多项目环境下time-cost置换问题建模与求解

针对多项目环境下的time-cost置换问题,以活动资源为决策变量,建立了以各项目总延迟最小与总成本最小的双目标time-cost置换模型。在总结前人对于多目标优化求解方法的基础上,针对多项目的特点,提出了基于NSGA-II非劣排序的局部直接搜索改进遗传算法,并考虑资源为连续与离散两种情况进行求解。与NSGA-II相比,算法可以较快地收敛到最优解,并且具有较好的离散变量搜索能力,与ZDT系列测试函数的比较也体现了算法的优越性。     

基于改进蚁群算法的项目组合工期——成本优化的研究

基于企业战略导向的项目组合工期——成本优化问题是企业进行多项目管理时需要解决的重要问题,对企业资源效益最大化发挥起到关键作用,它从本质上属于多目标优化问题。本文将蚁群算法引入项目组合工期——成本优化问题的求解,并针对蚁群算法存在的早熟、停止、局部最优的缺点,提出与混沌结合的改进蚁群算法,引进确定和不确定性搜索规则。实验结果表明,改进的蚁群算法能够有效地提高蚁群算法的全局寻优能力,对工期——成本优化问题的求解能够得出比较好的结果。     

基于改进蚁群算法的项目组合工期-成本优化

战略导向下的项目组合工期-成本优化是现代企业进行多项目管理所面临的重要问题之一,对企业实现资源效益最大化有着至关重要的促进作用。以战略导向下的项目组合工期-成本综合值最小化为研究对象,提出了优化组合项目中工序选择和执行次序的数学模型,在引入自适应权重法、调整信息素系数和混沌扰动变量的基础上,设计了求解该优化模型的改进蚁群算法。通过实例运算表明,改进后的蚁群算法,能够有效地提高算法全局搜索寻优能力和收敛速度,在求解战略导向下的项目组合工期-成本优化问题方面有较强的鲁棒性和实用价值。     

The risk element transmission theory research of multi-objective risk-time-cost trade-off

Risk management project is an important aspect of general project risk element transmission theory. To solve the multi-objective time-cost trade-off problem considering the risk elements effectively, this paper establishes an analytical model for multi-objective risk-time-cost trade-off problem based on general project risk element transmission theory. We divide risk elements into discrete model and continuous model to be discussed separately, and the two models for multi-objective risk-time-cost trade-off problem are established by taking Markov dynamic PERT network into classical PERT network. Thus, we combine Radial Basis Function (RBF) neural network to solve the discrete model of the problem. Finally, a practical example illustrates the effectiveness of the algorithm.     

The discrete time/cost trade-off problem: extensions and heuristic procedures

Time/cost trade-offs in project networks have been the subject of extensive research since the development of the critical path method (CPM) in the late 50s. Time/cost behaviour in a project activity basically describes the trade-off between the duration of the activity and its amount of non-renewable resources (e.g., money) committed to it. In the discrete version of the problem (the discrete time/cost trade-off problem), it is generally accepted that the trade-off follows a discrete non-increasing pattern, i.e., expediting an activity is possible by allocating more resources (i.e., at a larger cost) to it. However, due to its complexity, the problem has been solved for relatively small instances. In this paper we elaborate on three extensions of the well-known discrete time/cost trade-off problem in order to cope with more realistic settings: time/switch constraints, work continuity constraints, and net present value maximization. We give an extensive literature overview of existing procedures for these problem types and discuss a new meta-heuristic approach in order to provide near-optimal heuristic solutions for the different problems. We present computational results for the problems under study by comparing the results for both exact and heuristic procedures. We demonstrate that the heuristic algorithms produce consistently good results for two versions of the discrete time/cost trade-off problem.     

