Optimization of one-dimensional Bin Packing Problem with island parallel grouping genetic algorithms

The well-known one-dimensional Bin Packing Problem (BPP) of whose variants arise in many real life situations is a challenging NP-Hard combinatorial optimization problem. Metaheuristics are widely used optimization tools to find (near-) optimal solutions for solving large problem instances of BPP in reasonable running times. With this study, we propose a set of robust and scalable hybrid parallel algorithms that take advantage of parallel computation techniques, evolutionary grouping genetic metaheuristics, and bin-oriented heuristics to obtain solutions for large scale one-dimensional BPP instances. A total number of 1318 benchmark problems are examined with the proposed algorithms and it is shown that optimal solutions for 88.5% of these instances can be obtained with practical optimization times while solving the rest of the problems with no more than one extra bin. When the results are compared with the existing state-of-the-art heuristics, the developed parallel hybrid grouping genetic algorithms can be considered as one of the best one-dimensional BPP algorithms in terms of computation time and solution quality.     

A型变尺寸装箱问题之模型及算法研究

作为对经典一维装箱问题的推广,提出一种A型变尺寸装箱问题（A-shaped Variable-sized BinPacking Problem,简称A SVBP）,即在物品的装箱过程中,每样物品有高度和横截面积两个参数,并且箱子的大小不一。该问题在文件系统管理和日常生活中的运输等问题中有着广泛的应用背景。把装箱问题的经典算法以及遗传算法推广到A型变尺寸装箱问题,实验结果表明：按照本文提出的求解模式,离线情况下求解A型变尺寸装箱问题最终结果的质量取决于预先求解其退化为经典装箱问题时的算法,求解物品装箱序列时用首次适应混合遗传算法比用Next Fit算法、First Fit算法、Best Fit算法最终得到的结果要好。     

Using genetic algorithms to solve quality-related bin packing problem

The Bin Packing Problem is an industrial problem which involves grouping items into appropriate bin to minimize the cost and number of used bins. It provides a solution for assigning parts to optimize some predefined measures of productivity. In this study, Ion Plating (IP) industry requires similar approach on allocating production jobs into batches for producing better quality products and enabling to meet customer deadlines. The aim of this paper is to (i) develop a Bin Packing Genetic Algorithms (BPGA) with different weighting combinations, taking into account the quality of product and service; (ii) improve the production efficiency by reducing the production unit cost in IP. Genetic Algorithm was chosen because it is one of the best heuristics algorithms on solving optimization problems. In the case studies, industrial data of a precious metal finishing company was used to simulate the proposed BPGA model, and the computational results were compared with these industrial data. The results from three different weighting combinations demonstrated that fewer resources would be required by applying the proposed model in solving BP problem in the Ion Plating Cell.     

On Lazy Bin Covering and Packing problems

In this paper, we study two interesting variants of the classical bin packing problem, called Lazy Bin Covering (LBC) and Cardinality Constrained Maximum Resource Bin Packing (CCMRBP) problems. For the offline LBC problem, we first prove the approximation ratio of the First-Fit-Decreasing and First-Fit-Increasing algorithms, then present an APTAS. For the online LBC problem, we give a competitive analysis for the algorithms of Next-Fit, Worst-Fit, First-Fit, and a modified HARMONIC_M algorithm. The CCMRBP problem is a generalization of the Maximum Resource Bin Packing (MRBP) problem Boyar et al. (2006) [1]. For this problem, we prove that its offline version is no harder to approximate than the offline MRBP problem.     

超立方体网络中任务调度的一个新近似算法

本文研究超立方体中的多处理器任务调度问题,我们研究LDLPT算法并指出为什么这种算法对一些实例具有最差的逼近度,然后提出一种类似装箱算法的新算法-BPA算法,证明该算法和LDLPT算法在相互最差逼近度中具有互补性质,最后,组合这两种算法的基本方法提出了一种求解问题的新算法-CBPA算法,并证明新算法具有比LDLPT算法更好的逼近度。     

