Solving the traveling salesman problem using cooperative genetic ant systems

The travelling salesman problem (TSP) is a classic problem of combinatorial optimization and has applications in planning, scheduling, and searching in many scientific and engineering fields. Ant colony optimization (ACO) has been successfully used to solve TSPs and many associated applications in the last two decades. However, ACO has problem in regularly reaching the global optimal solutions for TSPs due to enormity of the search space and numerous local optima within the space. In this paper, we propose a new hybrid algorithm, cooperative genetic ant system (CGAS) to deal with this problem. Unlike other previous studies that regarded GA as a sequential part of the whole searching process and only used the result from GA as the input to subsequent ACO iterations, this new approach combines both GA and ACO together in a cooperative manner to improve the performance of ACO for solving TSPs. The mutual information exchange between ACO and GA in the end of the current iteration ensures the selection of the best solutions for next iteration. This cooperative approach creates a better chance in reaching the global optimal solution because independent running of GA maintains a high level of diversity in next generation of solutions. Compared with results from other GA/ACO algorithms, our simulation shows that CGAS has superior performance over other GA and ACO algorithms for solving TSPs in terms of capability and consistency of achieving the global optimal solution, and quality of average optimal solutions, particularly for small TSPs.     

Neural network and genetic algorithm-based hybrid approach to expanded job-shop scheduling

The expanded job-shop scheduling problem (EJSSP) is a practical production scheduling problem with processing constraints that are more restrictive and a scheduling objective that is more general than those of the standard job-shop scheduling problem (JSSP). A hybrid approach involving neural networks and genetic algorithm (GA) is presented to solve the problem in this paper. The GA is used for optimization of sequence and a neural network (NN) is used for optimization of operation start times with a fixed sequence.

After detailed analysis of an expanded job shop, new types of neurons are defined to construct a constraint neural network (CNN). The neurons can represent processing restrictions and resolve constraint conflicts. CNN with a gradient search algorithm, gradient CNN in short, is applied to the optimization of operation start times with a fixed processing sequence. It is shown that CNN is a general framework representing scheduling problems and gradient CNN can work in parallel for optimization of operation start times of the expanded job shop.

Combining gradient CNN with a GA for sequence optimization, a hybrid approach is put forward. The approach has been tested by a large number of simulation cases and practical applications. It has been shown that the hybrid approach is powerful for complex EJSSP.     

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.     

Application of heuristic and hybrid-GASA algorithms to tool-path optimization problem for minimizing airtime during machining

In this paper, heuristic algorithms such as simulated annealing (SA), genetic algorithm (GA) and hybrid algorithm (hybrid-GASA) were applied to tool-path optimization problem for minimizing airtime during machining. Many forms of SA rely on random starting points that often give poor solutions. The problem of how to efficiently provide good initial estimates of solution sets automatically is still an ongoing research topic. This paper proposes a hybrid approach in which GA provides a good initial solution for SA runs. These three algorithms were tested on three-axis-cartesian robot during milling of wood materials. Their performances were compared based on minimum path and consequently minimum airtime. In order to make a comparison between these algorithms, two cases among the several milling operations were given here. According to results obtained from these examples, hybrid algorithm gives better results than other heuristic algorithms alone. Due to combined global search feature of GA and local search feature of SA, hybrid approach using GA and SA produces about 1.5% better minimum path solutions than standard GA and 47% better minimum path solutions than standard SA.     

A hybrid genetic algorithm for the single machine scheduling problem with sequence-dependent setup times

This paper presents a hybrid approach based on the integration between a genetic algorithm (GA) and concepts from constraint programming, multi-objective evolutionary algorithms and ant colony optimization for solving a scheduling problem. The main contributions are the integration of these concepts in a GA crossover operator. The proposed methodology is applied to a single machine scheduling problem with sequence-dependent setup times for the objective of minimizing the total tardiness. A sensitivity analysis of the hybrid approach is carried out to compare the performance of the GA and the hybrid genetic algorithm (HGA) approaches on different benchmarks from the literature. The numerical experiments demonstrate the HGA efficiency and effectiveness which generates solutions that approach those of the known reference sets and improves several lower bounds.     

