A memetic ant colony optimization algorithm for the dynamic travelling salesman problem

Ant colony optimization (ACO) has been successfully applied for combinatorial optimization problems, e.g., the travelling salesman problem (TSP), under stationary environments. In this paper, we consider the dynamic TSP (DTSP), where cities are replaced by new ones during the execution of the algorithm. Under such environments, traditional ACO algorithms face a serious challenge: once they converge, they cannot adapt efficiently to environmental changes. To improve the performance of ACO on the DTSP, we investigate a hybridized ACO with local search (LS), called Memetic ACO (M-ACO) algorithm, which is based on the population-based ACO (P-ACO) framework and an adaptive inver-over operator, to solve the DTSP. Moreover, to address premature convergence, we introduce random immigrants to the population of M-ACO when identical ants are stored. The simulation experiments on a series of dynamic environments generated from a set of benchmark TSP instances show that LS is beneficial for ACO algorithms when applied on the DTSP, since it achieves better performance than other traditional ACO and P-ACO algorithms.     

Population-Based Incremental Learning With Associative Memory for Dynamic Environments

In recent years, interest in studying evolutionary algorithms (EAs) for dynamic optimization problems (DOPs) has grown due to its importance in real-world applications. Several approaches, such as the memory and multiple population schemes, have been developed for EAs to address dynamic problems. This paper investigates the application of the memory scheme for population-based incremental learning (PBIL) algorithms, a class of EAs, for DOPs. A PBIL-specific associative memory scheme, which stores best solutions as well as corresponding environmental information in the memory, is investigated to improve its adaptability in dynamic environments. In this paper, the interactions between the memory scheme and random immigrants, multipopulation, and restart schemes for PBILs in dynamic environments are investigated. In order to better test the performance of memory schemes for PBILs and other EAs in dynamic environments, this paper also proposes a dynamic environment generator that can systematically generate dynamic environments of different difficulty with respect to memory schemes. Using this generator, a series of dynamic environments are generated and experiments are carried out to compare the performance of investigated algorithms. The experimental results show that the proposed memory scheme is efficient for PBILs in dynamic environments and also indicate that different interactions exist between the memory scheme and random immigrants, multipopulation schemes for PBILs in different dynamic environments.     

Immigrant schemes for evolutionary algorithms in dynamic environments: Adapting the replacement rate

One approach for evolutionary algorithms (EAs) to address dynamic optimization problems (DOPs) is to maintain diversity of the population via introducing immigrants.So far all immigrant schemes developed for EAs have used fixed replacement rates.This paper examines the impact of the replacement rate on the performance of EAs with immigrant schemes in dynamic environments,and proposes a self-adaptive mechanism for EAs with immigrant schemes to address DOPs.Our experimental study showed that the new approach ...     

多维背包问题的一个蚁群优化算法

蚁群优化(ACO)是一种通用的启发式方法,已被用来求解很多离散优化问题.近年来,已提出几个ACO算法求解多维背包问题(MKP).这些算法虽然能获得较好的解但也耗用太多的CPU时间.为了降低用ACO求解MKP的复杂性,文章基于一种已提出但未实现过的MKP的信息素表示定义了新的选择概率的规则和相应的基于背包项的一种序的启发式信息,从而提出了一种计算复杂性较低、求解性能较好的改进型蚁群算法.实验结果表明,无论串行执行还是虚拟并行执行,在计算相同任务时,新算法耗用时间少且解的价值更高.不仅如此,在实验中,文中的新算法获得了ORLIB中测试算例5.250-22的两个"新"解.     

Modeling the dynamics of ant colony optimization

The dynamics of Ant Colony Optimization (ACO) algorithms is studied using a deterministic model that assumes an average expected behavior of the algorithms. The ACO optimization metaheuristic is an iterative approach, where in every iteration, artificial ants construct solutions randomly but guided by pheromone information stemming from former ants that found good solutions. The behavior of ACO algorithms and the ACO model are analyzed for certain types of permutation problems. It is shown analytically that the decisions of an ant are influenced in an intriguing way by the use of the pheromone information and the properties of the pheromone matrix. This explains why ACO algorithms can show a complex dynamic behavior even when there is only one ant per iteration and no competition occurs. The ACO model is used to describe the algorithm behavior as a combination of situations with different degrees of competition between the ants. This helps to better understand the dynamics of the algorithm when there are several ants per iteration as is always the case when using ACO algorithms for optimization. Simulations are done to compare the behavior of the ACO model with the ACO algorithm. Results show that the deterministic model describes essential features of the dynamics of ACO algorithms quite accurately, while other aspects of the algorithms behavior cannot be found in the model.     

