are motivated from the design of telecommunication networks and are known to be NP-complete [15].In this paper, we present a variable neighborhood search (VNS) algorithm for the CCMLST problem. The VNS algorithm uses neighborhoods defined on the labels. We also adapt the VNS algorithm to the LCMST problem. We then test the VNS algorithm on existing data sets as well as a large-scale dataset based on TSPLIB [12] instances ranging in size from 500 to 1000 nodes. For the LCMST problem, we compare the VNS procedure to a genetic algorithm (GA) and two local search procedures suggested in [15]. For the CCMLST problem, the procedures suggested in [15] can be applied by means of a binary search procedure. Consequently, we compared our VNS algorithm to the GA and two local search procedures suggested in [15]. The overall results demonstrate that the proposed VNS algorithm is of high quality and computes solutions rapidly. On our test datasets, it obtains the optimal solution in all instances for which the optimal solution is known. Further, it significantly outperforms the GA and two local search procedures described in [15].     

Minimizing makespan in permutation flow shop scheduling problems using a hybrid metaheuristic algorithm

This paper proposes a hybrid metaheuristic for the minimization of makespan in permutation flow shop scheduling problems. The solution approach is robust, fast, and simply structured, and comprises three components: an initial population generation method based on a greedy randomized constructive heuristic, a genetic algorithm (GA) for solution evolution, and a variable neighbourhood search (VNS) to improve the population. The hybridization of a GA with VNS, combining the advantages of these two individual components, is the key innovative aspect of the approach. Computational experiments on benchmark data sets demonstrate that the proposed hybrid metaheuristic reaches high-quality solutions in short computational times. Furthermore, it requires very few user-defined parameters, rendering it applicable to real-life flow shop scheduling problems.     

Hardware accelerator for solving 0–1 knapsack problems using binary harmony search

The 0–1 knapsack problem (KP) is a well-known intractable optimization problem with wide range of applications. Harmony Search (HS) is one of the most popular metaheuristic algorithms to successfully solve 0–1 KPs. Nevertheless, metaheuristic algorithms are generally compute intensive and slow when implemented in software. In this paper, we present an FPGA-based pipelined hardware accelerator to reduce computation time for solving large dimension 0–1 KPs using Binary Harmony Search algorithm. The proposed architecture exploits the intrinsic parallelism of population based metaheuristic algorithm and the flexibility and parallel processing capabilities of FPGAs to perform the computation concurrently thus enhancing performance. To validate the efficiency of the proposed hardware accelerator, experiments were conducted using a large number of 0–1 KPs. Comparative analysis on experimental results reveals that the proposed approach offers promising speedups of 51× – 111× as compared with a software implementation and 2× – 5× as compared with a hardware implementation of Binary Particle Swarm Optimization algorithm.     

Two metaheuristic approaches for solving multidimensional two-way number partitioning problem

In this paper, we address two metaheuristic approaches, a Variable Neighborhood Search (VNS) and an Electromagnetism-like metaheuristic (EM), on an NP-hard optimization problem: Multi-dimensional Two-way Number Partitioning Problem (MDTWNPP). MDTWNPP is a generalization of a Two-way Number Partitioning Problem (TWNPP), where a set of vectors is partitioned rather than a set of numbers. The simple k-swap neighborhoods allow an effective shaking procedure in the VNS search. The attraction–repulsion mechanism of EM is extended with a scaling procedure, which additionally moves EM points closer to local optima. Both VNS and EM use the same local search procedure based on 1-swap improvements. Computational results were obtained on 210 standard instances. Direct comparison with results from the literature confirm the significance of applying these methods to MDTWNPP.     

混合花粉算法求解全局优化问题

元启发式算法可以用作寻找近似最优解的有效工具,因此,对元启发式算法进行改进,提高算法性能是有必要的。本文介绍花粉算法(Flower Pollination Algorithm, FPA)的增强变体,将花粉算法与极值优化算法(Extremal Optimization, EO)混合形成FPA-EO算法。FPA-EO算法综合利用了FPA的全局搜索能力和EO的局部搜索能力,并将其应用于11个基准测试函数来测试新算法。同时将该算法与其他4种著名优化算法（标准花粉算法(FPA)、蝙蝠算法(BAT)、萤火虫算法(FA)、模拟退火算法(SA)）进行比较。综合结果表明,本文算法能够找到比其他4种算法更精确的解。     

