基于混合蚁群算法的生产系统设施规划问题研究

设施规划问题主要研究生产设备的布局规划,从而减小厂区内的物料搬运成本。一个有效的设施规划有利于生产过程中整体运作效率的提高。随着市场竞争的日趋激烈,市场环境处于不断的变化之中,制造企业需不断对设施布局进行重新规划来适应不断变化的市场环境对产品需求量的影响,并达到降低成本的目的。这一问题便需要用多阶段设施规划（MFLP）的方法来解决。本文提出了一种改进的混和蚁群算法（HACO）来解决带有财务预算约束的多阶段设施规划问题,并将此方法与其他一些典型的启发式算法进行了对比分析。结果表明,本文提出的HACO算法是求解带有财务预算约束的MFLP问题的一种有效的方法。     

基于ASRank和MMAS的蚁群算法求解飞机指派问题

本文将航班串的飞机指派问题归结为车辆路径问题,考虑连续航班串之间衔接时间、衔接机场的约束、每架飞机的总飞行时间约束,建立了带有飞行时间约束的车辆路径问题的混合整数规划模型。构造了蚁群系统算法,引入基于排序的蚂蚁系统和最大最小蚂蚁系统算法的信息素更新策略。选取某航空公司7组初始航班串集合进行测试,并对算法中的重要参数进行了分析。实验结果表明,本文设计的模型和算法可以有效地减少连续航班串之间的总衔接时间,在可接受的计算时间内获得满意解。     

A general space-time model for combinatorial optimization problems (and not only)

We consider the problem of defining a strategy consisting of a set of facilities taking into account also the location where they have to be assigned and the time in which they have to be activated. The facilities are evaluated with respect to a set of criteria. The plan has to be devised respecting some constraints related to different aspects of the problem such as precedence restrictions due to the nature of the facilities. Among the constraints, there are some related to the available budget. We consider also the uncertainty related to the performances of the facilities with respect to considered criteria and plurality of stakeholders participating to the decision. The considered problem can be seen as the combination of some prototypical operations research problems: knapsack problem, location problem and project scheduling. Indeed, the basic brick of our model is a variable x_ilt which takes value 1 if facility i is activated in location l at time t, and 0 otherwise. Due to the conjoint consideration of a location and a time in the decision variables, what we propose can be seen as a general space-time model for operations research problems. We discuss how such a model permits to handle complex problems using several methodologies including multiple attribute value theory and multiobjective optimization. With respect to the latter point, without any loss of the generality, we consider the compromise programming and an interactive methodology based on the Dominance-based Rough Set Approach. We illustrate the application of our model with a simple didactic example.     

Some graph optimization problems with weights satisfying linear constraints

In this paper, we study several graph optimization problems in which the weights of vertices or edges are variables determined by several linear constraints, including maximum matching problem under linear constraints (max-MLC), minimum perfect matching problem under linear constraints (min-PMLC), shortest path problem under linear constraints (SPLC) and vertex cover problem under linear constraints (VCLC). The objective of these problems is to decide the weights that are feasible to the linear constraints, and find the optimal solutions of corresponding graph optimization problems among all feasible choices of weights. We find that these problems are NP-hard and are hard to be approximated in general. These findings suggest us to explore various special cases of them. In particular, we show that when the number of constraints is a fixed constant, all these problems are polynomially solvable. Moreover, if the total number of distinct weights is a fixed constant, then max-MLC, min-PMLC and SPLC are polynomially solvable, and VCLC has a 2-approximation algorithm. In addition, we propose approximation algorithms for various cases of max-MLC.

