Solving a new stochastic multi-mode p-hub covering location problem considering risk by a novel multi-objective algorithm

In this paper, we develop a novel stochastic multi-objective multi-mode transportation model for hub covering location problem under uncertainty. The transportation time between each pair of nodes is an uncertain parameter and also is influenced by a risk factor in the network. We extend the traditional comprehensive hub location problem by considering two new objective functions. So, our multi-objective model includes (i) minimization of total current investment costs and (ii) minimization of maximum transportation time between each origin–destination pair in the network. Besides, a novel multi-objective imperialist competitive algorithm (MOICA) is proposed to obtain the Pareto-optimal solutions of the problem. The performance of the proposed solution algorithm is compared with two well-known meta-heuristics, namely, non-dominated sorting genetic algorithm (NSGA-II) and Pareto archive evolution strategy (PAES). Computational results show that MOICA outperforms the other meta-heuristics.     

关于最短路问题的一个双目标优化问题

本文研究了一个双目标最短路问题的变形问题,在该变形问题中,一个目标函数还是路的长度,另一个目标函数则是路的容量,在Pareto-optimal最优解的意义下,本文给出了一个时间复杂性为O（n^3 )的算法,在字典序最优解的意义下,本文给出了一个时间复杂性为O(n^3)的算法。     

An Application of a Multi-Objective Tabu Search Algorithm to a Bicriteria Flowshop Problem

This paper proposes a new tabu search algorithm for multi-objective combinatorial problems with the goal of obtaining a good approximation of the Pareto-optimal or efficient solutions. The algorithm works with several paths of solutions in parallel, each with its own tabu list, and the Pareto dominance concept is used to select solutions from the neighborhoods. In this way we obtain at each step a set of local nondominated points. The dispersion of points is achieved by a clustering procedure that groups together close points of this set and then selects the centroids of the clusters as search directions. A nice feature of this multi-objective algorithm is that it introduces only one additional parameter, namely, the number of paths. The algorithm is applied to the permutation flowshop scheduling problem in order to minimize the criteria of makespan and maximum tardiness. For instances involving two machines, the performance of the algorithm is tested against a Branch-and-Bound algorithm proposed in the literature, and for more than two machines it is compared with that of a tabu search algorithm and a genetic local search algorithm, both from the literature. Computational results show that the heuristic yields a better approximation than these algorithms.     

An adaptive membrane algorithm for solving combinatorial optimization problems

Membrane algorithms (MAs), which inherit from P systems, constitute a new parallel and distribute framework for approximate computation. In the paper, a membrane algorithm is proposed with the improvement that the involved parameters can be adaptively chosen. In the algorithm, some membranes can evolve dynamically during the computing process to specify the values of the requested parameters. The new algorithm is tested on a well-known combinatorial optimization problem, the travelling salesman problem. The empirical evidence suggests that the proposed approach is efficient and reliable when dealing with 11 benchmark instances, particularly obtaining the best of the known solutions in eight instances. Compared with the genetic algorithm, simulated annealing algorithm, neural network and a fine-tuned non-adaptive membrane algorithm, our algorithm performs better than them. In practice, to design the airline network that minimize the total routing cost on the CAB data with twenty-five US cities, we can quickly obtain high quality solutions using our algorithm.     

Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization

Dynamic optimization and multi-objective optimization have separately gained increasing attention from the research community during the last decade. However, few studies have been reported on dynamic multi-objective optimization (dMO) and scarce effective dMO methods have been proposed. In this paper, we fulfill these gabs by developing new dMO test problems and new effective dMO algorithm. In the newly designed dMO problems, Pareto-optimal decision values (i.e., Pareto-optimal solutions: POS) or both POS and Pareto-optimal objective values (i.e., Pareto-optimal front: POF) change with time. A new multi-strategy ensemble multi-objective evolutionary algorithm (MS-MOEA) is proposed to tackle the challenges of dMO. In MS-MOEA, the convergence speed is accelerated by the new offspring creating mechanism powered by adaptive genetic and differential operators (GDM); a Gaussian mutation operator is employed to cope with premature convergence; a memory like strategy is proposed to achieve better starting population when a change takes place. In order to show the advantages of the proposed algorithm, we experimentally compare MS-MOEA with several algorithms equipped with traditional restart strategy. It is suggested that such a multi-strategy ensemble approach is promising for dealing with dMO problems.     