A hybrid project scheduling and material ordering problem: Modeling and solution algorithms

A novel combination of a multimode project scheduling problem with material ordering, in which material procurements are exposed to the total quantity discount policy is investigated in this paper. The study aims at finding an optimal Pareto frontier for a triple objective model derived for the problem. While the first objective minimizes the makespan of the project, the second objective maximizes the robustness of the project schedule and finally the third objective minimizes the total costs pertaining to renewable and nonrenewable resources involved in a project. Four well-known multi-objective evolutionary algorithms including non-dominated sorting genetic algorithm II (NSGAII), strength Pareto evolutionary algorithm II (SPEAII), multi objective particle swarm optimization (MOPSO), and multi objective evolutionary algorithm based on decomposition (MOEAD) solve the developed triple-objective problem. The parameters of algorithms are tuned by the response surface methodology. The algorithms are carried out on a set of benchmarks and are compared based on five performance metrics evaluating their efficiencies in terms of closeness to the optimal frontier, diversity, and variance of results. Finally, a statistical assessment is conducted to analyze the results obtained by the algorithms. Results show that the NSGAII considerably outperforms others in 4 out of 5 metrics and the MOPSO performs better in terms of the remaining metric.     

Optimizing a bi-objective multi-product EPQ model with defective items,rework and limited orders: NSGA-II and MOPSO algorithms

In this paper, a bi-objective multi-products economic production quantity (EPQ) model is developed, in which the number of orders is limited and imperfect items that are re-workable are produced. The objectives of the problem are minimization of the total inventory costs as well as minimizing the required warehouse space. The model is shown to be of a bi-objective nonlinear programming type, and in order to solve it two meta-heuristic algorithms namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm, are proposed. To verify the solution obtained and to evaluate the performance of proposed algorithms, two-sample t-tests are employed to compare the means of the first objective value, the means of the second objective values, and the mean required CPU time of solving the problem using two algorithms. The results show while both algorithms are efficient to solve the model and the solution qualities of the two algorithms do not differ significantly, the computational CPU time of MOPSO is considerably lower than that of NSGA-II.     

PSO-Based Multiobjective Optimization With Dynamic Population Size and Adaptive Local Archives

Recently, various multiobjective particle swarm optimization (MOPSO) algorithms have been developed to efficiently and effectively solve multiobjective optimization problems. However, the existing MOPSO designs generally adopt a notion to “estimate” a fixed population size sufficiently to explore the search space without incurring excessive computational complexity. To address the issue, this paper proposes the integration of a dynamic population strategy within the multiple-swarm MOPSO. The proposed algorithm is named dynamic population multiple-swarm MOPSO. An additional feature, adaptive local archives, is designed to improve the diversity within each swarm. Performance metrics and benchmark test functions are used to examine the performance of the proposed algorithm compared with that of five selected MOPSOs and two selected multiobjective evolutionary algorithms. In addition, the computational cost of the proposed algorithm is quantified and compared with that of the selected MOPSOs. The proposed algorithm shows competitive results with improved diversity and convergence and demands less computational cost.      

On convergence of the multi-objective particle swarm optimizers

Several variants of the particle swarm optimization (PSO) algorithm have been proposed in recent past to tackle the multi-objective optimization (MO) problems based on the concept of Pareto optimality. Although a plethora of significant research articles have so far been published on analysis of the stability and convergence properties of PSO as a single-objective optimizer, till date, to the best of our knowledge, no such analysis exists for the multi-objective PSO (MOPSO) algorithms. This paper presents a first, simple analysis of the general Pareto-based MOPSO and finds conditions on its most important control parameters (the inertia factor and acceleration coefficients) that govern the convergence behavior of the algorithm to the optimal Pareto front in the objective function space. Computer simulations over benchmark MO problems have also been provided to substantiate the theoretical derivations.     

基于多目标飞蛾算法的电力系统无功优化研究

鉴于电力需求的日益增长与传统无功优化方法的桎梏,如何更加合理有效地解决电力系统的无功优化问题逐渐成为了研究的热点。提出一种多目标飞蛾扑火算法来解决电力系统多目标无功优化的问题,算法引入固定大小的外部储存机制、自适应的网格和筛选机制来有效存储和提升无功优化问题的帕累托最优解集,算法采用CEC2009标准多目标测试函数来进行仿真实验,并与两种经典算法进行性能的对比分析。此外,在电力系统IEEE 30节点上将该算法与MOPSO,NGSGA-II算法的求解结果进行比较分析的结果表明,多目标飞蛾算法具有良好的性能,并在解决电力系统多目标无功优化问题上具有良好的潜力。     