     

基于DNA遗传算法的表面贴装生产线负荷优化分配

印制电路板组装任务的负荷优化分配包含设备约束、工艺约束等大量约束,是电子行业表面贴装生产线中的一类重要优化问题。其优化目标是在生产节拍给定和一定约束条件下,使得不同贴装机负荷均衡,任务分配达到最优。首先,根据不同表面贴装机、不同吸嘴及多种类型元件匹配的的复杂性,提出贴装机任务分配组合优化的问题;然后分析设备和元件的参数、组装可行性、贴装时间,以及贴装优化关系等因素,并提出假设条件,建立了平衡率最大化条件下的负荷分配组合优化的数学模型;最后,针对贴装生产线负荷分配问题的复杂性与特殊性,通过改良编码方式后的DNA遗传算法来优化组合数学模型,计算适应度,并借助MATLAB进行仿真求解,进而找到最优解。结果表明：本文提出的贴装生产线负荷分配方法可以解决带复杂约束的印制电路板组装负荷优化分配问题,提高设备的平衡率和生产效率,促进生产线的优化运行。     

Evacuating People with Mobility‐Challenges in a Short‐Notice Disaster

In past disasters, arrangements have been made to evacuate people without their own transportation, requiring them to gather at select locations to be evacuated. Unfortunately, this type of plan does not help those people who are unable to move themselves to the designated meeting locations. In the United States, according to the Post‐Katrina Emergency Management Reform Act of 2006, state or local governments have the responsibility to coordinate evacuation plans for all populations. These include those with disabilities. However, few, if any, have plans in place for those who are mobility‐challenged. The problem of evacuating mobility‐challenged people from their individual locations in a short‐notice disaster is a challenging combinatorial optimization problem. In order to develop the model and select a solution approach, we surveyed related literature. Based on our review, we formulate the problem and develop an Ant Colony Optimization (ACO) algorithm to solve it. We then test two different versions of the ACO algorithm on five stylized datasets with several different parameter settings.     

An accounting control system structured on multiple objective planning models

An important problem confronting decision makers in modern organizations is how to plan and control in a multiple goal decision setting. The usual approach for attacking this problem is to assume one dominant goal and treat others as constraints for the budget planning purpose. The traditional accounting control system is a variance analysis which makes a comparison between an ex ante planning budget, a budget adjusted to the actual activity level, and actual results. The present paper describes how to set up multiple goal planning models by using goal programming and multiple objective linear programming techniques. And an opportunity cost concept of ex post accounting variance analysis (which a comparison is made between an ex ante budget, ex post optimum budget, and actual results) is used as a control device. This ex post analysis will signal a deviation in any data input parameter in the planning models.     

An integrated system for capacity planning and facility layout

In order to achieve efficient facility design for service type activities, operating under dynamic conditions and a large number of constraints, the use of a traditional approach has proved to be tedious and time consuming. Development of an efficient decision support system for such a situation calls for the consideration of the complex nature of interaction between the system parameters and the relationship between the working environment and the resources within the system. Mathematical programming techniques, e.g. linear and integer programming as well as queuing models, though useful in handling combinatorial optimization problems, are incapable of dealing with stochastic utilization problems normally encountered in the design of facilities of a fast changing environment. This paper makes use of a pattern search algorithm for the optimal allocation of service facility resources. The layout of the facilities has then been optimized by the use of the CLASS algorithm. The two separate algorithms have suitably been integrated together into a single simulation-based system. The effectiveness of the proposed methodology has been demonstrated by means of a real case study pertaining to design and layout optimization of a multi-functional gasoline service station in Bangkok.     

一种差异工件单机批调度问题的蚁群优化算法

由于在利用蚁群算法构建差异工件(即工件有尺寸差异)单机批调度问题的解时,批的加工时间是不确定的.从而不能类似于经典调度问题的蚁群算法把批加工时间的倒数作为蚁群算法中的启发式信息,引入批的利用率和批的负载均衡率作为蚁群算法中的启发式信息,提出了JACO(ant colony optimization based a job sequence)和BACO(ant colony optimization based a batch sequence)两种蚁群优化算法.在算法JACO中,解的编码为工件序列,它对应着用BF(best fit)分批规则生成的调度方案,信息素代表工件间的排列顺序;在算法BACO中,解的编码为批序列,信息素代表工件间的批相关性,由此信息素通过中间信息素量来构造相应的解,并引入特定的局部优化策略,提高了算法的搜索效率.实验表明,与以往文献中的SA(simula-ted annealing)、GA(genetic algorithm)算法以及FFLPT(first-fit longest processing time)、BFLPT (best-fit longest processing time)启发式规则相比,算法JACO和BACO明显优于它们,且BACO算法比JACO算法效果更好.     

