Some algorithms of solving minimax multiprocessor scheduling problem

A problem of constructing schedules of minimal length without interrupts and switches is considered for a multiprocessor system, in which the job execution time depends on the processor assigned to the job. To solve this problem, the branch and bound method is developed. The method is based on efficient algorithms for calculating lower and upper bounds of minimal length of the schedule. For the particular case when processors are identical, their number is fixed and the directive deadline is given, a pseudo-polynomial algorithm is proposed for constructing the admissible schedule. The number of processors required for efficient parallelizing of the algorithm is found.     

On the multi-product newsboy problem with two constraints

There is a growing interest in the applications of the constrained multi-product newsboy problem. In this paper, we develop a methodology to examine the dual of the solution space of this type of problem with two constraints and propose an approach to obtain the optimum batch size of each product. The approach is based on utilizing the Lagrangian Multipliers, Leibniz Rule, Kuhn–Tucker conditions, and when necessary it engages them into iterative techniques to obtain the optimum or near optimum solution values. Among the important features of the developed approach is its applicability to general probability distribution functions of products’ demands. Also, it can be utilized in cases when the constraints are so tight, hence allowing the decision-maker to either delete some of the products from the original list or increase the available resources. The paper shows how the parametric functions that envelope the dual solution space are developed and includes numerical examples to illustrate the application of the proposed approach.     

带实际约束的大规模车辆路径问题建模及求解

针对现有算法不能有效求解卷烟配送过程中, 问题规模大并具有诸多实际约束条件限制这类实际问题, 首先分析实际约束, 建立问题模型; 然后从模型出发设计多阶段算法, 通过地理信息的分级管理实现区域划分, 在降低问题规模的同时消除交通障碍; 采用改进的k 均值聚类法分派线路, 将问题转化为求解小规模旅行商问题; 最后以济南市区的卷烟配送为例, 通过与典型优化算法的比较表明了所提出多阶段算法在实际应用中的优越性.

     

New heuristic algorithms for solving the planar p-median problem

In this paper we propose effective heuristics for the solution of the planar p-median problem. We develop a new distribution based variable neighborhood search and a new genetic algorithm, and also test a hybrid algorithm that combines these two approaches. The best results were obtained by the hybrid approach. The best known solution was found in 466 out of 470 runs, and the average solution was only 0.000016% above the best known solution on 47 well explored test instances of 654 and 1060 demand points and up to 150 facilities.     

Heuristic algorithms for solving the maximum lateness scheduling problem with learning considerations

In many situations, a worker’s ability improves as a result of repeating the same or similar task; this phenomenon is known as the “learning effect”. In this paper, the learning effect is considered in a single-machine maximum lateness minimization problem. A branch-and-bound algorithm, incorporating several dominance properties, is provided to derive the optimal solution. In addition, two heuristic algorithms are proposed for this problem. The first one is based on the earliest due date (EDD) rule and a pairwise neighborhood search. The second one is based on the simulated annealing (SA) approach. Our computational results show that the SA algorithm is surprisingly accurate for a small to medium number of jobs. Moreover, the SA algorithm outperforms the traditional heuristic algorithm in terms of quality and execution time for a large number of jobs.     

分支定价方法求解带二维装箱约束的车辆路径问题EI北大核心CSCD

面向家具、电器等货物的物流配送场景,研究带二维装箱约束的车辆路径问题(2L–CVRP),构建了2L–CVRP的混合整数线性规划模型.为求解大规模2L–CVRP,构建了该问题集合划分模型,提出基于分支定价的方法.针对分支节点的松弛模型,基于列生成策略将其分解为线性规划主问题、带资源和二维装箱约束的最短路径子问题,并提出基于ng-route松弛策略的标签算法和基于禁忌搜索的装箱算法有效求解复杂子问题.仿真结果表明,提出的方法可高效求解大规模2L–CVRP,其中ng-route松弛策略能有效提升算法求解效率,研究成果为装箱约束下大规模车辆路径问题的高效求解提供了有效途径.     

求解可满足问题的改进的蚁群算法

可满足问题（SAT）是一个NP-hard问题,将SAT问题转换为无约束的离散优化（最小值）问题。并根据M Dorigo提出的蚁群算法,给出了一种求解SAT问题的新方法：改进的最大最小蚁群系统（MMAS-SAT）。在改进的算法中,给出了SAT问题的构造图,指出了启发式信息值的求法,对衰变系数进行了动态调整。测试问题的数值实验表明,采用MMAS-SAT的结果优于Gwsat、Walksat、Novelty等局部搜索算法,因此该算法是求解SAT问题的一种可行高效的算法。     

A meshless method for solving the free boundary problem associated with unilateral obstacle

In this paper, we discuss the numerical method for solving the first kind of elliptic variational inequality. We first use the fundamental solution as the basis function to approximate the solution of variational inequality, then we employ Uzawa's algorithm to determine the free boundary and the solution. Numerical examples are given to verify the efficiency of the method.     

On single-walk parallelization of the job shop problem solving algorithms

New parallel objective function determination methods for the job shop scheduling problem are proposed in this paper, considering makespan and the sum of jobs execution times criteria, however, the methods proposed can be applied also to another popular objective functions such as jobs tardiness or flow time. Parallel Random Access Machine (PRAM) model is applied for the theoretical analysis of algorithm efficiency. The methods need a fine-grained parallelization, therefore the approach proposed is especially devoted to parallel computing systems with fast shared memory (e.g. GPGPU, General-Purpose computing on Graphics Processing Units).     