A hybrid genetic and variable neighborhood descent algorithm for flexible job shop scheduling problems

This paper addresses the flexible job shop scheduling problem (fJSP) with three objectives: min makespan, min maximal machine workload and min total workload. We developed a hybrid genetic algorithm (GA) for the problem. The GA uses two vectors to represent solutions. Advanced crossover and mutation operators are used to adapt to the special chromosome structure and the characteristics of the problem. In order to strengthen the search ability, individuals of GA are first improved by a variable neighborhood descent (VND), which involves two local search procedures: local search of moving one operation and local search of moving two operations. Moving an operation is to delete the operation, find an assignable time interval for it, and allocate it in the assignable interval. We developed an efficient method to find assignable time intervals for the deleted operations based on the concept of earliest and latest event time. The local optima of moving one operation are further improved by moving two operations simultaneously. An extensive computational study on 181 benchmark problems shows the performance of our approach.     

一种求解车间作业调度问题的混合邻域结构搜索算法

车间作业调度问题是优化组合中一个著名的难题,问题的目标是在满足约束条件的前提下,使调度的加工周期尽可能小。文章中提出了利用新的混合邻域结构进行搜索来求解车间作业调度问题。对于算法关键的邻域构造问题以及跳坑策略给出了提高算法优度的解决方案。采用43个不同规模和难度的国际标准算例做为本算法的测试实验集,39个算例找到了最优解,其中包括著名的难例FT10。与当前国外学者提出的一种先进算法进行了比较,算法的优度高于被比较的先进算法。     

A neural network job-shop scheduler

This paper focuses on the development of a neural network (NN) scheduler for scheduling job-shops. In this hybrid intelligent system, genetic algorithms (GA) are used to generate optimal schedules to a known benchmark problem. In each optimal solution, every individually scheduled operation of a job is treated as a decision which contains knowledge. Each decision is modeled as a function of a set of job characteristics (e.g., processing time), which are divided into classes using domain knowledge from common dispatching rules (e.g., shortest processing time). A NN is used to capture the predictive knowledge regarding the assignment of operation’s position in a sequence. The trained NN could successfully replicate the performance of the GA on the benchmark problem. The developed NN scheduler was then tested against the GA, Attribute-Oriented Induction data mining methodology and common dispatching rules on a test set of randomly generated problems. The better performance of the NN scheduler on the test problem set compared to other methods proves the feasibility of NN-based scheduling. The scalability of the NN scheduler on larger problem sizes was also found to be satisfactory in replicating the performance of the GA.     

An Immune-based Genetic Algorithm with Reduced Search Space Coding for Multiprocessor Task Scheduling Problem

Multiprocessor task scheduling is an important problem in parallel applications and distributed systems. In this way, solving the multiprocessor task scheduling problem (MTSP) by heuristic, meta-heuristic, and hybrid algorithms have been proposed in literature. Although the problem has been addressed by many researchers, challenges to improve the convergence speed and the reliability of methods for solving the problem are still continued especially in the case that the communication cost is added to the problem frame work. In this paper, an Immune-based Genetic algorithm (IGA), a meta-heuristic approach, with a new coding scheme is proposed to solve MTSP. It is shown that the proposed coding reduces the search space of MTSP in many practical problems, which effectively influences the convergence speed of the optimization process. In addition to the reduced search space offered by the proposed coding that eventuate in exploring better solutions at a shorter time frame, it guarantees the validity of solutions by using any crossover and mutation operators. Furthermore, to overcome the regeneration phenomena in the proposed GA (generating similar chromosomes) which leads to premature convergence, an affinity based approach inspired from Artificial Immune system is employed which results in better exploration in the searching process. Experimental results showed that the proposed IGA surpasses related works in terms of found makespan (20% improvement in average) while it needs less iterations to find the solutions (90% improvement in average) when it is applied to standard test benches.     

Scheduling two-stage hybrid flow shops with parallel batch, release time, and machine eligibility constraints

This paper investigates a difficult scheduling problem on a specialized two-stage hybrid flow shop with multiple processors that appears in semiconductor manufacturing industry, where the first and second stages process serial jobs and parallel batches, respectively. The objective is to seek job-machine, job-batch, and batch-machine assignments such that makespan is minimized, while considering parallel batch, release time, and machine eligibility constraints. We first propose a mixed integer programming (MIP) formulation for this problem, then gives a heuristic approach for solving larger problems. In order to handle real world large-scale scheduling problems, we propose an efficient dispatching rule called BFIFO that assigns jobs or batches to machines based on first-in-first-out principle, and then give several reoptimization techniques using MIP and local search heuristics involving interchange, translocation and transposition among assigned jobs. Computational experiments indicate our proposed re-optimization techniques are efficient. In particular, our approaches can produce good solutions for scheduling up to 160 jobs on 40 machines at both stages within 10?min.     

