A multi-objective vehicle routing and scheduling problem with uncertainty in customers’ request and priority

In this paper, a multi-objective vehicle routing and scheduling problem with uncertainty in priority and request of customers is presented. In the proposed model, a set of dynamic requests is received over time, and the planner does not have any information regarding their location and size until they arrive. Moreover, the routing model aims to satisfy different customers according to their specific time windows which were predefined by an expert as (being very important, important, casual or unimportant). This paper uses the proposed model as a multi-objective problem where the total required number of vehicles, the total distance travelled and the waiting time imposed on vehicles are minimized, and the total customers’ satisfaction for service is maximized. An efficient framework for solving this model is designed and its performance is evaluated in different steps for various test problems generalized from Solomon’s VRPTW benchmark problems. The various heuristics and improvement concepts incorporate local exploitation in the evolutionary search, and the concept of Pareto optimality for the multi-objective optimization is used in the proposed procedure. The computational experiments on data sets illustrate the efficiency and effectiveness of the proposed approach.     

一种求解双目标flow shop排序问题的进化算法

提出一种求解双目标flow shop排序的递进多目标进化算法.算法采用改进的精英复制策略,在实现精英保留的前提下降低了计算复杂性;通过递进进化模式增加群体多样性,改善了算法收敛性;通过群体进化过程中对非劣解集进行竞争型可变邻域启发式搜索,增强了算法局部搜索性能.采用新算法和参照算法NSGA-II对31个标准双目标flow shop算例进行优化.研究结果表明,新算法在所有算例的求解中均获得了优于NSGA-II的非劣解集,验证了算法的有效性.     

A decision support approach for two-stage multi-objective index tracking using improved lagrangian decomposition

We present a decision support approach for a network structured stochastic multi-objective index tracking problem in this paper. Due to the non-convexity of this problem, the developed network is modeled as a Stochastic Mixed Integer Linear Program (SMILP). We also propose an optimization-based approach to scenario generation to protect against the risk of parameter estimation for the SMILP. Progressive Hedging (PH), an improved Lagrangian scheme, is designed to decompose the general model into scenario-based sub-problems. Furthermore, we innovatively combine tabu search and the sub-gradient method into PH to enhance the tracking capabilities of the model. We show the robustness of the algorithm through effectively solving a large number of numerical instances.     

A decision support methodology for strategic planning in maritime transportation

This paper presents a decision support methodology for strategic planning in tramp and industrial shipping. The proposed methodology combines simulation and optimization, where a Monte Carlo simulation framework is built around an optimization-based decision support system for short-term routing and scheduling. The simulation proceeds by considering a series of short-term routing and scheduling problems using a rolling horizon principle where information is revealed as time goes by. The approach is flexible in the sense that it can easily be configured to provide decision support for a wide range of strategic planning problems, such as fleet size and mix problems, analysis of long-term contracts and contract terms. The methodology is tested on a real case for a major Norwegian shipping company. The methodology provided valuable decision support on important strategic planning problems for the shipping company.     

震后初期应急物资配送的模糊多目标选址-多式联运问题

针对震后初期应急物资配送系统优化问题,考虑应急物资需求模糊情况下应急物资配送中心选址和应急物资多式联运安排的集成决策,以应急物资配送总时间最短和受灾点应急物资未满足的总损失最小为目标,建立了一个震后应急物资配送的多目标选址-多式联运问题优化模型,设计了一种采用二维编码的非支配排序多目标遗传算法,并对该算法进行了复杂性分析。算例分析结果表明:该算法可以在得到Pareto前沿的同时,根据决策者偏好在Pareto前沿面上给出各种优化决策方案。     

Supplier selection with multiple criteria in volume discount environments

Supplier selection is a multi-criteria decision making problem which includes both qualitative and quantitative factors. In order to select the best suppliers it is necessary to make a trade-off between these tangible and intangible factors some of which may conflict. When business volume discounts exist, this problem becomes more complicated as, in these circumstances, buyer should decide about two problems: which suppliers are the best and how much should be purchased from each selected supplier. In this article an integrated approach of analytical hierarchy process improved by rough sets theory and multi-objective mixed integer programming is proposed to simultaneously determine the number of suppliers to employ and the order quantity allocated to these suppliers in the case of multiple sourcing, multiple products, with multiple criteria and with supplier's capacity constraints. In this context, suppliers offer price discounts on total business volume, not on the quantity or variety of products purchased from them. A solution methodology is presented to solve the multi-objective model, and the model is illustrated using two numerical examples.     