基于信息熵权TOPSIS法的双腔半环面型CVT传动性能优化

针对双腔半环面型CVT的结构特点和应用背景,建立以输入扭矩分矩比和输出输入扭矩比为目标函数的优化模型。采用带有精英策略的非支配排序遗传算法(non-dominated sorting genetic algorithm with the elite strategy, NSGA-II)求解该模型的Pareto最优解。为了确定最佳的Pareto最优解,首先将获得的Pareto最优解构成决策矩阵,其次利用客观赋权的信息熵(information entropy weight, IEW)法计算各属性的权值,最后运用逼近理想解的排序法(technique for order preference by similarity to ideal solution, TOPSIS)对Pareto最优解排序。将最佳Pareto最优解对应的设计变量值代入输入扭矩分矩比、输出输入扭矩比以及传动效率的表达式,使用MATLAB软件绘制相应的特性曲线。结果表明,通过TOPSIS确定的最佳Pareto最优解能够实现双腔半环面型CVT高效率传动、大扭矩输出和无级变速单元承受较小输入扭矩的功能。     

A hybrid quantum-inspired immune algorithm for multiobjective optimization

This study suggests a novel quantum immune algorithm for finding Pareto-optimal solutions to multiobjective optimization problems based on quantum computing and immune system. In the proposed algorithm, there are distinct characteristics as follows. First, the encoding method is based on Q-bit representation, and thus a chaos-based approach is suggested to initialize the population. Second, a new chaos-based rotation gate and Q-gates are presented to perform mutation and improve the quality of the population, respectively. Finally, especially, a new truncation algorithm with similar individuals (TASI) is utilized to preserve the diversity of the population. Also, a new selection operator is proposed to create the new population based on TASI. Simulation results on six standard problems (ZDT6, CP, SP, VNT, OSY and KIT) show the proposed algorithm is able to find a much better spread of solutions and has better convergence near the true Pareto-optimal front compared to the vector immune algorithm (VIS) and the elitist non-dominated sorting genetic system (NSGA-II).     

公交网络时刻表再协同设计的多目标优化模型

为了改善公交服务质量,公交运营者试图调整现有时刻表的发车时间,使不同线路的车次协同到达换乘站点以方便乘客换乘。针对此场景,研究了公交时刻表重新协同设计问题,提出了求解该问题的多目标模型。模型考虑了对发车间隔灵敏的乘客需求、灵活的车次协同到站方式和发车时间的规则性,分析了该多目标模型的特征和计算复杂性,表明本文研究的问题是NP-hard问题,且它的帕累托最优前沿是非凸的,设计了基于非支配排序的遗传算法求解模型。算例表明,与枚举算法相比,提出的求解算法在较短的时间内可获得高质量的帕累托解。     

A predictive gradient strategy for multiobjective evolutionary algorithms in a fast changing environment

An essential feature of a dynamic multiobjective evolutionary algorithm (MOEA) is to converge quickly to the Pareto-optimal Set before it changes. In cases where the behavior of the dynamic problem follows a certain trend, convergence can be accelerated by anticipating the characteristics of future changes in the problem. A prediction model is usually used to exploit past information and estimate the location of the new Pareto-optimal Set. In this work, we propose the novel approach of tracking and predicting the changes in the location of the Pareto Set in order to minimize the effects of a landscape change. The predicted direction and magnitude of the next change, known as the predictive gradient, is estimated based on the history of previously discovered solutions using a weighted average approach. Solutions updated with the predictive gradient will remain in the vicinity of the new Pareto-optimal Set and help the rest of the population to converge. The prediction strategy is simple to implement, making it suitable for fast-changing problems. In addition, a new memory technique is introduced to exploit any periodicity in the dynamic problem. The memory technique selects only the more promising stored solutions for retrieval in order to reduce the number of evaluations used. Both techniques are incorporated into a variant of the multi-objective evolutionary gradient search (MO-EGS) and two other MOEAs for dynamic optimization and results indicate that they are effective at improving performance on several dynamic multiobjective test problems.     