Glass container production scheduling through hybrid multi-population based evolutionary algorithm

Driven by a real-world application in the capital-intensive glass container industry, this paper provides the design of a new hybrid evolutionary algorithm to tackle the short-term production planning and scheduling problem. The challenge consists of sizing and scheduling the lots in the most cost-effective manner on a set of parallel molding machines that are fed by a furnace that melts the glass. The solution procedure combines a multi-population hierarchically structured genetic algorithm (GA) with a simulated annealing (SA), and a tailor-made heuristic named cavity heuristic (CH). The SA is applied to intensify the search for solutions in the neighborhood of the best individuals found by the GA, while the CH determines quickly values for a relevant decision variable of the problem: the processing speed of each machine. The results indicate the superior performance of the proposed approach against a state-of-the-art commercial solver, and compared to a non-hybridized multi-population GA.     

On the design of hybrid bio-inspired meta-heuristics for complex multiattribute vehicle routing problems

This paper addresses a multiattribute vehicle routing problem, the rich vehicle routing problem, with time constraints, heterogeneous fleet, multiple depots, multiple routes, and incompatibilities of goods. Four different approaches are presented and applied to 15 real datasets. They are based on two meta-heuristics, ant colony optimization (ACO) and genetic algorithm (GA), that are applied in their standard formulation and combined as hybrid meta-heuristics to solve the problem. As such ACO-GA is a hybrid meta-heuristic using ACO as main approach and GA as local search. GA-ACO is a memetic algorithm using GA as main approach and ACO as local search. The results regarding quality and computation time are compared with two commercial tools currently used to solve the problem. Considering the number of customers served, one of the tools and the ACO-GA approach outperforms the others. Considering the cost, ACO, GA, and GA-ACO provide better results. Regarding computation time, GA and GA-ACO have been found the most competitive among the benchmark.     

机组短期负荷环境／经济调度多目标混合优化

环境/经济短期负荷调度主要由调度周期内的最优机组组合和负荷环境/经济分配组成,本文将变权重多目标进化算法与混沌局部优化相结合形成混合优化算法应用到电站机组环境/经济运行多目标优化问题中,在混合多目标优化算法中采用组合结构基因,其中机组基因用于机组组合全局粗寻优,参数基因用于负荷分配局部优化,基因修正与罚函数结合解决约束问题．通过对优秀个体进行基于线性搜索的混沌局部优化,可加快收敛速度和降低计算时间．实例仿真结果说明所提出的算法能获得较好分布的Pareto优化解．     

Embedded local search approaches for routing optimization

This paper presents a new class of heuristics which embed an exact algorithm within the framework of a local search heuristic. This approach was inspired by related heuristics which we developed for a practical problem arising in electronics manufacture. The basic idea of this heuristic is to break the original problem into small subproblems having similar properties to the original problem. These subproblems are then solved using time intensive heuristic approaches or exact algorithms and the solution is re-embedded into the original problem. The electronics manufacturing problem where we originally used the embedded local search approach, contains the Travelling Salesman Problem (TSP) as a major subproblem. In this paper we further develop our embedded search heuristic, HyperOpt, and investigate its performance for the TSP in comparison to other local search based approaches. We introduce an interesting hybrid of HyperOpt and 3-opt for asymmetric TSPs which proves more efficient than HyperOpt or 3-opt alone. Since pure local search seldom yields solutions of high quality we also investigate the performance of the approaches in an iterated local search framework. We examine iterated approaches of Large-Step Markov Chain and Variable Neighbourhood Search type and investigate their performance when used in combination with HyperOpt. We report extensive computational results to investigate the performance of our heuristic approaches for asymmetric and Euclidean Travelling Salesman Problems. While for the symmetric TSP our approaches yield solutions of comparable quality to 2-opt heuristic, the hybrid methods proposed for asymmetric problems seem capable of compensating for the time intensive embedded heuristic by finding tours of better average quality than iterated 3-opt in many less iterations and providing the best heuristic solutions known, for some instance classes.     

Minimizing makespan for flow shop scheduling problem with intermediate buffers by using hybrid approach of artificial immune system

In this study, three new meta-heuristic algorithms artificial immune system (AIS), iterated greedy algorithm (IG) and a hybrid approach of artificial immune system (AIS-IG) are proposed to minimize maximum completion time (makespan) for the permutation flow shop scheduling problem with the limited buffers between consecutive machines. As known, this category of scheduling problem has wide application in the manufacturing and has attracted much attention in academic fields. Different from basic artificial immune systems, the proposed AIS-IG algorithm is combined with destruction and construction phases of iterated greedy algorithm to improve the local search ability. The performances of these three approaches were evaluated over Taillard, Carlier and Reeves benchmark problems. It is shown that the AIS-IG and AIS algorithms not only generate better solutions than all of the well-known meta heuristic approaches but also can maintain their quality for large scale problems.     

