Exact procedures for solving the discrete ordered median problem

The discrete ordered median problem (DOMP) integrates classical discrete location problems, such as the N-median, N-center and Uncapacitated Facility Location problems. It was introduced by Nickel (In: Fleischmann B, Lasch R, Derigs U, Domschke W, Rieder U, editors. Operations Research Proceedings 2000, Berlin: Springer, 2001. p. 71–76), who formulated it as both a nonlinear and a linear integer program. We propose an alternative integer linear programming formulation for the DOMP, discuss relationships between both integer linear programming formulations, and show how properties of optimal solutions can be used to strengthen these formulations. Moreover, we present a specific branch and bound procedure to solve the DOMP more efficiently. We test the integer linear programming formulations and this branch and bound method computationally on randomly generated test problems.     

A revised particle swarm optimization based discrete Lagrange multipliers method for nonlinear programming problems

In this paper, a new algorithm for solving constrained nonlinear programming problems is presented. The basis of our proposed algorithm is none other than the necessary and sufficient conditions that one deals within a discrete constrained local optimum in the context of the discrete Lagrange multipliers theory. We adopt a revised particle swarm optimization algorithm and extend it toward solving nonlinear programming problems with continuous decision variables. To measure the merits of our algorithm, we provide numerical experiments for several renowned benchmark problems and compare the outcome against the best results reported in the literature. The empirical assessments demonstrate that our algorithm is efficient and robust.     

Ant colony optimization algorithm to solve for the transportation problem of cross-docking network

This paper addresses the transportation problem of cross-docking network where the loads are transferred from origins (suppliers) to destinations (retailers) through cross-docking facilities, without storing them in a distribution center (DC). We work on minimizing the transportation cost in a network by loading trucks in the supplier locations and then route them either directly to the customers or indirectly to cross-docking facilities so the loads can be consolidated. For generating a truck operating plan in this type of distribution network, the problem was formulated using an integer programming (IP) model and solved using a novel ant colony optimization (ACO) algorithm. We solved several numerical examples for verification and demonstrative purposes and found that our proposed approach finds solutions that significantly reduce the shipping cost in the network of cross-docks and considerably outperform Branch-and-Bound algorithm especially for large problems.     

Direct zigzag search for discrete multi-objective optimization

Multiple objective optimization (MOO) models and solution methods are commonly used for multi-criteria decision making in real-life engineering and management applications. Much research has been conducted for continuous MOO problems, but MOO problems with discrete or mixed integer variables and black-box objective functions arise frequently in practice. For example, in energy industry, optimal development problems of oil gas fields, shale gas hydraulic fracturing, and carbon dioxide geologic storage and enhanced oil recovery, may consider integer variables (number of wells, well drilling blocks), continuous variables (e.g. bottom hole pressures, production rates), and the field performance is typically evaluated by black-box reservoir simulation. These discrete or mixed integer MOO (DMOO) problems with black-box objective functions are more challenging and require new MOO solution techniques. We develop a direct zigzag (DZZ) search method by effectively integrating gradient-free direct search and zigzag search for such DMOO problems. Based on three numerical example problems including a mixed integer MOO problem associated with the optimal development of a carbon dioxide capture and storage (CCS) project, DZZ is demonstrated to be computationally efficient. The numerical results also suggest that DZZ significantly outperforms NSGA-II, a widely used genetic algorithms (GA) method.     

Representation of the non-dominated set in biobjective discrete optimization

This paper introduces several algorithms for finding a representative subset of the non-dominated point set of a biobjective discrete optimization problem with respect to uniformity, coverage and the ϵ-indicator. We consider the representation problem itself as multiobjective, trying to find a good compromise between these quality measures. These representation problems are formulated as particular facility location problems with a special location structure, which allows for polynomial-time algorithms in the biobjective case based on the principles of dynamic programming and threshold approaches. In addition, we show that several multiobjective variants of these representation problems are also solvable in polynomial time. Computational results obtained by these approaches on a wide range of randomly generated point sets are presented and discussed.     

A two-phase optimization procedure for integer programming problems

This paper presents a simple two-phase method for optimizing integer programming problems with a linear or nonlinear objective function subject to multiple linear or nonlinear constraints. The primary phase is based on a variation of the method of steepest descent in the feasible region, and a hem-stitching approach when a constraint is violated. The secondary phase zeros on the optimum solution by exploring the neighborhood of the suboptimum found in the first phase of the optimization process. The effectiveness of this method is illustrated through the optimization of several examples. The results from the proposed optimization approach are compared to those from methods developed specially for dealing with integer problems. The proposed method is simple, easy to implement yet very effective in dealing with a wide class of integer problems such as spare allocation, reliability optimization, and transportation problems.     

