A tabu method for a two-agent single-machine scheduling with deterioration jobs

In recent 10 years, the multi-agent idea applied in scheduling issues has received continuing attention. However, the study of the multi-agent scheduling with deteriorating jobs is relatively limited. In light of this, this paper deliberates upon a two-agent single-machine scheduling problem with deteriorating jobs. Taking the proposed model, the actual processing time of a job from both the first agent and the second agent is modeled as a linearly increasing function of its starting time. The goal of this paper is to minimize the total weighted number of tardy jobs of the first agent subject to the condition that the maximum lateness of the second agent is allowed to have an upper bound. The complexity of the model concerned in the paper is claimed as an NP-hard one. Following that, several dominance rules and a lower bound are proposed to be applied in a branch-and-bound algorithm for the optimal solution, and a tabu algorithm is applied to find near-optimal solutions for the problem. The simulation results obtained from all the proposed algorithms are also reported.     

Flow shop scheduling problems with decreasing linear deterioration under dominant machines

This paper considers the general, no-wait and no-idle flow shop scheduling problems with deteriorating jobs, respectively. By a deteriorating job, we mean that the processing time is a decreasing function of its execution starting time. The normal processing time proportional to its decreasing rate is assumed and some dominant relationships between machines can be satisfied. It is shown that for the problems to minimize the makespan or the weighted sum of completion time, polynomial algorithms still exist, although these problems are more complicated than the classical ones. When the objective is to minimize the maximum lateness, the solutions of a classical version may not hold.     

A two-agent single-machine scheduling problem with truncated sum-of-processing-times-based learning considerations

Scheduling with learning effects has received a lot of research attention lately. By learning effect, we mean that job processing times can be shortened through the repeated processing of similar tasks. On the other hand, different entities (agents) interact to perform their respective tasks, negotiating among one another for the usage of common resources over time. However, research in the multi-agent setting is relatively limited. Meanwhile, the actual processing time of a job under an uncontrolled learning effect will drop to zero precipitously as the number of jobs increases or a job with a long processing time exists. Motivated by these observations, we consider a two-agent scheduling problem in which the actual processing time of a job in a schedule is a function of the sum-of-processing-times-based learning and a control parameter of the learning function. The objective is to minimize the total weighted completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We develop a branch-and-bound and three simulated annealing algorithms to solve the problem. Computational results show that the proposed algorithms are efficient in producing near-optimal solutions.     

A hybrid genetic and linear programming algorithm for two-agent order acceptance and scheduling problem

In this paper, the simultaneous order acceptance and scheduling problem is developed by considering the variety of customers’ requests. To that end, two agents with different scheduling criteria including the total weighted lateness for the first and the weighted number of tardy orders for the second agent are considered. The objective is to maximize the sum of the total profit of the first and the total revenue of the second agents’ orders when the weighted number of tardy orders of the second agent is bounded by an upper bound value. In this study, it is shown that this problem is NP-hard in the strong sense, and then to optimally solve it, an integer linear programming model is proposed based on the properties of optimal solution. This model is capable of solving problem instances up to 60 orders in size. Also, the LP-relaxation of this model was used to propose a hybrid meta-heuristic algorithm which was developed by employing genetic algorithm and linear programming. Computational results reveal that the proposed meta-heuristic can achieve near optimal solutions so efficiently that for the instances up to 60 orders in size, the average deviation of the model from the optimal solution is lower than 0.2% and for the instances up to 150 orders in size, the average deviation from the problem upper bound is lower than 1.5%.     

Scheduling jobs under decreasing linear deterioration

This paper considers the scheduling problems under decreasing linear deterioration. Deterioration of a job means that its processing time is a function of its execution start time. Optimal algorithms are presented respectively for single machine scheduling of minimizing the makespan, maximum lateness, maximum cost and number of late jobs. For two-machine flow shop scheduling problem to minimize the makespan, it is proved that the optimal schedule can be obtained by Johnson's rule. If the processing times of operations are equal for each job, flow shop scheduling problems can be transformed into single machine scheduling problems.     

Fast computation of equispaced Pareto manifolds and Pareto fronts for multiobjective optimization problems

In this paper, we consider the problem of generating a well sampled discrete representation of the Pareto manifold or the Pareto front corresponding to the equilibrium points of a multi-objective optimization problem. We show how the introduction of simple additional constraints into a continuation procedure produces equispaced points in either of those two sets. Moreover, we describe in detail a novel algorithm for global continuation that requires two orders of magnitude less function evaluations than evolutionary algorithms commonly used to solve this problem. The performance of the methods is demonstrated on problems from the current literature.     

