A minisum location problem with regional demand considering farthest Euclidean distances

We consider a continuous multi-facility location-allocation problem that aims to minimize the sum of weighted farthest Euclidean distances between (closed convex) polygonal and/or circular demand regions, and facilities they are assigned to. We show that the single facility version of the problem has a straightforward second-order cone programming formulation and can therefore be efficiently solved to optimality. To solve large size instances, we adapt a multi-dimensional direct search descent algorithm to our problem which is not guaranteed to find the optimal solution. In a special case with circular and rectangular demand regions, this algorithm, if converges, finds the optimal solution. We also apply a simple subgradient method to the problem. Furthermore, we review the algorithms proposed for the problem in the literature and compare all these algorithms in terms of both solution quality and time. Finally, we consider the multi-facility version of the problem and model it as a mixed integer second-order cone programming problem. As this formulation is weak, we use the alternate location-allocation heuristic to solve large size instances.     

Solving the problem of negative synaptic weights in cortical models

In cortical neural networks, connections from a given neuron are either inhibitory or excitatory but not both. This constraint is often ignored by theoreticians who build models of these systems. There is currently no general solution to the problem of converting such unrealistic network models into biologically plausible models that respect this constraint. We demonstrate a constructive transformation of models that solves this problem for both feedforward and dynamic recurrent networks. The resulting models give a close approximation to the original network functions and temporal dynamics of the system, and they are biologically plausible. More precisely, we identify a general form for the solution to this problem. As a result, we also describe how the precise solution for a given cortical network can be determined empirically.     

The probabilistic gradual covering location problem on a network with discrete random demand weights

We study the gradual covering location problem on a network with uncertain demand. A single facility is to be located on the network. Two coverage radii are defined for each node. The demand originating from a node is considered fully covered if the shortest distance from the node to the facility does not exceed the smaller radius, and not covered at all if the shortest distance is beyond the larger radius. For a distance between these two radii, the coverage level is specified by a coverage decay function. It is assumed that demand weights are independent discrete random variables. The objective of the problem is to find a location for the facility so as to maximize the probability that the total covered demand weight is greater than or equal to a pre-selected threshold value. We show that the problem is NP-hard and that an optimal solution exists in a finite set of dominant points. We develop an exact algorithm and a normal approximation solution procedure. Computational experiment is performed to evaluate their performance.     

Robust stability and structured uncertainty bounded by the Euclidean norm

In the context of robust stability, the μ‐problem is generalized for uncertainty bounded by means of the Euclidean norm. In some cases, a weighted Euclidean norm may be preferable to the infinite norm, for example, when the deviation from the nominal parameters exhibits a Gaussian distribution, also in the case that the parameters of the system are estimated by the ellipsoid algorithm. Several polynomial‐time upper bounds for the new μ‐problem are proposed. Copyright © 2001 John Wiley & Sons, Ltd.     

A metaheuristic approach for the sequencing by hybridization problem with positive and negative errors

This work introduces a metaheuristic method for the reconstruction of the DNA string from its l-mer content in the presence of large amounts of positive and negative errors. The procedure consists of three parts: the formulation of the problem as an asymmetric traveling salesman problem (ATSP), a technique for handling the positive errors and an optimization algorithm that solves the formulated problem. The optimization algorithm is a variation of the threshold accepting method with intense local search and its function is controlled by a size diminishing shell. The optimization algorithm is used consecutively on ATSPs of continuously decreasing sizes till it reaches a final solution. The proposed method provides solutions of better quality compared to algorithms in the recent bibliography.     

Matrix corrections minimal with respect to the Euclidean norm for linear programming problems

We consider special algebraic constructions, namely minimal matrix solutions and corrections of systems of linear algebraic equations and pairs of conjugate systems of linear algebraic equations. We build the corresponding mathematical apparatus that also lets us solve inverse linear programming problems (construct model linear programming problems with given properties), study and solve approximate and singular linear programming problems. We give statements of the theorems and numerical examples.     