Multi-mode resource constrained project scheduling and contractor selection: Mathematical formulation and metaheuristic algorithms

Contractor selection is a matter of particular attraction for project managers whose aim is to complete projects considering time, cost and quality issues. Traditionally, project scheduling and contractor selection decisions are made separately and sequentially. However, it is usually necessary to satisfy some principles and obligations that impose hard constraints to the problem under consideration. Ignoring this important issue and making project scheduling and contractor selection decisions consecutively may be suboptimal to a holistic view that makes all interrelated decisions in an integrated manner. In this paper, an integrated bi-objective optimization model is proposed to deal with Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP) and Contractor Selection (CS) problem, simultaneously. The objective of the proposed model is to minimize the total costs of the project, and minimize the makespan of the project, simultaneously. To solve the integrated MRCPSP-CS, two multi-objective meta-heuristic algorithms, Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization algorithm (MOPSO), are adopted, and 30 test problems of different sizes are solved. The parameter tuning is performed using the Taguchi method. Then, diversification metric (DM), mean ideal distance (MID), quality metric (QM) and number of Pareto solutions (NPS) are used to quantify the performance of meta-heuristic algorithms. Analytic Hierarchy Process (AHP), as a prominent multi-attribute decision-making method, is used to determine the relative importance of performance metrics. Computational results show the superior performance of MOPSO compared to NSGA-II for small-, medium- and large-sized test problems. Moreover, a sensitivity analysis shows that by increasing the number of available contractors, not only the makespan of the project is shortened, but also, the value of NPS in the Pareto front increases, which means that the decision maker(s) can make a wider variety of decisions in a more flexible manner.     

模糊网络计划工期成本优化方法

工程项目管理中项目工期的确定包括许多不确定因素,传统的网络计划方法不能解决此类不确定问题,基于模糊集合理论对工程项目工期的不确定性进行了分析论证,将三角模糊数引入到项目工期分析中,给出了工期的隶属度函数。建立一个基于遗传算法的工期一成本综合模糊优化模型,将模糊理论和遗传算法结合起来,提出一种模糊网络计划的工期一成本问题的优化方法。实验结果表明,该方法对模糊网络计划的工期一成本的优化有一定的灵活性和适应性。     

基于协作频谱感知的智能电网通信网性能研究

将认知无线电频谱感知技术应用于智能电网的通信网中,可以有效提高频谱资源的利用率。现有研究仅考虑单用户单供电商,但是对需求响应管理性能与感知能耗权衡问题却没有给出理想的解决方案。建立基于多节点协作频谱感知的多用户单供电商智能电网通信网模型。在此基础上,为求解该模型需求响应管理和能耗感知性能权衡问题,提出基于多目标粒子群(MOPSO)的求解方法。仿真结果表明,所提协作频谱感知模型可以显著提高系统需求响应管理性能;MOPSO算法可实现系统需求响应管理性能和感知能耗的最佳权衡,有利于决策者根据实际要求灵活选择最优方案。     

A particle swarm optimization for a fuzzy multi-objective unrelated parallel machines scheduling problem

This paper proposes a novel multi-objective model for an unrelated parallel machine scheduling problem considering inherent uncertainty in processing times and due dates. The problem is characterized by non-zero ready times, sequence and machine-dependent setup times, and secondary resource constraints for jobs. Each job can be processed only if its required machine and secondary resource (if any) are available at the same time. Finding optimal solution for this complex problem in a reasonable time using exact optimization tools is prohibitive. This paper presents an effective multi-objective particle swarm optimization (MOPSO) algorithm to find a good approximation of Pareto frontier where total weighted flow time, total weighted tardiness, and total machine load variation are to be minimized simultaneously. The proposed MOPSO exploits new selection regimes for preserving global as well as personal best solutions. Moreover, a generalized dominance concept in a fuzzy environment is employed to find locally Pareto-optimal frontier. Performance of the proposed MOPSO is compared against a conventional multi-objective particle swarm optimization (CMOPSO) algorithm over a number of randomly generated test problems. Statistical analyses based on the effect of each algorithm on each objective space show that the proposed MOPSO outperforms the CMOPSO in terms of quality, diversity and spacing metrics.     