Utopian point based decomposition for multi-objective optimization problems with complicated Pareto fronts

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been considered as a promising method for solving multi-objective optimization problems (MOPs). It devotes most of its effort on convergence by optimizing a set of scalar optimization subproblems in a collaborative manner, while maintaining the diversity by using a set of uniformly distributed weight vectors. However, more recent studies illustrated that MOEA/D faces difficulties on MOPs with complicated Pareto fronts, mainly because the uniformity of weight vectors no longer lead to an evenly scattered approximation of the Pareto fronts in these cases. To remedy this, we suggest replacing the ideal point in the reciprocal Tchebycheff decomposition method with a more optimistic utopian point, with the aim of alleviating the sensitivity of MOEA/D to the Pareto front shape of MOPs. Experimental studies on benchmark and real-world problems have shown that such simple modification can significantly improve the performances of MOEA/D with reciprocal Tchebycheff decomposition on MOPs with complicated Pareto fronts.     

A self-adaptive linear evolutionary algorithm for solving constrained optimization problems

In many real-world applications of evolutionary algorithms, the fitness of an individual requires a quantitative measure. This paper proposes a self-adaptive linear evolutionary algorithm (ALEA) in which we introduce a novel strategy for evaluating individual’s relative strengths and weaknesses. Based on this strategy, searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ‘good’ individuals of the performance for a multiobjective optimization application, regardless of original space complexity. This is considered as our main contribution. In addition, the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase, namely, crossover and mutation. Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective, and provides good performance in terms of uniformity and diversity of solutions.     

Genetic algorithms for a two-agent single-machine problem with release time

Scheduling with two competing agents has drawn a lot of attention lately. However, it is assumed that all the jobs are available in the beginning in most of the research. In this paper, we study a single-machine problem in which jobs have different release times. The objective is to minimize the total tardiness of jobs from the first agent given that the maximum tardiness of jobs from the second agent does not exceed an upper bound. Three genetic algorithms are proposed to obtain the near-optimal solutions. Computational results show that the branch-and-bound algorithm could solve most of the problems with 16 jobs within a reasonable amount of time. In addition, it shows that the performance of the combined genetic algorithm is very good with mean error percentages of less than 0.2% for all the cases.     

求解机械优化的Pareto多目标中心粒子群算法

针对基于权重法的多目标算法无法求解约束多目标问题的缺陷,将中心粒子群算法与Pareto解集搜索算法相结合,提出一种Pareto多目标中心粒子群算法。将此方法用来优化气门弹簧的模型,实验结果表明,该优化方法能够快速准确地收敛于Pareto解集,并且使其对应的目标域均匀地分布于Pareto最优目标域。     

An investigation on a two-agent single-machine scheduling problem with unequal release dates

This paper addresses a two-agent scheduling problem on a single machine with arbitrary release dates, where the objective is to minimize the tardiness of one agent, while keeping the lateness of the other agent below or at a fixed level Q. A mixed integer programming model is first presented for its optimal solution, admittedly not to be practical or useful in the most cases, but theoretically interesting since it models the problem. Thus, as an alternative, a branch-and-bound algorithm incorporating with several dominance properties and a lower bound is provided to derive the optimal solution and a marriage in honey-bees optimization algorithm (MBO) is developed to derive the near-optimal solutions for the problem. Computational results are also presented to evaluate the performance of the proposed algorithms.     

A discrete version of particle swarm optimization for flowshop scheduling problems

Particle swarm optimization (PSO) is a novel metaheuristic inspired by the flocking behavior of birds. The applications of PSO to scheduling problems are extremely few. In this paper, we present a PSO algorithm, extended from discrete PSO, for flowshop scheduling. In the proposed algorithm, the particle and the velocity are redefined, and an efficient approach is developed to move a particle to the new sequence. To verify the proposed PSO algorithm, comparisons with a continuous PSO algorithm and two genetic algorithms are made. Computational results show that the proposed PSO algorithm is very competitive. Furthermore, we incorporate a local search scheme into the proposed algorithm, called PSO-LS. Computational results show that the local search can be really guided by PSO in our approach. Also, PSO-LS performs well in flowshop scheduling with total flow time criterion, but it requires more computation times.     

A Pareto archive particle swarm optimization for multi-objective job shop scheduling

In this paper, we present a particle swarm optimization for multi-objective job shop scheduling problem. The objective is to simultaneously minimize makespan and total tardiness of jobs. By constructing the corresponding relation between real vector and the chromosome obtained by using priority rule-based representation method, job shop scheduling is converted into a continuous optimization problem. We then design a Pareto archive particle swarm optimization, in which the global best position selection is combined with the crowding measure-based archive maintenance. The proposed algorithm is evaluated on a set of benchmark problems and the computational results show that the proposed particle swarm optimization is capable of producing a number of high-quality Pareto optimal scheduling plans.     