Degree-constrained minimum spanning tree problem with uncertain edge weights

Uncertainty theory has shown great advantages in solving many nondeterministic problems, one of which is the degree-constrained minimum spanning tree (DCMST) problem in uncertain networks. Based on different criteria for ranking uncertain variables, three types of DCMST models are proposed here: uncertain expected value DCMST model, uncertain α-DCMST model and uncertain most chance DCMST model. In this paper, we give their uncertainty distributions and fully characterize uncertain expected value DCMST and uncertain α-DCMST in uncertain networks. We also discover an equivalence relation between the uncertain α-DCMST of an uncertain network and the DCMST of the corresponding deterministic network. Finally, a related genetic algorithm is proposed here to solve the three models, and some numerical examples are provided to illustrate its effectiveness.     

The network p-median problem with discrete probabilistic demand weights

We study the problem of locating p facilities to serve clients residing at the nodes of a network with discrete probabilistic demand weights. The objective is to maximize the probability that the total weighted distance from a client to the closest facility does not exceed a given threshold value. The problem is formulated as an integer program but can be solved only for very small instances because of the exponential number of decision variables and constraints. We analyze the problem and, using a normal approximation of the total weighted distance we develop branch and bound solution procedures for various cases of the problem. We also develop heuristics and meta-heuristics to solve the problem. Based on our computational experiments we make recommendations on which approach to use and when.     

不确定条件下配送回收中心选址配送问题研究

针对制造商、零售商、一个废弃处理中心和多个配送回收中心构成的闭环供应链,解决模糊随机环境下的配送回收中心选址配送问题。引用模糊随机理论处理产品回收率和可再利用率随机变量,以成本最低和碳排放最小为双重目标,以设施能力,设施间流量以及设施数量为约束,建立多目标闭环供应链配送回收中心选址配送模型。改进了全局-局部-邻域粒子群算法,设计了基于优先级的全局-局部-邻域粒子群算法方案,并用案例验证了模型及算法的有效性和先进性。     

A global shooting algorithm for the facility location and capacity acquisition problem on a line with dense demand

This paper describes the development of an exact allocation-based solution algorithm for the facility location and capacity acquisition problem (LCAP) on a line with dense demand data. Initially, the n-facility problem on a line is studied and formulated as a dynamic programming model in the allocation decision space. Next, we cast this dynamic programming formulation as a two-point boundary value problem and provide conditions for the existence and uniqueness of solutions. We derive sufficient conditions for non-empty service regions and necessary conditions for interior facility locations. We develop an efficient exact shooting algorithm to solve the problem as an initial value problem and illustrate on an example. A computational study is conducted to study the effect of demand density and other problem parameters on the solutions.     

Iterative methods to compute weighted normal pseudosolutions with positive definite weights

We construct iterative processes to compute the weighted normal pseudosolution with positive definite weights (weighted least squares solutions with weighted minimum Euclidean norm) for systems of linear algebraic equations (SLAE) with an arbitrary rectangular real matrix. We examine two iterative processes based on the expansion of the weighted pseudoinversc matrix into matrix power series. The iterative processes are applied to solve constrained least squares problems that arise in mathematical programming and to findL-pseudosolutions. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 116–124, March–April, 1998.     

A two-stage approach to the orienteering problem with stochastic weights

The Orienteering Problem (OP) is a routing problem which has many interesting applications in logistics, tourism and defense. The aim of the OP is to find a maximum profit path or tour, which is feasible with respect to a capacity constraint on the total weight of the selected arcs. In this paper we consider the Orienteering Problem with Stochastic Weights (OPSWs) to reflect uncertainty in real-life applications. We approach this problem by formulating a two-stage stochastic model with recourse for the OPSW where the capacity constraint is hard. The model takes into account the effect that stochastic weights have on the expected total profit value to be obtained, already in the modeling stage. Since the expected profit is in general non-linear, we introduce a linearization that models the total profit that can be obtained for a given tour and a given scenario of weight realizations. This linearization allows for the application of Sample Average Approximation (SAA). The SAA solution asymptotically converges to the optimal solution of the two-stage model, but is computationally expensive. Therefore, to solve large instances, we developed a heuristic that exploits the problem structure of the OPSW and explicitly takes the associated uncertainty into account. In our computational experiments, we evaluate the benefits of our approach to the OPSW, compared to both a standard deterministic approach, and a deterministic approach that is extended with utilization of real-time information.     

Evolutionary model for the Steiner tree problem with flow-dependent weights

An evolutionary model developed for solving the Steiner tree problem with flow-dependent weights is discussed. The solution search is simulated as an evolutionary process at two interconnected levels, accidental speciation and the evolution of individual-species populations. For this purpose, original genetic operators are applied.     