基于离散粒子群算法的动态网络路由重组

寻找最优路由作为动态网络研究的一个重要方面,对于提高网络资源的利用率及可靠性具有现实的应用价值,但无论在理论上还是实际的网络条件下,最优问题一直都是研究难点。针对不同的网络实际条件,提出一种改进的离散粒子群算法来寻找网络中任意两个节点间的最优路由。在以寻找最小路由总延时作为目标函数的情况下,仿真结果显示该算法能较准确地在网络拓扑结构变化的情况下较快地寻找到最优路径,且显示出了比蚁群算法更好的收敛性能,获得了较好的寻优结果。     

A network flow model for clustering segments and minimizing total maintenance and rehabilitation cost

Because of shrinking budgets, transportation agencies are facing severe challenges in the preservation of deteriorating pavements. There is an urgent need to develop a methodology that minimizes maintenance and rehabilitation (M&R) cost. To minimize total network M&R cost of clustering pavement segments, we propose an integer programming model similar to an uncapacitated facility location problem (UFLP) that clusters pavement segments contiguously. Based on the properties of contiguous clustered pavement segments, we have transformed the clustering problem into an equivalent network flow problem in which each possible clustering corresponds to a path in the proposed acyclic network model. Our proposed shortest-path algorithm gives an optimal clustering of segments that can be calculated in a time polynomial to the number of segments. Computational experiments indicate our proposed network model and algorithm can efficiently deal with real-world spatial clustering problems.     

An identity-based cryptographic model for discrete logarithm and integer factoring based cryptosystem

In 1984, Shamir proposed the concept of the identity-based (ID-based) cryptosystem. Instead of generating and publishing a public key for each user, the ID-based scheme permits each user to choose his name or network address as his public key. This is advantageous to public-key cryptosystems because the public-key verification is so easy and direct. In such a way, a large publickey file is not required. Since new cryptographic schemes always face security challenges and many discrete logarithm and integer factorization problem-based cryptographic systems have been deployed, therefore, the purpose of this paper is to design a transformation process that can transfer all the discrete logarithm and integer factorization based cryptosystems into the ID-based systems rather than re-invent a new system. In addition, no modification of the original discrete logarithm and integer factorization based cryptosystems is necessary.     

Evolution strategies for solving discrete optimization problems

A method to solve discrete optimization problems using evolution strategies (ESs) is described. The ESs imitate biological evolution in nature and have two characteristics that differ from other conventional optimization algorithms: (a) ESs use randomized operators instead of the usual deterministic ones; (b) instead of a single design point, the ESs work simultaneously with a population of design points in the space of variables. The important operators of ESs are mutation, selection and recombination. The ESs are commonly applied for continuous optimization problems. For the application to discrete problems, several modifications on the operators mutation and recombination are suggested here. Several examples from the literature are solved with this modified ES and the results compared. The examples show that the modified ES is robust and suitable for discrete optimization problems.     

基于混合粒子群的RFID网络的优化部署*

在RFID网络系统中,贴有标签的物品可能随机地布置着,针对如何有效地放置阅读器,使得阅读器可以读取多个标签信息同时减小冲突的问题,建立了RFID网络系统的优化模型,提出了一种混合粒子群算法来优化部署阅读器的位置。实验结果表明,混合粒子群算法分别比传统的粒子群(PSO)和遗传算法(GA)在收敛速度和寻优能力上具有更好的性能,体现出混合粒子群算法的优越性。     

基于改进微粒群算法的直觉模糊整数规划

提出了一种基于改进微粒群算法的直觉模糊整数规划。首先定义了目标函数和约束函数的隶属和非隶属函数,通过直觉模糊“最小-最大”算子,提出了直觉模糊整数规划模型;然后通过对微粒群算法进行改进,对直觉模糊整数规划进行了求解,并通过一个算例表明本文的算法性能优于其他几种算法。     

Corporates’ control strategies using network optimization

The ownership of a quoted company is usually spread among various shareholders. This dispersion can be characterized by an oriented network, whose nodes represent the companies, and an arc between companies i and j, with weight s_ij, indicates that company i owns s_ij percent of company j, being denoted by stock shareholding network (SSN). Given two sets of companies T and C₀ from a SSN, we say that the companies in C₀ control those in T if they own or imply ownership of at least α_j percent of companies’ T shares. So, given a targeting set T, our problem is to find a set of companies C₀ in which we invest such that the entire investment cost is the lowest. This problem has relevant applications in corporate governance and it can be modeled within network optimization. We discuss its applicability using a broad set of companies in the European stock market.     