基于悲观度的双边匹配决策问题研究

双边匹配决策问题一直是经济管理和计算几何等领域研究的热点和难点问题之一。针对双边主体偏好信息为序值的双边匹配决策问题,提出基于悲观度的新方法,给出具有序值形式信息的双边匹配决策问题的描述,引入能够反映功利型中介悲观度的满意度和支付的计算公式。在此基础上,考虑到匹配主体对之间的满意度和功利型中介的收益,构建求解双边匹配决策问题的多目标优化模型。运用基于隶属函数的加权和方法将多目标优化模型转化为单目标优化模型,运用Hungarian法进行求解获得双边匹配方案,通过算例说明给出方法的有效性。计算结果表明,悲观度取值不同,运用该方法获得的双边匹配方案也可能会不同,即双边匹配方案能反映不同功利型中介的不同风险偏好。     

Multimode time-cost-robustness trade-off project scheduling problem under uncertainty

The time/cost trade-off problem is a well-known project scheduling problem that has been extensively studied. In recent years, many researchers have begun to focus on project scheduling problems under uncertainty to cope with uncertain factors, such as resource idleness, high inventory, and missing deadlines. To reduce the disturbance from uncertain factors, the aim of robust scheduling is to generate schedules with time buffers or resource buffers, which are capped by project makespan and project cost. This paper addresses a time-cost-robustness trade-off project scheduling problem with multiple activity execution modes under uncertainty. A multiobjective optimization model with three objectives (makespan minimization, cost minimization, and robustness maximization) is constructed and three propositions are proposed. An epsilon-constraint method-based genetic algorithm along with three improvement measures is designed to solve this NP-hard problem and to develop Pareto schedule sets, and a large-scale computational experiment on a randomly generated dataset is performed to validate the effectiveness of the proposed algorithm and the improvement measures. The final sensitivity analysis of three key parameters shows their distinctive influences on the three objectives, according to which several suggestions are given to project managers on the effective measures to improve the three objectives.

     

Distributed Decision‐Making in Supply Chains and Private E‐Marketplaces

This paper develops a distributed decision‐making framework for the players in a supply chain or a private e‐marketplace to collaboratively arrive at a global Pareto‐optimal solution. In this model, no player has complete knowledge about all the costs and constraints of the other players. The decision‐making framework employs an iterative procedure, based on the Integer L‐shaped method, in which a master problem is solved to propose global solutions, and each player uses his local problems to construct feasibility and optimality cuts on the master problem. The master problem is modeled as a mixed‐integer program, and the players' local problems are formulated as linear programs. Collaborative planning scenarios in private e‐marketplaces and in supply chains were formulated and solved for test data. The results show that this distributed model is able to achieve near‐optimal solutions considerably faster than the traditional centralized approach.     

Ethics, Decision Analysis, and Public Risk

In any analysis of a decision problem involving public risks, ethical implications are introduced. In some cases, these ethical implications may be introduced simply because an analysis is being done. Additional ethical implications may be inherently part of the methodology being utilized or introduced into the specific analysis of the decision problem. In this paper, we investigate where and how ethical implications enter when using the methodology of decision analysis to examine problems involving public risks. We conclude that the methodology of decision analysis is sufficiently robust to allow for numerous different ethical viewpoints to be accounted for in any specific analysis. Stated alternatively, decision analyses of public risks can be conducted in a manner consistent with utilitarianism, deontological theories, libertarianism, egalitarianism, and so forth. However, any specific analysis has embedded within it numerous ethical implications. This suggests that the careful ethical scrutiny of analyses involving the methodology of decision analysis should be placed on the specific application and not on the methodology per se or on the fact that an analysis is undertaken.     

基于多小波的数字水印优化

为了提高数字水印的实用性,必须保证水印的鲁棒性和透明性,为此充分考虑人类视觉系统特性,提出了一种基于多小波的数字水印优化方法。该方法利用Sa4多小波基进行数字水印嵌入,引入多目标优化手段对其嵌入深度进行优化调整,得到最佳嵌入效果。通过遗传算法实现的结果表明,该算法不仅对水印的攻击具有强鲁棒性,且能兼顾载体图像的质量。     

绿色物流网络系统建模与效率边界分析

绿色物流对于我国保护环境、节约资源和实施可持续发展战略具有重要的意义。绿色物流要求在进行物流网络系统设计时不能只考虑成本,还要考虑物流活动对于环境的影响。因此如何平衡物流成本和环境质量是一个关键问题。本文提出了绿色物流网络设计步骤和模型,将环境质量和物流成本作为优化的目标,利用多目标优化方法获得物流成本和环境质量之间的效率边界。通过分析效率边界的性质,指出了效率边界的作用。最后通过实例计算对影响效率边界的参数进行了分析,能为有效的实施绿色物流提供决策工具。     

On linear bilevel problems with multiple objectives at the lower level

Bilevel programming problems provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. This paper focuses on bilevel problems for which the lower level problem is a linear multiobjective program and constraints at both levels define polyhedra. This bilevel problem is reformulated as an optimization problem over a nonconvex region given by a union of faces of the polyhedron defined by all constraints. This reformulation is obtained when dealing with efficient solutions as well as weakly efficient solutions for the lower level problem. Assuming that the upper level objective function is quasiconcave, then an extreme point exists which solves the problem. An exact and a metaheuristic algorithm are developed and their performance is analyzed and compared.     