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.     

A Hybrid Immigrants Scheme for Genetic Algorithms in Dynamic Environments

Dynamic optimization problems are a kind of optimization problems that involve changes over time.They pose a serious challenge to traditional optimization methods as well as conventional genetic algorithms since the goal is no longer to search for the optimal solution(s) of a fixed problem but to track the moving optimum over time.Dynamic optimization problems have attracted a growing interest from the genetic algorithm community in recent years.Several approaches have been developed to enhance the performance of genetic algorithms in dynamic environments.One approach is to maintain the diversity of the population via random immigrants.This paper proposes a hybrid immigrants scheme that combines the concepts of elitism,dualism and random immigrants for genetic algorithms to address dynamic optimization problems.In this hybrid scheme,the best individual,i.e.,the elite,from the previous generation and its dual individual are retrieved as the bases to create immigrants via traditional mutation scheme.These elitism-based and dualism-based immigrants together with some random immigrants are substituted into the current population,replacing the worst individuals in the population.These three kinds of immigrants aim to address environmental changes of slight,medium and significant degrees respectively and hence efficiently adapt genetic algorithms to dynamic environments that are subject to different severities of changes.Based on a series of systematically constructed dynamic test problems,experiments are carried out to investigate the performance of genetic algorithms with the hybrid immigrants scheme and traditional random immigrants scheme.Experimental results validate the efficiency of the proposed hybrid immigrants scheme for improving the performance of genetic algorithms in dynamic environments.     

Adaptive Primal–Dual Genetic Algorithms in Dynamic Environments

Recently, there has been an increasing interest in applying genetic algorithms (GAs) in dynamic environments. Inspired by the complementary and dominance mechanisms in nature, a primal-dual GA (PDGA) has been proposed for dynamic optimization problems (DOPs). In this paper, an important operator in PDGA, i.e., the primal-dual mapping (PDM) scheme, is further investigated to improve the robustness and adaptability of PDGA in dynamic environments. In the improved scheme, two different probability-based PDM operators, where the mapping probability of each allele in the chromosome string is calculated through the statistical information of the distribution of alleles in the corresponding gene locus over the population, are effectively combined according to an adaptive Lamarckian learning mechanism. In addition, an adaptive dominant replacement scheme, which can probabilistically accept inferior chromosomes, is also introduced into the proposed algorithm to enhance the diversity level of the population. Experimental results on a series of dynamic problems generated from several stationary benchmark problems show that the proposed algorithm is a good optimizer for DOPs.     

A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems

Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments.     

Ant Colony Optimization with Global Pheromone Evaluation for Scheduling a Single Machine

Ant Colony Optimization (ACO) is a metaheuristic that has recently been applied to scheduling problems. We propose an ACO algorithm for the Single Machine Total Weighted Tardiness Problem and compare it to an existing ACO algorithm for the unweighted problem. The proposed algorithm has some novel properties that are of general interest for ACO optimization. A main novelty is that the ants are guided on their way through the decision space by global pheromone information instead of using only local pheromone information. It is also shown that the ACO optimization behaviour can be improved when priority scheduling heuristics are adapted so that they appropriately reflect absolute quality differences between the alternatives before they are used by the ants. Further improvements can be obtained by identifying situations where the ants can perform optimal decisions.     

动态环境下一种具有记忆能力的分布估计算法

以概率模型为基本记忆元素,对动态优化过程中所产生的历史信息进行记忆和利用,提出一种具有记忆能力的分布估计算法用以求解二进制编码动态优化问题.设计了基于环境辨识技术的记忆管理策略,并对种群多样性进行动态补偿.实验结果表明,该算法具有良好的通用性,所采用的多样性补偿策略能够保证算法种群对最优解的持续搜索能力.在对5个动态优化问题的实验中,该算法在绝大多数情况下都显著优于现有的另外两种动态进化算法.     

