Extensions to the repetitive branch and bound algorithm for globally optimal clusterwise regression

A branch and bound strategy is proposed for solving the clusterwise regression problem, extending Brusco's repetitive branch and bound algorithm (RBBA). The resulting strategy relies upon iterative heuristic optimization, new ways of observation sequencing, and branch and bound optimization of a limited number of ending subsets. These three key features lead to significantly faster optimization of the complete set and the strategy has more general applications than only for clusterwise regression. Additionally, an efficient implementation of incremental calculations within the branch and bound search algorithm eliminates most of the redundant ones. Experiments using both real and synthetic data compare the various features of the proposed optimization algorithm and contrasts them against a benchmark mixed logical-quadratic programming formulation optimized by CPLEX. The results indicate that all components of the proposed algorithm provide significant improvements in processing times, and, when combined, generally provide the best performance, significantly outperforming CPLEX.     

A branch and bound algorithm for the cyclic job-shop problem with transportation

The cyclic job-shop problem with transportation can be used to describe optimization problems in fully automated manufacturing systems or assembly lines. We study the problem where the machines have no buffers, which rapidly decreases the number of feasible solutions and, therefore, makes it a lot harder to find those feasible solutions. After formulating the problem, we will characterize feasible solutions based on the route of the robot and their properties. With the aim of minimizing the cycle time, we have developed a tree search method to construct feasible solutions and combined it with a bounding procedure. Computational results are reported and compared to those gained by solving the problem with an LP solver.     

A 2-phase algorithm for solving the single allocation p-hub center problem

The single allocation p-hub center problem is an NP-hard location–allocation problem which consists of locating hub facilities in a network and allocating non-hub nodes to hub nodes such that the maximum distance/cost between origin–destination pairs is minimized. In this paper we present an exact 2-phase algorithm where in the first phase we compute a set of potential optimal hub combinations using a shortest path based branch and bound. This is followed by an allocation phase using a reduced sized formulation which returns the optimal solution. In order to get a good upper bound for the branch and bound we developed a heuristic for the single allocation p-hub center problem based on an ant colony optimization approach. Numerical results on benchmark instances show that the new solution approach is superior over traditional MIP-solver like CPLEX. As a result we are able to provide new optimal solutions for larger problems than those reported previously in literature. We are able to solve problems consisting of up to 400 nodes in reasonable time. To the best of our knowledge these are the largest problems solved in the literature to date.     

Stabilized branch and price with dynamic parameter updating for discontinuous tour scheduling

In this paper we address the problem of staff scheduling at check-in counters with time varying demand. The main objective is to minimize a cost function based on the assigned shifts for a given workforce subject to flexible labor regulations and flexible assignments of lunch breaks. To solve the problem we developed a branch and price algorithm that uses master variable branching. However, since convergence of the column generation subroutine was really slow, we integrated stabilization techniques to speed up the algorithm. We introduced a new dynamic parameter updating procedure for the stabilized column generation. Our computational results show the superior behavior of stabilized column generation compared to the non-stabilized version. Since slow convergence might occur at each node in the search tree and consequently reductions are realized at each node investigated. Furthermore, we perform an in-depth investigation of the updating parameters and give useful insights to choose them. Finally, we tackle realistic problem instances with up to 65 service workers and show the efficiency of the algorithm.     

A branch and price approach for deployment of multi-tier software services in clouds

This paper considers a service deployment problem that combines service placement and replication level decisions in a cloud computing context. The services are composed of multiple components that are to be placed on nodes in the private cloud of the service provider or, if the private cloud has limited capacity, partly in a public cloud. In the service delivery, the provider has to take into account the quality of service guarantees offered to his end-users. To solve the problem, we develop a branch and price algorithm, where the subproblems both are formulated as a linear mixed integer program and a shortest path problem with resource constraints (SPPRC) on a network with a special structure. The SPPRC can be solved by an exact label-setting algorithm, but to speed up the solution process, we develop a heuristic label-setting algorithm based on a reduced network and simplified dominance rule. Our results show that using the heuristic subproblem solver is efficient. Furthermore, the branch and price algorithm performs better than a previously developed pre-generation algorithm for the same problem. In addition, we analyze and discuss the differences in solutions that utilize resources in a public cloud to different degrees. By conducting this analysis we are able to identify some essential characteristics of good solutions.     

A branch and price algorithm for the pharmacy duty scheduling problem

Pharmacy Duty Scheduling (PDS) is the activity of assigning pharmacies to days during a planning horizon with the purpose of serving society outside regular working hours. In Turkey, pharmacies are retailers who operate during the working hours in weekdays. However, demand for medicine at nights, at the weekends and on holidays must be satisfied by allocating times to pharmacies to open at these times. The problem is a multi-period p-median problem with the additional problem specific constraints, and it is NP-Hard. In this study, we develop a branch-and-price algorithm to solve the PDS to optimality. We decompose the problem into single period problems and apply column generation on the decomposed problem. We propose several enhancements on the algorithm and conduct computational tests on randomly generated instances to compare the performance of the developed algorithm with the state-of-art general purpose solver. The branch-and-price algorithm outperforms the state-of-art general purpose solver.     