A two-leveled symbiotic evolutionary algorithm for clustering problems

Because of its unsupervised nature, clustering is one of the most challenging problems, considered as a NP-hard grouping problem. Recently, several evolutionary algorithms (EAs) for clustering problems have been presented because of their efficiency for solving the NP-hard problems with high degree of complexity. Most previous EA-based algorithms, however, have dealt with the clustering problems given the number of clusters (K) in advance. Although some researchers have suggested the EA-based algorithms for unknown K clustering, they still have some drawbacks to search efficiently due to their huge search space. This paper proposes the two-leveled symbiotic evolutionary clustering algorithm (TSECA), which is a variant of coevolutionary algorithm for unknown K clustering problems. The clustering problems considered in this paper can be divided into two sub-problems: finding the number of clusters and grouping the data into these clusters. The two-leveled framework of TSECA and genetic elements suitable for each sub-problem are proposed. In addition, a neighborhood-based evolutionary strategy is employed to maintain the population diversity. The performance of the proposed algorithm is compared with some popular evolutionary algorithms using the real-life and simulated synthetic data sets. Experimental results show that TSECA produces more compact clusters as well as the accurate number of clusters.     

基于基因水平多样性的微种群教与学优化算法

种群多样性对微种群教与学优化算法的性能有极大影响。为进一步提高其性能,提出一种基于基因水平多样性的微种群教与学优化算法(MTLBO-GLD)。该算法从基因水平上对种群多样性进行监测;并使用混沌搜索和余弦函数分阶段进行扰动以增加种群多样性。所提算法与八种元启发式算法(四种微种群算法和四种非微种群算法)在13个测试函数上进行性能比较。实验结果表明,MTLBO-GLD的整体性能要显著好于其他八种对比算法。     

可用性约束资源预留与分配算法

给定一系列作业和只能在有限的时间段可用的资源,如何预留和分配资源以实现作业的最大完成时间最小化的问题是NP难的。本文将其归结为一种新型的尺寸可变装箱问题并给出了作业信息和资源信息完全已知条件下的六种离线算法,理论分析表明所给算法的渐进最坏比为2,在作业相互独立的务件下推广的降序最佳适合(Best Fit Decreasing)算法的平均性能最优,在作业有先后依赖关系的条件下推广的最佳适合(Best Fit)算法的平均性能最优。     

A note on the variance of rank-based selection strategies for genetic algorithms and genetic programming

This paper evaluates different forms of rank-based selection that are used with genetic algorithms and genetic programming. Many types of rank based selection have exactly the same expected value in terms of the sampling rate allocated to each member of the population. However, the variance associated with that sampling rate can vary depending on how selection is implemented. We examine two forms of tournament selection and compare these to linear rank-based selection using an explicit formula. Because selective pressure has a direct impact on population diversity, we also examine the interaction between selective pressure and different mutation strategies.     

A diversity control mechanism in many objective optimizations

Multi-objective evolutionary optimization algorithms are among the best optimizers for solving problems in control systems, engineering and industrial planning. The performance of these algorithms degrades severely due to the loss of selection pressure exerted by the Pareto dominance relation which will cause the algorithm to act randomly. Various recent methods tried to provide more selection pressure but this would cause the population to converge to a specific region which is not desirable. Diversity reduction in high dimensional problems which decreases the capabilities of these approaches is a decisive factor in the overall performance of these algorithms. The novelty of this paper is to propose a new diversity measure and a diversity control mechanism which can be used in combination to remedy the mentioned problem. This measure is based on shortest Hamiltonian path for capturing an order of the population in any dimension. In order to control the diversity of population, we designed an adaptive framework which adjusts the selection operator according to diversity variation in the population using different diversity measures as well as our proposed one. This study incorporates the proposed framework in MOEA/D, an efficient widely used evolutionary algorithm. The obtained results validate the motivation on the basis of diversity and performance measures in comparison with the state-of-the-art algorithms and demonstrate the applicability of our algorithm/method in handling many-objective problems. Moreover, an extensive comparison with several diversity measure algorithms reveals the competitiveness of our proposed measure.     