Nonlinear continuous multi-response problems: a novel two-phase hybrid genetic based metaheuristic

Generally the most real world production systems are tackling several different responses and the problem is optimizing these responses concurrently. This study strives to present a new two-phase hybrid genetic based metaheuristic for optimizing nonlinear continuous multi-response problems. Premature convergence and getting stuck in local optima, which makes the algorithm time consuming, are common problems dealing with genetic algorithms (GAs). So we hybridize GA with a clustering approach and particle swarm optimization algorithm (PSO) to make a balanced relationship between time consuming and premature termination. The proposed algorithm also tries to find Ideal Points (IPs) for response functions. IPs are considered as improvement measures that determine when PSO should start. PSO based local search exploit Pareto archive solutions to enhance performance of the algorithm by expanding the search space. Since there is no standard benchmark in this field, we use two case studies from distinguished paper in multi-response optimization and compare the results with some of the mentioned algorithms in the literature. Results show the outperformance of the proposed algorithm than all of them.     

Variable neighborhood search for multi-objective resource allocation problems

The Resource Allocation Problem (RAP) is a classical problem in the field of operations management that has been broadly applied to real problems such as product allocation, project budgeting, resource distribution, and weapon-target assignment. In addition to focusing on a single objective, the RAP may seek to simultaneously optimize several expected but conflicting goals under conditions of resources scarcity. Thus, the single-objective RAP can be intuitively extended to become a Multi-Objective Resource Allocation Problem (MORAP) that also falls in the category of NP-Hard. Due to the complexity of the problem, metaheuristics have been proposed as a practical alternative in the selection of techniques for finding a solution. This study uses Variable Neighborhood Search (VNS) algorithms, one of the extensively used metaheuristic approaches, to solve the MORAP with two important but conflicting objectives—minimization of cost and maximization of efficiency. VNS searches the solution space by systematically changing the neighborhoods. Therefore, proper design of neighborhood structures, base solution selection strategy, and perturbation operators are used to help build a well-balanced set of non-dominated solutions. Two test instances from the literature are used to compare the performance of the competing algorithms including a hybrid genetic algorithm and an ant colony optimization algorithm. Moreover, two large instances are generated to further verify the performance of the proposed VNS algorithms. The approximated Pareto front obtained from the competing algorithms is compared with a reference Pareto front by the exhaustive search method. Three measures are considered to evaluate algorithm performance: D1_R, the Accuracy Ratio, and the number of non-dominated solutions. The results demonstrate the practicability and promise of VNS for solving multi-objective resource allocation problems.     

A VNS heuristic for escaping local extrema entrapment in normalized cut clustering

Normalized cut is one of the most popular graph clustering criteria. The main approaches proposed for its resolution are spectral clustering methods and a multilevel approach of Dhillon et al. (TPAMI 29:1944–1957, 2007), called graclus. Their aim is to obtain good solutions in a small amount of time for large instances. Metaheuristics are general frameworks for stochastic searches often employed in global optimization to improve the solutions obtained by other heuristics. Variable neighborhood search (VNS) is a metaheuristic which exploits systematically the idea of neighborhood change during the search. In this paper, we propose a VNS heuristic for normalized cut segmentation. Computational experiments show that in most cases this VNS heuristic improves significantly, and in moderate time, the solutions obtained by the current state-of-the-art algorithms, i.e., graclus and a spectral method proposed by Yu and Shi (ICCV, 2003).     

Parallel-machine scheduling problems with sequence-dependent setup times using an ACO,SA and VNS hybrid algorithm

This paper proposes a hybrid metaheuristic for the minimization of makespan in scheduling problems with parallel machines and sequence-dependent setup times. The solution approach is robust, fast, and simply structured, and comprises three components: an initial population generation method based on an ant colony optimization (ACO), a simulated annealing (SA) for solution evolution, and a variable neighborhood search (VNS) which involves three local search procedures to improve the population. The hybridization of an ACO, SA with VNS, combining the advantages of these three individual components, is the key innovative aspect of the approach. Two algorithms of a hybrid VNS-based algorithm, SA/VNS and ACO/VNS, and the VNS algorithm presented previously are used to compare with the proposed hybrid algorithm to highlight its advantages in terms of generality and quality for large instances.     