On the modelling and solving of the truss design problem with global stability constraints

The goal of this paper is to find a computationally tractable formulation of the optimum truss design problem involving a constraint on the global stability of the structure. The stability constraint is based on the linear buckling phenomenon. We formulate the problem as a nonconvex semidefinite programming problem and briefly discuss an interior point technique for the numerical solution of this problem. We further discuss relation to other models. The paper is concluded by a series of numerical examples.     

Improved differential evolution algorithms for solving generalized assignment problem

This paper presents algorithms based on differential evolution (DE) to solve the generalized assignment problem (GAP) with the objective to minimize the assignment cost under the limitation of the agent capacity. Three local search techniques: shifting, exchange, and k-variable move algorithms are added to the DE algorithm in order to improve the solutions. Eight DE-based algorithms are presented, each of which uses DE with a different combination of local search techniques. The experiments are carried out using published standard instances from the literature. The best proposed algorithm using shifting and k-variable move as the local search (DE-SK) techniques was used to compare its performance with those of Bee algorithm (BEE) and Tabu search algorithm (TABU). The computational results revealed that the BEE and DE-SK are not significantly different while the DE-SK outperforms the TABU algorithm. However, even though the statistical test shows that DE-SK is not significantly different compared with the BEE algorithm, the DE-SK is able to obtain more optimal solutions (87.5%) compared to the BEE algorithm that can obtain only 12.5% optimal solutions. This is because the DE-SK is designed to enhance the search capability by improving the diversification using the DE's operators and the k-variable moves added to the DE can improve the intensification. Hence, the proposed algorithms, especially the DE-SK, can be used to solve various practical cases of GAP and other combinatorial optimization problems by enhancing the solution quality, while still maintaining fast computational time.     

Efficiently solving general weapon-target assignment problem by genetic algorithms with greedy eugenics

A general weapon-target assignment (WTA) problem is to find a proper assignment of weapons to targets with the objective of minimizing the expected damage of own-force asset. Genetic algorithms (GAs) are widely used for solving complicated optimization problems, such as WTA problems. In this paper, a novel GA with greedy eugenics is proposed. Eugenics is a process of improving the quality of offspring. The proposed algorithm is to enhance the performance of GAs by introducing a greedy reformation scheme so as to have locally optimal offspring. This algorithm is successfully applied to general WTA problems. From our simulations for those tested problems, the proposed algorithm has the best performance when compared to other existing search algorithms.     

动态搜索算法求解时间依赖型旅行商问题研究

时间依赖型旅行商问题(TDTSP)是旅行商问题(TSP)的延伸.在该问题中,任意两节点间的旅行时间(成本)不仅取决于节点间的距离,还依赖于一天中具体时段或节点在哈密顿圈中所处的具体位置.对基于节点所处哈密顿圈中具体位置的TDTSP问题建立相应的数学模型,并提出求解该问题的动态搜索算法.通过实验仿真,验证了动态搜索算法优于目前在邻域搜索领域求解该问题最有效的动态规划启发式算法.     

A coarse-to-fine quasi-physical optimization method for solving the circle packing problem with equilibrium constraints

This paper addresses an important extension of the circle packing problem (CPP), the circle packing problem with equilibrium constraints (CPPEC). It considers the dense packing of n circular disks in a large circular container at the same time satisfying the equilibrium constraints. Under the industrial background of the layout design on satellite modules, this NP-hard global optimization problem is important in both theory and practice. We introduce two new quasi-physical models for solving CPPEC in this paper. One is to mimic the elastic movement driven by repelling forces from extruded disks, the other is to simulate a whole translation movement of the disks driven by a pulling force from an imaginative elastic rope connecting the centroid of the disks and the center of the container. Then, inspired by the coarse-to-fine control strategy in the manufacture industry, we propose a coarse-to-fine quasi-physical (CFQP) optimization method that adopts the two quasi-physical models for the quasi-physical descent procedure and combines a basin hopping with tabu method for the search procedure. In this way, not only could CFQP take into account the diversity of the search space to facilitate the global search, but it also does fine search to find the corresponding local minimum in a promising local area. Experiments were on two sets of 11 representative test instances. Computational results showed that CFQP achieved new and better results on four instances, at the same time it matched the current best records on the other six (accurate to 0.0001). Moreover, CFQP resulted in smaller equilibrium deviations than that of others published in the literature. In addition, we generated 34 new CPPEC instances basing on the CPP benchmarks, and provided computational results on the two sets of 34 new CPPEC instances, and the container radii obtained are close to the published results on CPP.     

Comparison of two algorithms for solving STIFF differential equations

Many algorithms are available for solving differential equations. Of these, two methods—GEAR and STIFF3, which were developed specifically for stiff differential equations, are compared based on their performance on five test problems. The performance criteria are both accuracy of the numerical solution and efficiency of the method. The results indicate that GEAR, although the older of the two methods, is the preferred algorithm, for stiff differential equations.     

Exact and heuristic algorithms for solving the generalized vehicle routing problem with flexible fleet size

The generalized vehicle routing problem with flexible fleet size (GVRP‐flex) extends the classical capacitated vehicle routing problem (CVRP) by partitioning the set of required nodes into clusters and has interesting applications such as humanitarian logistics. The problem aims at minimizing the total cost for a set of routes, such that each cluster is visited exactly once and its total demand is delivered to one of its nodes. An exact method based on column generation (CG) and two metaheuristics derived from iterated local search are proposed for the case with flexible fleet size. On five sets of benchmarks, including a new one, the CG approach often provides good upper and lower bounds, whereas the metaheuristics find, in a few seconds, solutions with small optimality gaps.