多目标拆卸线平衡问题的Pareto细菌觅食算法*

拆卸线平衡问题的优化涉及多个目标,为克服传统方法在求解多目标拆卸线平衡问题时不能很好处理各子目标间冲突及易于早熟等不足,提出了一种多目标细菌觅食优化算法。算法采用Pareto非劣排序技术对种群进行分级,并结合拥挤距离机制评价同级个体的优劣。为提高算法收敛性能,在趋向性操作结束后引入精英保留策略保留优秀个体,并采用全局信息共享策略引导菌群不断向均匀分布的Pareto最优前沿趋近。通过不同规模算例的对比验证表明了算法的有效性与优越性。     

Solving software project scheduling problems with ant colony optimization

Software project scheduling problem (SPSP) is one of the important and challenging problems faced by the software project managers in the highly competitive software industry. As the problem is becoming an NP-hard problem with the increasing numbers of employees and tasks, only a few algorithms exist and the performance is still not satisfying. To design an effective algorithm for SPSP, this paper proposes an ant colony optimization (ACO) approach which is called ACS-SPSP algorithm. Since a task in software projects involves several employees, in this paper, by splitting tasks and distributing dedications of employees to task nodes we get the construction graph for ACO. Six domain-based heuristics are designed to consider the factors of task efforts, allocated dedications of employees and task importance. Among these heuristic strategies, the heuristic of allocated dedications of employees to other tasks performs well. ACS-SPSP is compared with a genetic algorithm to solve the SPSP on 30 random instances. Experimental results show that the proposed algorithm is promising and can obtain higher hit rates with more accuracy compared to the previous genetic algorithm solution.     

一种基于Pareto最优概念和神经网络混合策略的多目标进化算法

基于Pareto最优的多目标进化算法得到了广泛地应用,但不适用于目标函数为非解析式的情况。基于神经网络和Pareto最优的联合策略,提出了一种解决此类问题的新方法：首先采用神经网络对历史数据进行学习,建立有效的神经网络模型来代替目标函数解析式;然后将神经网络模型嵌入多目标进化算法,进行进化计算;最后,将本文方法应用于卷烟配方比例掺配问题。实验结果表明,该方法优于传统方法,能较好地解决问题。     

Restarted Iterated Pareto Greedy algorithm for multi-objective flowshop scheduling problems

Multi-objective optimisation problems have seen a large impulse in the last decades. Many new techniques for solving distinct variants of multi-objective problems have been proposed. Production scheduling, as with other operations management fields, is no different. The flowshop problem is among the most widely studied scheduling settings. Recently, the Iterated Greedy methodology for solving the single-objective version of the flowshop problem has produced state-of-the-art results. This paper proposes a new algorithm based on Iterated Greedy technique for solving the multi-objective permutation flowshop problem. This algorithm is characterised by an effective initialisation of the population, management of the Pareto front, and a specially tailored local search, among other things. The proposed multi-objective Iterated Greedy method is shown to outperform other recent approaches in comprehensive computational and statistical tests that comprise a large number of instances with objectives involving makespan, tardiness and flowtime. Lastly, we use a novel graphical tool to compare the performances of stochastic Pareto fronts based on Empirical Attainment Functions.     

基于混沌的多目标粒子群优化算法

针对多目标优化问题,提出了一种改进的粒子群算法.该算法为了寻找新解,引入了混沌搜索技术,同时采用了一种新的方法--拥挤距离法定义解的适应度.并采取了精英保留策略,在提高非劣解集多样性的同时,使解集更加趋近于Pareto集.最后,把算法应用到4个典型的多目标测试函数.数值结果表明,该算法能够有效的收敛到Pareto非劣最优目标域,并沿着Pareto非劣目标域有很好的分散性.     

Two-machine flow shop scheduling with linear decreasing job deterioration

In this paper, we consider a two-machine flow shop scheduling problem with deteriorating jobs. By a deteriorating job, we mean that the processing time is a decreasing function of its execution start time. A proportional linear decreasing deterioration function is assumed. The objective is to find a sequence that minimizes total completion time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and some lower bounds are derived to speed up the elimination process of a branch-and-bound algorithm. A heuristic algorithm is also proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational results for randomly generated problem instances are presented, which show that the heuristic algorithm effectively and efficiently in obtaining near-optimal solutions.     

一种多目标优化问题的理想灰色粒子群算法*

针对逼近理想解的排序方法对Pareto前端的距离跟踪以及灰色关联度能够很好地分析非劣解集曲线与Pareto最优解集曲线的相似性,提出了一种求解多目标优化问题的理想灰色粒子群算法。该算法利用理想解理论与灰色关联度理论来求解粒子与理想解之间的相对适应度和灰色关联度系数,把两者的和定义为相对理想度,通过相对理想度来判别粒子的优劣,以确定个体极值和全局极值。通过四组不同类型的基准函数测试算法性能,并与目标加权法和灰色粒子群算法比较分析,结果表明该算法能够较好地收敛到Pareto最优解集,不但具有较好的收敛性和分布