A branch and bound algorithm for an identical parallel machine scheduling problem with a job splitting property

We focus on the problem of scheduling n independent jobs on m identical parallel machines with the objective of minimizing total tardiness of the jobs considering a job splitting property. In this problem, it is assumed that a job can be split into sub-jobs and these sub-jobs can be processed independently on parallel machines. We develop several dominance properties and lower bounds for the problem, and suggest a branch and bound algorithm using them. Computational experiments are performed on randomly generated test problems and results show that the suggested algorithm solves problems of moderate sizes in a reasonable amount of computation time.     

A fast algorithm for the generalized parametric minimum cut problem and applications

Many combinatorial optimization problems are solved by a sequence of network flow computations on a network whose edge capacities are given as a function of a parameter . Recently Galloet al. [7] made a major advance in solving such parametric flow problems. They showed that for an important class of networks, calledmonotone parametric flow networks, a sequence ofO(n) flow computations could be solved in the same worst-case time bound as a single flow. However, these results require one of two special assumptions: either that the values are presented in increasing or decreasing order; or that the edge capacity functions are affine functions of . In this paper we show how to remove both of these assumptions while obtaining the same running times as in [7]. This observation generalizes and unifies the two major results of [7], and allows its ideas to be applied to many new combinatorial problems. Of greatest importance, it allows the efficient application of binary search and successive binary search to a sequence of network flow problems.This research was partially supported by Grants CCR-8803704 and CCR-8722848 from the National Science Foundation.     

A branch, bound, and remember algorithm for the 1|r i |∑t i scheduling problem

This paper presents a modified Branch and Bound (B&B) algorithm called, the Branch, Bound, and Remember (BB&R) algorithm, which uses the Distributed Best First Search (DBFS) exploration strategy for solving the 1|r _i |∑t _i scheduling problem, a single machine scheduling problem where the objective is to find a schedule with the minimum total tardiness. Memory-based dominance strategies are incorporated into the BB&R algorithm. In addition, a modified memory-based dynamic programming algorithm is also introduced to efficiently compute lower bounds for the 1|r _i |∑t _i scheduling problem. Computational results are reported, which shows that the BB&R algorithm with the DBFS exploration strategy outperforms the best known algorithms reported in the literature.     

A branch and bound method for isolation of faulty variables through missing variable analysis

Fault detection and diagnosis is a critical approach to ensure safe and efficient operation of manufacturing and chemical processing plants. Although multivariate statistical process monitoring has received considerable attention, investigation into the diagnosis of the source or cause of the detected process fault has been relatively limited. This is partially due to the difficulty in isolating multiple variables, which jointly contribute to the occurrence of fault, through conventional contribution analysis. In this work, a method based on probabilistic principal component analysis is proposed for fault isolation. Furthermore, a branch and bound method is developed to handle the combinatorial nature of problem involving finding the contributing variables, which are most likely to be responsible for the occurrence of fault. The efficiency of the method proposed is shown through benchmark examples, such as Tennessee Eastman process, and randomly generated cases.     

A Tabu search algorithm for the network pricing problem

In this paper, we propose an efficient Tabu Search procedure for solving the NP-hard network pricing problem. By exploiting the problem's features, the algorithm allows the near-optimal solution of problem instances that are out of reach of exact combinatorial methods.     

A cross entropy algorithm for the Knapsack problem with setups

In this article we propose a new metaheuristic-based algorithm for the Integer Knapsack Problem with Setups. This problem is a generalization of the standard Integer Knapsack Problem, complicated by the presence of setup costs in the objective function as well as in the constraints. We propose a cross entropy based algorithm, where the metaheuristic scheme allows to relax the original problem to a series of well chosen standard Knapsack problems, solved through a dynamic programming algorithm. To increase the computational effectiveness of the proposed algorithm, we use a turnpike theorem, which sensibly reduces the number of iterations of the dynamic algorithm. Finally, to testify the robustness of the proposed scheme, we present extensive computational results. First, we illustrate the step-by-step behavior of the algorithm on a smaller, yet difficult, problem. Subsequently, to test the solution quality of the algorithm, we compare the results obtained on very large scale instances with the output of a branch and bound scheme. We conclude that the proposed algorithm is effective in terms of solution quality as well as computational time.     

A penalty search algorithm for the obstacle neutralization problem

We consider a path planning problem wherein an agent needs to swiftly navigate from a source to a destination through an arrangement of obstacles in the plane. We suppose the agent has a limited neutralization capability in the sense that it can safely pass through an obstacle upon neutralization at a cost added to the traversal length. The agent׳s goal is to find the sequence of obstacles to be neutralized en route that minimizes the overall traversal length subject to the neutralization limit. We call this problem the obstacle neutralization problem (ONP), which is essentially a variant of the intractable weight-constrained shortest path problem in the literature. In this study, we propose a simple, yet efficient and effective suboptimal algorithm for ONP based on the idea of penalty search and we present special cases where our algorithm is provably optimal. Computational experiments involving both real and synthetic naval minefield data are also presented.     