On solving permutation scheduling problems with ant colony optimization

A new approach for solving permutation scheduling problems with ant colony optimization (ACO) is proposed in this paper. The approach assumes that no precedence constraints between the jobs have to be fulfilled. It is tested with an ACO algorithm for the single-machine total weighted deviation problem. In the new approach the ants allocate the places in the schedule not sequentially, as in the standard approach, but in random order. This leads to a better utilization of the pheromone information. It is shown by experiments that adequate combinations between the standard approach which can profit from list scheduling heuristics and the new approach perform particularly well.     

蚁群算法在求解旅行商问题中的应用综述

旅行商问题作为组合优化研究中最具挑战的问题之一, 自被提出以来就引起了学术界的广泛关注并提出了大量的方法来解决它. 蚁群算法是求解复杂组合优化问题的一种启发式仿生进化算法, 是求解旅行商问题的有效手段. 本文分别介绍蚁群算法中几个有代表性的算法, 综述了蚁群算法的改进、融合和应用的文献研究进展, 以评价近年来不同版本的蚁群算法为解决旅行商问题的发展和研究成果, 并针对改进蚁群算法结构框架、算法参数的设置及优化、信息素优化和混合算法等方面, 对现被提出的改进算法进行了分类综述. 对蚁群算法在未来对旅行商问题及其他不同领域的研究内容和研究热点的进一步发展提供了展望和依据.     

具有路径平滑和信息动态更新的蚁群算法

蚁群算法具有很强的寻优能力,但仍存在搜索时间过长、易于停滞等问题。针对这些不足,提出了一种具有路径平滑和信息动态更新的蚁群算法。新算法引入了路径平滑概念,加强了对蚁群前期搜索的引导,扩大了蚁群后期搜索空间;同时,通过动态调节信息素挥发因子,使得路径间信息素浓度差异不会增长过快,有效地避免了算法陷入局部解。实验结果表明,具有路径平滑和信息动态更新的蚁群算法明显优于基本蚁群算法。     

基于视觉抓取的并联桁架机器人最优路径控制

针对元件的抓取路径规划问题,提出一种以最小化时间为目的,结合蚁群算法和禁忌搜索算法的混合优化算法。首先,将基于机器视觉抓取元件的问题确定为有约束的旅行商问题（TSP）;然后,分析了元件大小和抓取放置过程对于路径规划的综合影响,对路径选择概率和禁忌域进行了适应性改进;其次,一方面引入了2-opt局部优化以及信息素惩罚、奖励机制以改善蚂蚁的搜索能力,另一方面对信息挥发因子作适应性改进以提高蚂蚁的自适应能力;最后,针对基本算法和改进的混合优化算法,仿真实验和平台实验分别进行了性能指标和抓取时间的对比分析。实验结果表明,仿真环境下,与蚁群优化（ACO）算法和禁忌搜索（TS）算法相比,混合优化算法的平均迭代次数降低了约50%,且其他性能较为优越,平台测试的抓取用时测试结果也说明了混合优化算法较随机结果和基本算法的优越性,可以快速完成元件抓取任务。     

奖惩蚁群算法

由于传统蚁群算法所采用的是随机概率搜索策略,收敛速度慢是其主要问题。为了提高算法的收敛速度,这里提出一种带奖惩策略的蚁群算法（PPACO）。新算法中,每次循环中发现的较优解都被挑选出来加以奖励,而普通解则被惩罚,这样就加快了较优路径和普通路径上信息素的差异;另外,为了不使这种差异对算法产生过多的影响,所有路径上的信息素都被限制在一定的范围[τmin,τmax]内,同时,信息素的挥发系数被设为相对较高值。通过典型模拟实验证明,新算法对解决复杂组合优化问题非常有效。     

A hybrid ant colony optimization algorithm for optimal multiuser detection in DS-UWB system