MOPSO算法及其在水库优化调度中的应用

提出了一种新的多目标粒子群优化(MOPSO)算法，该算法采用自适应网格方法来估计非劣解集中粒子的密度信息、平衡全局和局部搜索能力的Pareto最优解的搜索机制、删除品质差的多余粒子的Archive集的修剪技术。通过对三峡梯级多目标优化调度问题的计算，表明该算法是求解大规模复杂多目标优化问题的一种有效手段。     

Minimizing makespan subject to minimum flowtime on two identical parallel machines

We consider the problem of scheduling jobs on two parallel identical machines where an optimal schedule is defined as one that gives the smallest makespan (the completion time of the last job) among the set of schedules with optimal total flowtime (the sum of the completion times of all jobs). We propose an algorithm to determine optimal schedules for the problem, and describe a modified multifit algorithm to find an approximate solution to the problem in polynomial computational time. Results of a computational study to compare the performance of the proposed algorithms with a known heuristic shows that the proposed heuristic and optimization algorithms are quite effective and efficient in solving the problem.Scope and purposeMultiple objective optimization problems are quite common in practice. However, while solving scheduling problems, optimization algorithms often consider only a single objective function. Consideration of multiple objectives makes even the simplest multi-machine scheduling problems NP-hard. Therefore, enumerative optimization techniques and heuristic solution procedures are required to solve multi-objective scheduling problems. This paper illustrates the development of an optimization algorithm and polynomially bounded heuristic solution procedures for the scheduling jobs on two identical parallel machines to hierarchically minimize the makespan subject to the optimality of the total flowtime.     

Comparisons of some improving strategies on MOPSO for multi-objective (r, Q) inventory system

This paper presents comparisons of some recent improving strategies on multi-objective particle swarm optimization (MOPSO) algorithm which is based on Pareto dominance for handling multiple objective in continuous review stochastic inventory control system. The complexity of considering conflict objectives such as cost minimization and service level maximization in the real-world inventory control problem needs to employ more exact optimizers generating more diverse and better non-dominated solutions of a reorder point and order size system. At first, we apply the original MOPSO employed for the multi-objective inventory control problem. Then we incorporate the mutation operator to maintain diversity in the swarm and explore all the search space into the MOPSO. Next we change the leader selection strategy used that called geographically-based system (Grids) and instead of that, crowding distance factor is also applied to select the global optimal particle as a leader. Also we use ε-dominance concept to bound archive size and maintain more diversity and convergence in the MOPSO for optimizing the inventory control problem. Finally, the MOPSO algorithms created using these strategies are evaluated and compared with each other in terms of some performance metrics taken from the literature. The results indicate that these strategies have significant influences on computational time, convergence, and diversity of generated Pareto optimal solutions.     

软件开发团队的多目标优化构建研究

分析了客户需求与候选成员能力的关系,使用模糊排序聚类算法得到专业领域分工的集群;同时依据迈尔斯—布里格斯性格类型指标得到候选成员协作关系的量化评估。建立了以成员综合能力和性格匹配度最大化为目标的团队构建模型。最后,结合一个具体案例,采用带有判断与修复算子的微粒群算法对模型进行求解,得到表示团队构建候选方案集合的帕累托解,从而验证了该优化模型及算法的有效性和实用性。     

解决多目标优化问题的拟态物理学优化算法

提出一种解决多目标优化问题的多目标拟态物理学优化(MOAPO)算法。该算法利用为每个目标赋予随机权重的方法求得全局总目标,由此选取全局最好及最差适应值,并利用拟态物理学优化算法实现对Pareto最优解集的搜索。通过3个典型多目标优化测试函数对MOAPO和MOPSO进行比较,结果表明了MOAPO算法的有效性,特别是在保持解集分布性方面具有较好的性能。