A modified particle swarm optimization for aggregate production planning

Particle swarm optimization (PSO) originated from bird flocking models. It has become a popular research field with many successful applications. In this paper, we present a scheme of an aggregate production planning (APP) from a manufacturer of gardening equipment. It is formulated as an integer linear programming model and optimized by PSO. During the course of optimizing the problem, we discovered that PSO had limited ability and unsatisfactory performance, especially a large constrained integral APP problem with plenty of equality constraints. In order to enhance its performance and alleviate the deficiencies to the problem solving, a modified PSO (MPSO) is proposed, which introduces the idea of sub-particles, a particular coding principle, and a modified operation procedure of particles to the update rules to regulate the search processes for a particle swarm. In the computational study, some instances of the APP problems are experimented and analyzed to evaluate the performance of the MPSO with standard PSO (SPSO) and genetic algorithm (GA). The experimental results demonstrate that the MPSO variant provides particular qualities in the aspects of accuracy, reliability, and convergence speed than SPSO and GA.     

On finding representative non-dominated points for bi-objective integer network flow problems

This paper proposes a new algorithm to find a representation of the set of all non-dominated points of the bi-objective integer network flow problem. The algorithm solves a sequence of ε-constraint problems with a branch-and-bound algorithm to find a subset of non-dominated points that represents the set of all non-dominated points well in the sense of coverage or uniformity. At each iteration of the algorithm, one non-dominated point, determined by solving one ε-constraint problem, is added to the representation until it is guaranteed that the representation has the desired quality. Computational experiments on different problem types show the efficacy of the algorithm.     

Model-based methods for continuous and discrete global optimization

The use of surrogate models is a standard method for dealing with complex real-world optimization problems. The first surrogate models were applied to continuous optimization problems. In recent years, surrogate models gained importance for discrete optimization problems. This article takes this development into consideration. The first part presents a survey of model-based methods, focusing on continuous optimization. It introduces a taxonomy, which is useful as a guideline for selecting adequate model-based optimization tools. The second part examines discrete optimization problems. Here, six strategies for dealing with discrete data structures are introduced. A new approach for combining surrogate information via stacking is proposed in the third part. The implementation of this approach will be available in the open source R package SPOT2. The article concludes with a discussion of recent developments and challenges in continuous and discrete application domains.     

基于线性规划和遗传–粒子群算法的烧结配料多目标综合优化方法

针对钢铁企业二次配料工艺,本文采用将硫含量折算为可比成本,兼顾节能减排目标和配料成本,建立了二次配料多目标优化模型;提出了一种基于线性规划和遗传–粒子群算法（GA–PSO）的钢铁烧结配料优化方法.首先采用线性规划算法进行求解,若线性规划方法无法求得最优解,则采用GA–PSO算法进行搜索.该方法应用于某钢铁企业360m2生产线的＂配料优化与决策支持系统＂中,实际运行结果表明,该算法在保证烧结矿质量的前提下,能够有效地减少二氧化硫排放,降低配料成本.     

基于深度自适应动态规划的孤岛主动配电网发电控制与优化一体化算法

随着多种分布式新能源的并网,如风电与光伏发电、生物质能发电、储能与电动汽车等,传统情况下孤岛配电网的发电控制方法已很难达到高品质频率稳定控制的要求.为解决此问题,本文提出了一种新颖的深度自适应动态规划算法.该算法将自适应动态规划算法中的神经网络替换为机器学习领域中的深度神经网络,并在其中添加深度模型预测网络.所提算法能一次性完成传统模式下"发电控制算法+指令优化分配算法"共同完成的工作.最后,为验证深度自适应动态规划算法的鲁棒性,设计了多种配电网的仿真实验,即正常情况、"即插即用"启停机情况、通讯故障情况、全天扰动仿真情况、变拓扑结构的孤岛配网情况和变参数模型的仿真,设置的总仿真时长达25年.仿真结果验证了所设计的深度自适应动态规划算法有效性、可行性与强鲁棒性.     

基于离散粒子群算法的测试用例优先排序

测试用例优先排序技术能够有效提高回归测试效率,是软件测试的热点研究课题之一。针对基于需求的测试用例优先排序方法可操作性差的问题,提出了一种改进的基于测试点覆盖和离散粒子群优化算法的求解方法（TCP-DPSO）。首先,把影响排序的各种因素分为测试收益型因素和测试成本型因素两大类,通过加权平均的方式进行归一化,得到基于需求的通用测试平均收益率评价指标;然后,利用交换子和基本交换序列定义粒子的位置和速度,借鉴遗传算法（GA）变异策略引入变异算子,采用时变惯性权重调整粒子的探索能力和开发能力,促进可持续进化和逼近优化目标。实验结果表明,TCP-DPSO在最优解质量上与遗传算法相当,大幅优于随机测试,在最优解成功率和平均求解时间上优于遗传算法,具有更好的算法稳定性。