A very fast TS/SA algorithm for the job shop scheduling problem

The job shop scheduling problem (JSP) is one of the most notoriously intractable NP-complete optimization problems. Over the last 10–15 years, tabu search (TS) has emerged as an effective algorithmic approach for the JSP. However, the quality of solutions found by tabu search approach depends on the initial solution. To overcome this problem and provide a robust and efficient methodology for the JSP, the heuristics search approach combining simulated annealing (SA) and TS strategy is developed. The main principle of this approach is that SA is used to find the elite solutions inside big valley (BV) so that TS can re-intensify search from the promising solutions. This hybrid algorithm is tested on the standard benchmark sets and compared with the other approaches. The computational results show that the proposed algorithm could obtain the high-quality solutions within reasonable computing times. For example, 17 new upper bounds among the unsolved problems are found in a short time.     

基于混合粒子群算法的云计算任务调度研究

任务调度是云计算系统可靠运行的关键,云计算环境中要处理的任务量巨大,考虑到云计算任务调度和QoS的优化问题,提出一种混合粒子群优化算法用于云任务调度。算法中引入遗传算法的交叉和变异思想,并结合随迭代次数变化的变异指数,保证种群进化初期具有较高的全局搜索能力,避免出现"早熟",同时将爬山算法引入粒子群算法,改善局部搜索能力。实验结果显示该算法具有很好的寻优能力,是一种有效的云计算任务调度算法。     

A hybrid computational strategy for identification of structural parameters

By identifying parameters such as stiffness values of a structural system, the numerical model can be updated to give more accurate response prediction or to monitor the state of the structure. Considerable progress has been made in this subject area, but most research works have considered only small systems. A major challenge lies in obtaining good identification results for systems with many unknown parameters. In this study, a non-classical approach is adopted involving the use of genetic algorithms (GA). Nevertheless, direct application of GA does not necessarily work, particularly with regards to computational efficiency in fine-tuning when the solution approaches the optimal value. A hybrid computational strategy is thus proposed, combining GA with a compatible local search operator. Two hybrid methods are formulated and illustrated by numerical simulation studies to perform significantly better than the GA method without local search. A fairly large structural system with 52 unknown parameters is identified with good results, taking into consideration the effects of incomplete measurement and noisy data.     

An adaptive hybrid genetic algorithm for the three-matching problem

This paper presents a hybrid genetic algorithm (GA) with an adaptive application of genetic operators for solving the 3-matching problem (3MP), an NP-complete graph problem. In the 3MP, we search for the partition of a point set into minimal total cost triplets, where the cost of a triplet is the Euclidean length of the minimal spanning tree of the three points. The problem is a special case of grouping and facility location problems. One common problem with GA applied to hard combinatorial optimization, like the 3MP, is to incorporate problem-dependent local search operators into the GA efficiently in order to find high-quality solutions. Small instances of the problem can be solved exactly, but for large problems, we use local optimization. We introduce several general heuristic crossover and local hill-climbing operators, and apply adaptation to choose among them. Our GA combines these operators to form an effective problem solver. It is hybridized as it incorporates local search heuristics, and it is adaptive as the individual recombination/improvement operators are fired according to their online performance. Test results show that this approach gives approximately the same or even slightly better results than our previous, fine tuned GA without adaptation. It is better than a grouping GA for the partitioning considered. The adaptive combination of operators eliminates a large set of parameters, making the method more robust, and it presents a convenient way to build a hybrid problem solver     

Hybridization of very large neighborhood search for ready-mixed concrete delivery problems

Companies in the concrete industry are facing the following scheduling problem on a daily basis: concrete produced at several plants has to be delivered at customers’ construction sites using a heterogeneous fleet of vehicles in a timely, but cost-effective manner. The distribution of ready-mixed concrete (RMC) is a highly complex problem in logistics and combinatorial optimization.This paper proposes two hybrid solution procedures for dealing with this problem. They are based on a combination of an exact algorithm and a variable neighborhood search (VNS) approach. The VNS is used at first to generate feasible solutions and is trying to further improve them. The exact method is based on a mixed integer linear programming (MILP) formulation, which is solved (after an appropriated variable fixing phase) by using a general-purpose MILP solver. An approach based on very large neighborhood search (VLNS) determines which variables are supposed to be fixed. In a sense, the approaches follows a local branching scheme. The hybrid metaheuristics are compared with the pure VNS approach and the conclusion is that the new metaheuristics outperform the VNS if applied solely.