Optimal wafer cutting in shuttle layout problems

A major cost in semiconductor manufacturing is the generation of photo masks which are used to produce the dies. When producing smaller series of chips it can be advantageous to build a shuttle mask (or multi-project wafer) to share the startup costs by placing different dies on the same mask. The shuttle layout problem is frequently solved in two phases: first, a floorplan of the shuttle is generated. Then, a cutting plan is found which minimizes the overall number of wafers needed to satisfy the demand of each die type. Since some die types require special production technologies, only compatible dies can be cut from a given wafer, and each cutting plan must respect various constraints on where the cuts may be placed. We present an exact algorithm for solving the minimum cutting plan problem, given a floorplan of the dies. The algorithm is based on delayed column generation, where the pricing problem becomes a maximum vertex-weighted clique problem in which each clique consists of cutting compatible dies. The resulting branch-and-price algorithm is able to solve realistic cutting problems to optimality in a couple of seconds.     

Linear solution schemes for Mean-SemiVariance Project portfolio selection problems: An application in the oil and gas industry

We study the Mean-SemiVariance Project (MSVP) portfolio selection problem, where the objective is to obtain the optimal risk-reward portfolio of non-divisible projects when the risk is measured by the semivariance of the portfolio׳s Net-Present Value (NPV) and the reward is measured by the portfolio׳s expected NPV. Similar to the well-known Mean-Variance portfolio selection problem, when integer variables are present (e.g., due to transaction costs, cardinality constraints, or asset illiquidity), the MSVP problem can be solved using Mixed-Integer Quadratic Programming (MIQP) techniques. However, conventional MIQP solvers may be unable to solve large-scale MSVP problem instances in a reasonable amount of time. In this paper, we propose two linear solution schemes to solve the MSVP problem; that is, the proposed schemes avoid the use of MIQP solvers and only require the use of Mixed-Integer Linear Programming (MILP) techniques. In particular, we show that the solution of a class of real-world MSVP problems, in which project returns are positively correlated, can be accurately approximated by solving a single MILP problem. In general, we show that the MSVP problem can be effectively solved by a sequence of MILP problems, which allow us to solve large-scale MSVP problem instances faster than using MIQP solvers. We illustrate our solution schemes by solving a real MSVP problem arising in a Latin American oil and gas company. Also, we solve instances of the MSVP problem that are constructed using data from the PSPLIB library of project scheduling problems.     

Constraint-based model for the cyclic multi-hoists scheduling problem

This article presents a method for the resolution of a material handling scheduling problem. The case studied is a real industrial problem. It consists of finding a cyclic schedule for hoist movements in a treatment surface shop. In this kind of facility, several hoists are used for all the handling operations and they have to share common zones. Then it is necessary to control that there is no collision. The mathematical formulation of the problem is based on a combination of disjunctive constraints. The constraints describe either movement schedule or collision avoidance. The resolution procedure presented identifies all the collision configurations and then uses a branch and bound-like algorithm to find the optimal solution of a given problem. The language chosen for our implementation is the constraint logic programming language: Prolog IV, which is able to solve constraints with rational variables. It actively uses the constraint propagation mechanism that can be found in several languages.     