Facility location and scale decision problem with customer preference

This paper addresses the facility location problem that aims to optimize the location and scale of a new facility in consideration of customer restrictions, including customer preference and the minimum number of customers required to open the facility. In a classic covering problem, the customer is assumed to be covered if he/she is located within the critical distance zone around the facility and is otherwise not covered. This problem is caused by customer facility selection, which differs from the classic covering problem in which services are determined only by proximity. This paper proposes a mixed integer programming formulation based on customer restrictions and also develops a heuristic solution procedure using Lagrangian relaxation. The suggested solution procedure is shown to yield acceptable results in a reasonable computation time.     

Semi-supervised nonnegative matrix factorization with positive and negative label propagations

Applied Intelligence - Semi-supervised nonnegative matrix factorization (SNMF) methods yield the enhanced representation ability over nonnegative matrix factorization (NMF) by incorporating the...     

An efficient distributed protocol for finding shortest paths innetworks with negative weights

The design is discussed of distributed algorithms for the single-source shortest-path problem to run on an asynchronous directed network in which some of the edges may be associated with negative weights, and thus in which a cycle of negative total weight may also exist. The only existing solution in the literature for this problem is due to K.M. Chandy and J. Misra (1982), and it has, in the worst case, an unbounded message complexity. A synchronous version of the Chandy-Misra algorithm is described and studied, and it is proved that for a network with m edges and n nodes, the worst case message and time complexities of this algorithm are O(mn ) and O(n), respectively. This algorithm is then combined with an efficient synchronizer to yield an asynchronous protocol that retains the same message and time complexities     

Capacitated facility location problem with general setup cost

This paper presents an extension of the capacitated facility location problem (CFLP), in which the general setup cost functions and multiple facilities in one site are considered. The setup costs consist of a fixed term (site setup cost) plus a second term (facility setup costs). The facility setup cost functions are generally non-linear functions of the size of the facility in the same site. Two equivalent mixed integer linear programming (MIP) models are formulated for the problem and solved by general MIP solver. A Lagrangian heuristic algorithm (LHA) is also developed to find approximate solutions for this NP-hard problem. Extensive computational experiments are taken on randomly generated data and also well-known existing data (with some necessary modifications). The detailed results are provided and the heuristic algorithm is shown to be efficient.     

P-中心选址问题的一种降阶回溯算法

运筹学研究领域中的应急服务设施选址问题有许多求解模型,选取了P-中心模型进行研究,首先研究了该问题的数学性质,并给出了证明,利用这些数学性质能对问题进行降阶从而缩小问题的规模;然后在此基础上设计一个基于上界和下界的回溯算法来求解该问题;最后通过一个示例分析进一步阐述了该算法的原理,并证明了该算法能在较短时间内求得问题的最优解。     

GRASP with path relinking for the symmetric Euclidean clustered traveling salesman problem

In this paper, we propose new heuristics using several path-relinking strategies to solve the Clustered Traveling Salesman Problem (CTSP). The CTSP is a generalization of the Traveling Salesman Problem (TSP) in which the set of vertices is partitioned into clusters and the objective is to find a minimum cost Hamiltonian cycle such that the vertices of each cluster are visited continuously. A comparison among the performance of the several different adopted path-relinking strategies is presented using instances with up to 2000 vertices and clusters varying between 4 and 150 vertices. Also computational experiments were performed to compare the performance of the proposed heuristics with an exact algorithm and a Genetic Algorithm. The obtained computational results showed that the proposed heuristics were able to obtain competitive results related to the quality of the solutions and computational execution time.     

Hermitian tridiagonal solution with the least norm to quaternionic least squares problem

Quaternionic least squares (QLS) is an efficient method for solving approximate problems in quaternionic quantum theory. In view of the extensive applications of Hermitian tridiagonal matrices in physics, in this paper we list some properties of basis matrices and subvectors related to tridiagonal matrices, and give an iterative algorithm for finding Hermitian tridiagonal solution with the least norm to the quaternionic least squares problem by making the best use of structure of real representation matrices, we also propose a preconditioning strategy for the Algorithm LSQR-Q in Wang, Wei and Feng (2008) [14] and our algorithm. Numerical experiments are provided to verify the effectiveness of our method.