Heuristic approaches to determine base-stock levels in a serial supply chain with a single objective and with multiple objectives

This paper deals with the problem of determination of installation base-stock levels in a serial supply chain. The problem is treated first as a single-objective inventory-cost optimization problem, and subsequently as a multi-objective optimization problem by considering two cost components, namely, holding costs and shortage costs. Variants of genetic algorithms are proposed to determine the best base-stock levels in the single-objective case. All variants, especially random-key gene-wise genetic algorithm (RKGGA), show an excellent performance, in terms of convergence to the best base-stock levels across a variety of supply chain settings, with minimum computational effort. Heuristics to obtain base-stock levels are proposed, and heuristic solutions are introduced in the initial population of the RKGGA to expedite the convergence of the genetic search process. To deal with the multi-objective supply-chain inventory optimization problem, a simple multi-objective genetic algorithm is proposed to obtain a set of non-dominated solutions.     

包含随机客户的选择性旅行商问题建模及求解

针对快递配送过程中客户需求具有不确定性的特征,提出一种新的路径优化问题——包含随机客户的选择性旅行商问题,在该问题中客户每天是否具有配送需求存在一定概率,并且对客户进行配送可获取一定利润。同时考虑以上两种因素,建立该问题的数学模型, 目标为在满足行驶距离限制的条件下,找出一条经过部分客户的预优化路径,使得该路径的期望利润最大。其可用于模拟构建最后一公里快递配送的路径问题,提供更具有经济效益的配送路径。随后提出包含精细化局部搜索策略的改进遗传算法,算法根据问题特点构建初始可行解。最后通过多个计算比对结果表明,该算法具有较高的计算效率。     

Higher and lower-level knowledge discovery from Pareto-optimal sets

Innovization (innovation through optimization) is a relatively new concept in the field of multi-objective engineering design optimization. It involves the use of Pareto-optimal solutions of a problem to unveil hidden mathematical relationships between variables, objectives and constraint functions. The obtained relationships can be thought of as essential properties that make a feasible solution Pareto-optimal. This paper proposes two major extensions to innovization, namely higher-level innovization and lower-level innovization. While the former deals with the discovery of common features among solutions from different Pareto-optimal fronts, the latter concerns features commonly occurring among solutions that belong to a specified (or preferred) part of the Pareto-optimal front. The knowledge of such lower-level information is extremely beneficial to a decision maker, since it focuses on a preferred set of designs. On the other hand, higher-level innovization reveals interesting knowledge about the general problem structure. Neither of these crucial aspects concerning multi-objective designs has been addressed before, to the authors’ knowledge. We develop methodologies for handling both levels of innovization by extending the authors’ earlier automated innovization algorithm and apply them to two well-known engineering design problems. Results demonstrate that the proposed methodologies are generic and are ready to be applied to other engineering design problems.     

Generating pareto-optimal alternatives by a nonfeasible hierarchical method

A hierarchical algorithm for generating Pareto-optimal alternatives for convex multicriteria problems is derived. At the upper level, values for Lagrange multipliers of the coupling constraints are first given. Then at the subsystems, Pareto-optimal values are determined for the subsystem objectives, whereby an additional term or an additional objective is included due to the Lagrange multipliers. In the subsystem optimizations, the coupling equations between the subsystems are not satisfied; therefore, the method is called nonfeasible. Finally, the upper level checks which of the subsystem solutions satisfy the coupling constraints; these solutions are Pareto-optimal solutions for the overall system.     

Multi-objective Pareto-optimal control: an application to wastewater management

This work treats, within a multi-objective framework, of an economical-ecological problem related to the optimal management of a wastewater treatment system consisting of several purifying plants. The problem is formulated as a multi-objective parabolic optimal control problem and it is studied from a cooperative point of view, looking for Pareto-optimal solutions. The weighting method is used here to characterize the Pareto solutions of our problem. To obtain them, a numerical algorithm—based in a characteristics-Galerkin discretization—is proposed and numerical results for a real world situation in the estuary of Vigo (NW Spain) are also presented.     

A comprehensive note on: An economic order quantity with imperfect quality and quantity discounts

Lin [T.Y. Lin, An economic order quantity with imperfect quality and quantity discounts, Appl. Math. Model. 34 (10) (2010) 3158–3165] recently proposed an EOQ model with imperfect quality and quantity discounts, where the lot-splitting shipments policy is adopted. In this note we first rectify the holding cost terms showed in Lin to obtain a new objective function, then resolve the problem and develop an easy to implement algorithm to find the overall optimal solutions for the model. Besides, we present a new model for items with imperfect quality, where lot-splitting shipments and different holding costs for good and defective items are considered. The closed-form formulas for determining the optimal ordering and shipping policies are derived. Also, the results are examined analytically and numerically to gain more insights of the solutions.     