基数约束投资组合问题的一种混合元启发式算法求解

针对资产数目和投资资金比例受约束的投资组合选择这一NP难问题,基于混沌搜索、粒子群优化和引力搜索算法提出了一种新的混合元启发式搜索算法。该算法能很好地平衡开发能力和勘探能力,有效抑制了算法早熟收敛现象。标准测试函数的测试结果表明混合算法与标准的粒子群优化和引力搜索算法相比具有更好的寻优效率;实证分析进一步对混合算法与遗传算法及粒子群优化算法在求解这类投资组合选择问题的性能进行了比较。数值结果表明,混合算法在搜索具有高预期回报的非支配投资组合方面表现更好,取得了更为满意的结果。     

改进的元启发式优化算法及其在图像分割中的应用

元启发式算法自20世纪60年代提出以后,由于其具有可以有效地减少计算量、提高优化效率等优点而得到了广泛应用.该类算法以模仿自然界中各类运行机制为特点,具有自我调节的特征,解决了诸如梯度法、牛顿法和共轭下降法等这些传统优化算法计算效率低、收敛性差等缺点,在组合优化、生产调度、图像处理等方面均有很好的效果.提出了一种改进的元启发式优化算法——NBAS算法.该算法通过将传统天牛须算法（BAS）离散化得到二进制离散天牛须算法（BBAS）,并与原始天牛须算法进行混合得出.算法平衡了局部与全局搜索,有效地弥补了算法容易陷入局部最优的不足.为了验证NBAS算法的有效性,将NBAS算法与二维K熵算法结合,提出了一种快速、准确的NBAS-K熵图像分割算法.该方法解决了优化图像阈值分割函数的优化算法易陷入局部最优、算法寻优个体数多、设计复杂度高所导致的计算量大、耗时长等问题.NBAS-K熵算法与BAS-K熵算法、BBAS-K熵算法、遗传K熵算法（GA-K熵）、粒子群K熵算法（PSO-K熵）和蚱蜢K熵算法（GOA-K熵）在Berkeley数据集、人工加噪图像以及遥感图像上的实验结果表明,该分割方法不仅具有较好的抗噪性能,而且具有较高的精度和鲁棒性,能够较为有效地实现复杂图像分割.     

A Genetic Algorithm Based on Relaxation Induced Neighborhood Search in a Local Branching Framework for Capacitated Multicommodity Network Design

The fixed-charge Capacitated Multicommodity Network Design (CMND) is a well-known problem of both practical and theoretical significance. This article proposes the Genetic Algorithm (GA) cooperative Relaxation Induced Neighborhood Search (RINS) in a Local Branching (LB) framework for CMND problem. GA algorithm is started by initial population which is made by two parents obtain from hybrid LB and RINS algorithms. The basic idea of the proposed solution method is to use the GA algorithm to explore the search space and the hybrid LB and RINS methods to move from current solution to neighbor solution. Adapting the metaheuristic algorithm with RINS method to fit within an LB framework represents an interesting challenge. To evaluate the proposed algorithm, the standard problems with different sizes are used. The parameters of the algorithm are tuned by design of experiments. In order to prove the efficiency and effectiveness of the proposed algorithm, the results are compared with the best results available in the literature. The statistical analysis shows high performance of the proposed algorithm.     

A two phase variable neighborhood search for the multi-product inventory routing problem

We address a multi-product inventory routing problem and propose a two-phase Variable Neighborhood Search (VNS) metaheuristic to solve it. In the first phase, VNS is used to solve a capacitated vehicle routing problem at each period to find an initial solution without taking into account the inventory. In the second phase, we iteratively improve the initial solution while minimizing both the transportation and inventory costs. For this, we propose two different algorithms, a Variable Neighborhood Descent and a Variable Neighborhood Search. We present an heuristic and a Linear Programming formulation, which are applied after each local search move, to determine the amount of products to collect from each supplier at each period. During the exploration, we use priority rules for suppliers and vehicles, based on the current delivery schedule over the planning horizon. Computational results show the efficiency of the proposed two-phase approach.     

混和进化算法求解具有分段恶化效应的并行机调度问题

本文提出了一种新的混合进化算法求解具有线性恶化的并行机调度问题,目标是使总完工时间最小.该算法采用对立策略以及最小比率优先规则生成初始种群,并且引入种群多样度指标加快算法的收敛;同时加入含有3-opt扰动算子的变邻域搜索算法对遗传算法得到的结果进行局部搜索.通过对不同规模算例的实验进行仿真,其结果与传统GA和VNS算法相比,效果均有所提升.