A hybrid ant colony optimization algorithm is proposed by introducing extremal optimization local-search algorithm to the ant colony optimization (ACO) algorithm, and is applied to multiuser detection in direct sequence ultra wideband (DS-UWB) communication system in this paper. ACO algorithms have already successfully been applied to combinatorial optimization; however, as the pheromone accumulates, we may not get a global optimum because it can get stuck in a local minimum resulting in a bad steady state. Extremal optimization (EO) is a recently developed local-search heuristic method and has been successfully applied to a wide variety of optimization problems. Hence in this paper, a hybrid ACO algorithm, named ACO-EO algorithm, is proposed by introducing EO to ACO to improve the local-search ability of the algorithm. The ACO-EO algorithm is applied to multiuser detection in DS-UWB communication system, and via computer simulations it is shown that the proposed hybrid ACO algorithm has much better performance than other ACO algorithms and even equal to the optimal multiuser detector.     

An improved firefly algorithm for solving dynamic multidimensional knapsack problems

There is a wide range of publications reported in the literature, considering optimization problems where the entire problem related data remains stationary throughout optimization. However, most of the real-life problems have indeed a dynamic nature arising from the uncertainty of future events. Optimization in dynamic environments is a relatively new and hot research area and has attracted notable attention of the researchers in the past decade. Firefly Algorithm (FA), Genetic Algorithm (GA) and Differential Evolution (DE) have been widely used for static optimization problems, but the applications of those algorithms in dynamic environments are relatively lacking. In the present study, an effective FA introducing diversity with partial random restarts and with an adaptive move procedure is developed and proposed for solving dynamic multidimensional knapsack problems. To the best of our knowledge this paper constitutes the first study on the performance of FA on a dynamic combinatorial problem. In order to evaluate the performance of the proposed algorithm the same problem is also modeled and solved by GA, DE and original FA. Based on the computational results and convergence capabilities we concluded that improved FA is a very powerful algorithm for solving the multidimensional knapsack problems for both static and dynamic environments.     

An effective ant colony optimization algorithm for multi-objective job-shop scheduling with equal-size lot-splitting

This paper proposes several novel hybrid ant colony optimization (ACO)-based algorithms to resolve multi-objective job-shop scheduling problem with equal-size lot splitting. The main issue discussed in this paper is lot-splitting of jobs and tradeoff between lot-splitting costs and makespan. One of the disadvantages of ACO is its uncertainty on time of convergence. In order to enrich search patterns of ACO and improve its performance, five enhancements are made in the proposed algorithms including: A new type of pheromone and greedy heuristic function; Three new functions of state transition rules; A nimble local search algorithm for the improvements of solution quality; Mutation mechanism for divisive searching; A particle swarm optimization (PSO)-based algorithm for adaptive tuning of parameters. The objectives that are used to measure the quality of the generated schedules are weighted-sum of makespan, tardiness of jobs and lot-splitting cost. The developed algorithms are analyzed extensively on real-world data obtained from a printing company and simulated data. A mathematical programming model is developed and paired-samples t-tests are performed between obtained solutions of mathematical programming model and proposed algorithms in order to verify effectiveness of proposed algorithms.     

Applying multi-objective ant colony optimization algorithm for solving the unequal area facility layout problems

The unequal area facility layout problem (UA-FLP) which deals with the layout of departments in a facility comprises of a class of extremely difficult and widely applicable multi-objective optimization problems with constraints arising in diverse areas and meeting the requirements for real-world applications. Based on the heuristic strategy, the problem is first converted into an unconstrained optimization problem. Then, we use a modified version of the multi-objective ant colony optimization (MOACO) algorithm which is a heuristic global optimization algorithm and has shown promising performances in solving many optimization problems to solve the multi-objective UA-FLP. In the modified MOACO algorithm, the ACO with heuristic layout updating strategy which is proposed to update the layouts and add the diversity of solutions is a discrete ACO algorithm, with a difference from general ACO algorithms for discrete domains which perform an incremental construction of solutions but the ACO in this paper does not. We propose a novel pheromone update method and combine the Pareto optimization based on the local pheromone communication and the global search based on the niche technology to obtain Pareto-optimal solutions of the problem. In addition, the combination of the local search based on the adaptive gradient method and the heuristic department deformation strategy is applied to deal with the non-overlapping constraint between departments so as to obtain feasible solutions. Ten benchmark instances from the literature are tested. The experimental results show that the proposed MOACO algorithm is an effective method for solving the UA-FLP.