A hybrid simulated annealing and column generation approach for capacitated multicommodity network design

This paper presents a hybrid simulated annealing (SA) and column generation (CG) algorithm for the path-based formulation of the capacitated multicommodity network design (PCMND) problem. In the proposed method, the SA metaheuristic algorithm manages open and closed arcs. Several strategies for adding and dropping arcs are suggested and evaluated. For a given design vector in the proposed hybrid approach, the PCMND problem becomes a capacitated multicommodity minimum cost flow (CMCF) problem. The exact evaluation of the CMCF problem is performed using the CG algorithm. The parameter tuning is done by means of design of experiments approach. The performance of the proposed algorithm is evaluated by solving several benchmark instances. The results of the proposed algorithm are compared with the solutions of CPLEX solver and the best-known method in the literature under different time limits. Statistical analysis proves that the proposed algorithm is able to obtain better solutions.     

Exact hybrid algorithms for solving a bi-objective vehicle routing problem

The paper investigates a capacitated vehicle routing problem with two objectives: (1) minimization of total travel cost and (2) minimization of the length of the longest route. We present algorithmic variants for the exact determination of the Pareto-optimal solutions of this bi-objective problem. Our approach is based on the adaptive ε-constraint method. For solving the resulting single-objective subproblems, we apply a branch-and-cut technique, using (among others) a novel implementation of Held-Karp-type bounds. Incumbent solutions are generated by means of a single-objective genetic algorithm and, alternatively, by the multi-objective NSGA-II algorithm. Experimental results for a benchmark of 54 test instances from the TSPLIB are reported.     

The multicriteria p-facility median location problem on networks

In this paper we discuss the multicriteria p-facility median location problem on networks with positive and negative weights. We assume that the demand is located at the nodes and can be different for each criterion under consideration. The goal is to obtain the set of Pareto-optimal locations in the graph and the corresponding set of non-dominated objective values. To that end, we first characterize the linearity domains of the distance functions on the graph and compute the image of each linearity domain in the objective space. The lower envelope of a transformation of all these images then gives us the set of all non-dominated points in the objective space and its preimage corresponds to the set of all Pareto-optimal solutions on the graph. For the bicriteria 2-facility case we present a low order polynomial time algorithm. Also for the general case we propose an efficient algorithm, which is polynomial if the number of facilities and criteria is fixed.     

带有资源转移时间的RCPSP资源流模型及算法

本文在传统资源受限项目调度问题(resource-constrained project scheduling problem, RCPSP)中引入资源转移时间,为有效获得问题的最优解,采用资源流编码方式表示可行解,建立了带有资源转移时间的RCPSP资源流优化模型,目标为最小化项目工期。根据问题特征设计了改进的资源流重构邻域算子,分别设计了改进的禁忌搜索算法和贪心随机自适应禁忌搜索算法求解模型。数据实验结果表明,相较于现有文献中的方法,所提两种算法均可针对更多的项目实例求得最优解,并且得到最优解的时间更短,求解效率更高。此外,分析了算法在求解具有不同特征的项目实例时的性能,所得结果为项目经理结合项目特征评价算法适用性提供了指导。     

面向韧性提升的相互依赖关键基础设施网络灾后修复模型研究

科学合理制定相互依赖关键基础设施网络(Interdependent Critical Infrastructure Network, ICINs)遭灾后毁坏组件的修复计划是其安全管理的至关重要内容。本文首先明确了ICINs的韧性测度,分析了其灾后修复策略;然后基于网路流理论,以最大化ICINs的韧性为目标,构建了在有限灾后修复资源约束下,ICINs的灾后修复任务选择与调度的混合整数规划模型,并设计了遗传算法进行求解;最后通过不同规模的用例实验对模型和遗传算法进行了测试。研究表明:(1)该模型具有解决相关问题的可行性与有效性;(2)设计的遗传算法能获得质量较高的满意解,且对于大规模问题,遗传算法的求解时间与求解结果优于Cplex软件;(3)将网络之间的功能与空间相互依赖同时纳入模型中,能使ICINs的韧性达到更高。研究可为ICINs的灾后修复决策提供辅助。