具有时间转换约束的离散时间-费用权衡问题研究

离散时间-费用权衡问题(DTCTP)是项目进度中研究最多的双目标优化问题,它通常以三种形式出现:(1)P1:截止日期问题,在项目截止日期约束下使完成项目的总费用最小;(2)P2:预算问题,在费用预算约束下使项目工期最短;(3)P3:工期-费用曲线问题,找出全部有效的工期-费用模式集合。然而,考虑时间转换约束(TSC)的DTCTP却很少被关注。本文首先介绍时间转换约束的问题描述,在此基础上,建立具有活动类型时间转换约束的DTCTPTSC-P2模型;从实用角度出发,设计求解模型的遗传算法;最后,用一个真实项目实例说明模型的合理性和算法的有效性,对算例分析结果表明,该模型对承包商更准确地进行项目工期-费用权衡决策具有借鉴意义。     

Subset sum problems with digraph constraints

We introduce and study optimization problems which are related to the well-known Subset Sum problem. In each new problem, a node-weighted digraph is given and one has to select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints called digraph constraints and maximality need to be satisfied. The digraph constraint imposes that a node must belong to the solution if at least one of its predecessors is in the solution. An alternative of this constraint says that a node must belong to the solution if all its predecessors are in the solution. The maximality constraint ensures that no superset of a feasible solution is also feasible. The combination of these constraints provides four problems. We study their complexity and present some approximation results according to the type of input digraph, such as directed acyclic graphs and oriented trees.     

A method combining genetic algorithm with simultaneous perturbation stochastic approximation for linearly constrained stochastic optimization problems

This paper considers the optimization of linearly constrained stochastic problem which only noisy measurements of the loss function are available. We propose a method which combines genetic algorithm (GA) with simultaneous perturbation stochastic approximation (SPSA) to solve linearly constrained stochastic problems. The hybrid method uses GA to search for optimum over the whole feasible region, and SPSA to search for optimum at local region. During the GA and SPSA search process, the hybrid method generates new solutions according to gradient projection direction, which is calculated based on active constraints. Because the gradient projection method projects the search direction into the subspace at a tangent to the active constraints, it ensures new solutions satisfy all constraints strictly. This paper applies the hybrid method to nine typical constrained optimization problems and the results coincide with the ideal solutions cited in the references. The numerical results reveal that the hybrid method is suitable for multimodal constrained stochastic optimization problem. Moreover, each solution generated by the hybrid method satisfies all linear constraints strictly.     

On residual approximation in solution extension problems

The solution extension variant of a problem consists in, being given an instance and a partial solution, finding the best solution comprising the given partial solution. Many problems have been studied with a similar approach. For instance the Pre-Coloring Extension problem, the clustered variant of the Travelling Salesman problem, or the General Routing Problem are in a way typical examples of solution extension variant problems. Motivated by practical applications of such variants, this work aims to explore different aspects around extension on classical optimization problems. We define residue-approximations as algorithms whose performance ratio on the non-prescribed part can be bounded, and corresponding complexity classes. Using residue-approximation, we classify problems according to their residue-approximability, exhibit distinct behaviors and give several examples and first interesting results.     

BAB算法中集成CPT求解job-shop调度问题

CSP(constraintsatisfactoryproblem)的优势在于能够处理复杂约束,获得一个满足约束的解,但难以保证解的质量.OR(operationresearch)的优点是获得最优解或近优解,但它求解复杂约束的优化问题非常困难.CPT(constraintpropagationtechnique)是CSP的主要搜索技术,BAB(branch_and_bound)是OR常用的优化算法.提出了一种将CPT集成于BAB中的混合算法,从一个新的角度解决具有一般性与挑战性的job shop调度问题.其主要特点是,通过在BAB算法中嵌入动态可调的时间窗口约束和加强一致性CPT搜索方法,融合BAB的优化能力和CPT处理复杂约束的能力,提高BAB的优化性能及实际应用能力.实验结果令人满意,证明了算法的有效性.     