An exact constructive algorithm for the knapsack sharing problem

In this paper, we study the knapsack sharing problem (KSP), a variant of the well-known NP-hard single knapsack problem. We propose an exact constructive tree search that combines two complementary procedures: a reduction interval search and a branch and bound. The reduction search has three phases. The first phase applies a polynomial reduction strategy that decomposes the problem into a series of knapsack problems. The second phase is a size reduction strategy that makes the resolution more efficient. The third phase is an interval reduction search that identifies a set of optimal capacities characterizing the knapsack problems. Experimental results provide computational evidence of the better performance of the proposed exact algorithm in comparison to KSPs best exact algorithm, to Cplex and to KSPs latest heuristic approach. Furthermore, they emphasize the importance of the reduction strategies.     

Reduction strategies and exact algorithms for the disjunctively constrained knapsack problem

In this paper, we optimally solve the disjunctively constrained knapsack problem (DCKP), which is a variant of the standard knapsack problem with special disjunctive constraints. First, we develop a generic exact approach which can be considered as a three-phase procedure. The first phase tries to estimate a starting lower bound. The second phase applies a reduction procedure, combined with the lower bound, in order to fix some decision variables to the optimum. The third phase uses an exact branch and bound algorithm that identifies the optimal values of the free decision variables. Second, we design a specialized exact algorithm based upon a dichotomous search combined with a reduction procedure. Third and last, we propose a modified dichotomous search version which is based upon constructing an equivalent model to the DCKP, adding some dominating constraints, and injecting the so-called covering cut. We evaluate the performance of all versions of the algorithm and compare the obtained results to those of other exact algorithms of the literature. Encouraging results have been obtained.     

A new ant colony optimization algorithm for the multidimensional Knapsack problem

The paper proposes a new ant colony optimization (ACO) approach, called binary ant system (BAS), to multidimensional Knapsack problem (MKP). Different from other ACO-based algorithms applied to MKP, BAS uses a pheromone laying method specially designed for the binary solution structure, and allows the generation of infeasible solutions in the solution construction procedure. A problem specific repair operator is incorporated to repair the infeasible solutions generated in every iteration. Pheromone update rule is designed in such a way that pheromone on the paths can be directly regarded as selecting probability. To avoid premature convergence, the pheromone re-initialization and different pheromone intensification strategy depending on the convergence status of the algorithm are incorporated. Experimental results show the advantages of BAS over other ACO-based approaches for the benchmark problems selected from OR library.     

基于一种新型分支定价算法的电动车支线镇际快递配送路径规划研究

针对由电动汽车支持的支线镇际快递配送系统,提出一类新型的分支定价算法实现对车辆和货物的路径规划.研究利用时空网络将时间离散化构建模型,同时考虑了车辆资源、仓储资源和充电桩资源的管理问题.在分支定价算法中,分支策略和割平面策略的结合有效削弱了时间离散化所带来的对称性问题.强化策略则通过对生成路径变量进行有效筛选,并利用求...     

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

The vehicle routing problem with time windows is a complex combinatorial problem with many real-world applications in transportation and distribution logistics. Its main objective is to find the lowest distance set of routes to deliver goods, using a fleet of identical vehicles with restricted capacity, to customers with service time windows. However, there are other objectives, and having a range of solutions representing the trade-offs between objectives is crucial for many applications. Although previous research has used evolutionary methods for solving this problem, it has rarely concentrated on the optimization of more than one objective, and hardly ever explicitly considered the diversity of solutions. This paper proposes and analyzes a novel multi-objective evolutionary algorithm, which incorporates methods for measuring the similarity of solutions, to solve the multi-objective problem. The algorithm is applied to a standard benchmark problem set, showing that when the similarity measure is used appropriately, the diversity and quality of solutions is higher than when it is not used, and the algorithm achieves highly competitive results compared with previously published studies and those from a popular evolutionary multi-objective optimizer.     

A branch and bound method for the line balancing problem in U-shaped assembly lines with equipment requirements

In this study we consider a U-shaped assembly line balancing problem where each task uses a specified set of equipments and each type of equipment has a specified cost. Our problem is to assign the tasks together with their equipments to the workstations so as to minimize the total equipment cost. We formulate the problem as a mixed integer linear programming model that is capable of solving small sized instances. We propose a branch and bound algorithm that uses efficient precedence relations and lower bounds. We find that the algorithm is able to solve moderate sized problem instances in reasonable times.     

一种求解QAP问题的混合嵌套分区优化算法

提出一种基于嵌套分区算法(NPM)框架求解二次分配问题(QAP)的混合优化算法.算法利用嵌套分区树来描述二次分配过程,对可行域进行系统性分区,采用禁忌抽样算子对分区进行抽样并评估各个分区的性能.在每次迭代中,算法重点跟踪和搜索优良解最有希望出现的分区,并结合禁忌搜索算法来实现分区转移.数值仿真实验表明,引入更加有效的禁忌抽样算子后,NPM算法具有更好的寻优能力.