Heuristic evaluation techniques for bin packing approximation algorithms

Performance analysis of approximation algorithms purposes to give upper bounds on the ratio «approximate solution cost»/«optimal solution cost». We say that standard analysis brings to «a priori» evaluation since the bounds it provides refer to the overall worst-case performance: really those evaluations do not take into account useful information relevant to the performance that approximate solution might contain themselves. In this paper we show how the performances of the Any Fit Decreasing algorithms for Bin Packing can be evaluated more precisely than it is done in the standard «a priori» analysis, by means of demonstration techniques of «a posteriori» analysis. In fact, we show how approximate solutions of Bin Packing given by Any Fit Decreasing algorithms can be put in three classes of performances. Belongings to the first class imply really optimality of solutions (those events could remain unspected if one clings only to the 5/4 bound, as forecast by standard «a priori» evaluations). Also belonging to the second class of performances may involve remarkable revaluation of solutions in hand, although optimality cannot be recognized; an inequality is provided which permits to compute upper bounds on the evaluation ratios. The same inequality permits to recognize approximate solutions which could not be improved neither by First Fit nor Best Fit Decreasing algorithms. The third class refers to those performances for which the considered levels of inspection cannot offer a more precise evaluation that the «a priori» one.     

基于选择压力的全局优化元胞遗传算法分析

元胞遗传算法将遗传操作限制在邻域内进行,减缓了优势个体在群体中的扩散速度,具有更好的全局收敛性,在求解复杂优化问题中显示出优越性。与传统遗传算法对比,以选择压力作为分析手段,对元胞遗传算法进行定性分析。通过求解具有不同特征的函数,分析进化过程群体多样性变化,从进化过程群体分布图,直观得出元胞遗传算法具有较好的维持群体多样性能力;从计算的统计结果,得出元胞遗传算法能极大提高全局收敛率,并且求解稳定性更好。     

基于改进遗传算法的可重构计算任务划分

为实现可重构计算中的软硬件任务自动划分,引入了遗传算法来搜寻最优解。为解决标准遗传算法可能出现种群早熟和种群进化后期收敛速度慢的问题,使用了小生境技术来保护种群中基因的多样性。设计了能够随适应度自动改变的自适应遗传算子（杂交算子和变异算子）。对算法进行了50次随机实验,并对结果进行分析。实验表明,改进后的遗传算法搜寻到全局最优任务划分的概率和搜寻到最优任务划分时的进化代数都要优于标准遗传算法。     

GENITOR II: a distributed genetic algorithm

Abstract

GENITOR is a genetic algorithm which employs one-at-a-time reproduction and allocates reproductive opportunities according to rank to achieve selective pressure. Theoretical arguments and empirical evidence suggest that GENITOR is less vulnerable to some of the biases that degrade performance in standard genetic algorithms.

A distributed version of GENITOR which uses many smaller distributed populations in place of a single large population is introduced. GENITOR II is able to optimize a broad range of sample problems more accurately and more consistently than GENITOR with a single population. GENITOR II also appears to be more robust than a single population genetic algorithm, yielding better performance without parameter tuning. We present some preliminary analyses to explain the performance advantage of the distributed algorithm. A distributed search is shown to yield improved search on several classes of problems, including binary encoded feedforward neural networks, the Traveling Salesman Problem, and a set of ‘ deceptive problems’ specially designed to be hard for genetic algorithms.     

Cellular genetic algorithms without additional parameters

Cellular genetic algorithms (cGAs) are a kind of genetic algorithms (GAs) with decentralized population in which interactions among individuals are restricted to close ones. The use of decentralized populations in GAs allows to keep the population diversity for longer, usually resulting in a better exploration of the search space and, therefore, in a better performance of the algorithm. However, it supposes the need of several new parameters that have a major impact on the behavior of the algorithm. In the case of cGAs, these parameters are the population and neighborhood shapes. We propose in this work two innovative cGAs with new adaptive techniques that allow removing the neighborhood and population shape from the algorithm’s configuration. As a result, the new adaptive cGAs are highly competitive (statistically) with all the compared cGAs in terms of the average solutions found in the continuous and combinatorial domains, while finding, in general, the best solutions for the considered problems, and with less computational effort.     