The maximum flow problem with disjunctive constraints

We study the maximum flow problem subject to binary disjunctive constraints in a directed graph: A negative disjunctive constraint states that a certain pair of arcs in a digraph cannot be simultaneously used for sending flow in a feasible solution. In contrast to this, positive disjunctive constraints force that for certain pairs of arcs at least one arc has to carry flow in a feasible solution. It is convenient to represent the negative disjunctive constraints in terms of a so-called conflict graph whose vertices correspond to the arcs of the underlying graph, and whose edges encode the constraints. Analogously we represent the positive disjunctive constraints by a so-called forcing graph. For conflict graphs we prove that the maximum flow problem is strongly $\mathcal{NP}$ -hard, even if the conflict graph consists only of unconnected edges. This result still holds if the network consists only of disjoint paths of length three. For forcing graphs we also provide a sharp line between polynomially solvable and strongly $\mathcal{NP}$ -hard instances for the case where the flow values are required to be integral. Moreover, our hardness results imply that no polynomial time approximation algorithm can exist for both problems. In contrast to this we show that the maximum flow problem with a forcing graph can be solved efficiently if fractional flow values are allowed.     

The density maximization problem in graphs

We consider a framework for bi-objective network construction problems where one objective is to be maximized while the other is to be minimized. Given a host graph G=(V,E) with edge weights w _e ∈? and edge lengths ? _e ∈? for e∈E we define the density of a pattern subgraph H=(V′,E′)?G as the ratio ?(H)=∑ _e∈E′ w _e /∑ _e∈E′ ? _e . We consider the problem of computing a maximum density pattern H under various additional constraints. In doing so, we compute a single Pareto-optimal solution with the best weight per cost ratio subject to additional constraints further narrowing down feasible solutions for the underlying bi-objective network construction problem. First, we consider the problem of computing a maximum density pattern with weight at least W and length at most L in a host G. We call this problem the biconstrained density maximization problem. This problem can be interpreted in terms of maximizing the return on investment for network construction problems in the presence of a limited budget and a target profit. We consider this problem for different classes of hosts and patterns. We show that it is NP-hard, even if the host has treewidth 2 and the pattern is a path. However, it can be solved in pseudo-polynomial linear time if the host has bounded treewidth and the pattern is a graph from a given minor-closed family of graphs. Finally, we present an FPTAS for a relaxation of the density maximization problem, in which we are allowed to violate the upper bound on the length at the cost of some penalty. Second, we consider the maximum density subgraph problem under structural constraints on the vertex set that is used by the patterns. While a maximum density perfect matching can be computed efficiently in general graphs, the maximum density Steiner-subgraph problem, which requires a subset of the vertices in any feasible solution, is NP-hard and unlikely to admit a constant-factor approximation. When parameterized by the number of vertices of the pattern, this problem is W[1]-hard in general graphs. On the other hand, it is FPT on planar graphs if there is no constraint on the pattern and on general graphs if the pattern is a path.     

A genetic algorithm-based decomposition approach to solve an integrated equipment-workforce-service planning problem

We develop a new genetic algorithm to solve an integrated Equipment-Workforce-Service Planning problem, which features extremely large scales and complex constraints. Compared with the canonical genetic algorithm, the new algorithm is innovative in four respects: (1) The new algorithm addresses epistasis of genes by decomposing the problem variables into evolutionary variables, which evolve with the genetic operators, and the optimization variables, which are derived by solving corresponding optimization problems. (2) The new algorithm introduces the concept of Capacity Threshold and calculates the Set of Efficient and Valid Equipment Assignments to preclude unpromising solution spaces, which allows the algorithm to search much narrowed but promising solution spaces in a more efficient way. (3) The new algorithm modifies the traditional genetic crossover and mutation operators to incorporate the gene dependency in the evolutionary procedure. (4) The new algorithm proposes a new genetic operator, self-evolution, to simulate the growth procedure of an individual in nature and use it for guided improvements of individuals. The new genetic algorithm design is proven very effective and robust in various numerical tests, compared to the integer programming algorithm and the canonical genetic algorithm. When the integer programming algorithm is unable to solve the large-scale problem instances or cannot provide good solutions in acceptable times, and the canonical genetic algorithm is incapable of handling the complex constraints of these instances, the new genetic algorithm obtains the optimal or close-to-optimal solutions within seconds for instances as large as 84 million integer variables and 82 thousand constraints.