考虑稳定匹配条件的双边满意匹配决策方法

双边匹配问题是指如何在两个不相交的主体集合中依据各主体针对潜在匹配对象给出的偏好信息来确定合适的匹配结果,其在经济管理领域中存在着大量的实际背景,是许多学者关注的研究课题。在本文中,针对双边主体给出偏好序值信息的双边匹配问题,给出了一种考虑稳定匹配条件的双边满意匹配决策方法。首先给出了双边匹配、稳定匹配和满意匹配的相关概念;然后考虑到稳定匹配条件,并以双边主体满意度最大为目标,构建了多目标双边匹配优化模型;进一步地,采用线性加权法将多目标优化模型转换为单目标优化模型,并通过求解优化模型来获得最优匹配结果。最后,通过一个算例说明了本文提出方法的实用性和有效性。     

Quantitative Comparison of Approximate Solution Sets for Bi‐criteria Optimization Problems*

We present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near‐pareto‐optimal solutions to bi‐criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives.     

Interactive fuzzy goal programming for multi-objective transportation problems

This paper presents an interactive fuzzy goal programming approach to determine the preferred compromise solution for the multi-objective transportation problem. The proposed approach considers the imprecise nature of the input data by implementing the minimum operator and also assumes that each objective function has a fuzzy goal. The approach focuses on minimizing the worst upper bound to obtain an efficient solution which is close to the best lower bound of each objective function. The solution procedure controls the search direction via updating both the membership values and the aspiration levels. An important characteristic of the approach is that the decision maker's role is concentrated only in evaluating the efficient solution to limit the influences of his/her incomplete knowledge about the problem domain. In addition, the proposed approach can be applied to solve other multi-objective decision making problems. The performance of this solution approach is evaluated by comparing its results with that of the two existing methods in the literature.     

多性质多目标模糊指派模型在市政工程开发商选择中的应用

考虑了指派问题中涉及到多个目标要求的情况,包括定量目标和定性目标。首先,使用模糊数学的方法将定量目标下的效率值矩阵转化为优选决策矩阵,同时提出了定性目标的量化方法,并建立了定性目标的优选决策矩阵。然后,将各个目标要求下的优选决策矩阵进行了合成,考虑了综合效益对于“优”和“劣”之间多个等级的相对隶属度,建立了多性质、多目标模糊数学模型,得到了分级特征值矩阵。最后,与传统指派模型相结合形成了多性质、多目标模糊指派数学模型,使用匈牙利算法对该模型进行了求解,并结合市政工程在开发商之间分配的例子进行了分析说明。     

A heuristic framework for the bi-objective enhanced index tracking problem

The index tracking problem is the problem of determining a portfolio of assets whose performance replicates, as closely as possible, that of a financial market index chosen as benchmark. In the enhanced index tracking problem the portfolio is expected to outperform the benchmark with minimal additional risk. In this paper, we study the bi-objective enhanced index tracking problem where two competing objectives, i.e., the expected excess return of the portfolio over the benchmark and the tracking error, are taken into consideration. A bi-objective Mixed Integer Linear Programming formulation for the problem is proposed. Computational results on a set of benchmark instances are given, along with a detailed out-of-sample analysis of the performance of the optimal portfolios selected by the proposed model. Then, a heuristic procedure is designed to build an approximation of the set of Pareto optimal solutions. We test the proposed procedure on a reference set of Pareto optimal solutions. Computational results show that the procedure is significantly faster than the exact computation and provides an extremely accurate approximation.     

A simulation-based multi-objective optimization framework: A case study on inventory management

We propose a simulation-based solution framework for tackling the multi-objective inventory optimization problem. The goal is to find appropriate settings of reorder point and order quantity to minimize three objective functions simultaneously, which are the expected values of the total inventory cost, the average inventory level, and the frequency of inventory shortage. We develop new algorithms that can exploit statistically valid ranking and selection (R&S) procedures and the desirable mechanics of conventional multi-objective optimization techniques. Two simulation algorithms are proposed to be applied in different scenarios depending on the preference information that is revealed either during or after the actual optimization process. Experimental results are provided to evaluate the efficiency of the developed algorithms and other existing solution frameworks.     

Energy-efficient no-wait permutation flow shop scheduling by adaptive multi-objective variable neighborhood search

This paper considers an energy-efficient no-wait permutation flow shop scheduling problem to minimize makespan and total energy consumption, simultaneously. The processing speeds of machines can be dynamically adjusted for different jobs. In general, lower processing speeds require less energy consumption but result in longer processing times, while higher speeds take the opposite effect. To reach the Pareto front of the problem, we propose an adaptive multi-objective variable neighborhood search (AM-VNS) algorithm. Specifically, we first design two basic speed adjusting heuristics which can reduce the energy consumption of a given solution without worsening its makespan. Two widely used neighborhood-generating operations, i.e., insertion and swap, are adapted and integrated into the variable neighborhood descent phase. With respect to their executing order, two variable neighborhood descent structures can be designed. We adopt an adaptive mechanism to dynamically determine which structure will be selected to handle the current solution. To further improve the performance of the algorithm, we develop a novel problem-specific shake procedure. We also introduce accelerating techniques to speed up the algorithm. Computational results show that the AM-VNS algorithm outperforms multi-objective evolutionary algorithms NSGA-II and SPEA-II.