基于跳跃基因算子的改进实数遗传算法

为了避免遗传算法在求解数值优化问题时出现搜索能力差、多样性缺失等弊端,提出一种基于实数编码的改进遗传算法(IRCGA).算法集成两个特别设计的算子:模拟二进制跳跃基因算子(SBJG)和多方向交叉算子(MX).SBJG算子以染色体为操作对象,本质上模拟了二进制跳跃基因操作中的插入运动,即利用一种随机的方式将选定的染色体块插入到染色体位点,实现种群内部染色体间的转位,为种群提供额外的遗传多样性;MX算子通过增加交叉方向的方式扩大算子的搜索区域,从而提升后代个体质量与算法的搜索能力.在11个实例的基础上进行对比实验,结果表明,采用改进算子能够明显提升算法在求解数值优化问题时的性能,同时,相比于其他先进有效的算法,IRCGA具有较强的搜索能力且能够维持一定的种群多样性,从而验证了改进算法的有效性和可行性.     

Genetic algorithms with memory- and elitism-based immigrants in dynamic environments

Abstract In recent years the genetic algorithm community has shown a growing interest in studying dynamic optimization problems. Several approaches have been devised. The random immigrants and memory schemes are two major ones. The random immigrants scheme addresses dynamic environments by maintaining the population diversity while the memory scheme aims to adapt genetic algorithms quickly to new environments by reusing historical information. This paper investigates a hybrid memory and random immigrants scheme, called memory-based immigrants, and a hybrid elitism and random immigrants scheme, called elitism-based immigrants, for genetic algorithms in dynamic environments. In these schemes, the best individual from memory or the elite from the previous generation is retrieved as the base to create immigrants into the population by mutation. This way, not only can diversity be maintained but it is done more efficiently to adapt genetic algorithms to the current environment. Based on a series of systematically constructed dynamic problems, experiments are carried out to compare genetic algorithms with the memory-based and elitism-based immigrants schemes against genetic algorithms with traditional memory and random immigrants schemes and a hybrid memory and multi-population scheme. The sensitivity analysis regarding some key parameters is also carried out. Experimental results show that the memory-based and elitism-based immigrants schemes efficiently improve the performance of genetic algorithms in dynamic environments.     

Genetic diversity as an objective in multi-objective evolutionary algorithms

A key feature of an efficient and reliable multi-objective evolutionary algorithm is the ability to maintain genetic diversity within a population of solutions. In this paper, we present a new diversity-preserving mechanism, the Genetic Diversity Evaluation Method (GeDEM), which considers a distance-based measure of genetic diversity as a real objective in fitness assignment. This provides a dual selection pressure towards the exploitation of current non-dominated solutions and the exploration of the search space. We also introduce a new multi-objective evolutionary algorithm, the Genetic Diversity Evolutionary Algorithm (GDEA), strictly designed around GeDEM and then we compare it with other state-of-the-art algorithms on a well-established suite of test problems. Experimental results clearly indicate that the performance of GDEA is top-level.     

Cuckoo search based resource optimization of datacenters

With advancements in virtualization technology, datacenters are often faced with the challenge of managing large numbers of virtual machine (VM) requests. Due to this large amount of VM requests, it has become practically impossible to search all possible VM placements in order to find a solution that best optimizes certain design objectives. As a result, managers of datacenters have resorted to the employment of heuristic optimization algorithms for VM placement. In this paper, we employ the cuckoo search optimization (CSO) algorithm to solve the VM placement problem of datacenters. Firstly, we use the CSO to optimize the datacenter for the minimization of the number of physical machines used for placement. Secondly, we implement a multiobjective CSO algorithm to simultaneously optimize the power consumption and resource wastage of the datacenter. Simulation results show that both CSO algorithms outperform the reordered grouping genetic algorithm (RGGA), the grouping genetic algorithm (GGA), improved least-loaded (ILL) and improved FFD (IFFD) methods of VM placement.     

Variable mesh optimization for continuous optimization problems

Population-based meta-heuristics are algorithms that can obtain very good results for complex continuous optimization problems in a reduced amount of time. These search algorithms use a population of solutions to maintain an acceptable diversity level during the process, thus their correct distribution is crucial for the search. This paper introduces a new population meta-heuristic called “variable mesh optimization” (VMO), in which the set of nodes (potential solutions) are distributed as a mesh. This mesh is variable, because it evolves to maintain a controlled diversity (avoiding solutions too close to each other) and to guide it to the best solutions (by a mechanism of resampling from current nodes to its best neighbour). This proposal is compared with basic population-based meta-heuristics using a benchmark of multimodal continuous functions, showing that VMO is a competitive algorithm.