Mining cohesive subgraphs from a network is a fundamental problem in network analysis. Most existing cohesive subgraph models are mainly tailored to unsigned networks. In this paper, we study the problem of seeking co...
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Mining cohesive subgraphs from a network is a fundamental problem in network analysis. Most existing cohesive subgraph models are mainly tailored to unsigned networks. In this paper, we study the problem of seeking cohesive subgraphs in a signed network, in which each edge can be positive or negative, denoting friendship or conflict, respectively. We propose a novel model, called maximal (alpha, k)-clique, that represents a cohesive subgraph in signed networks. Specifically, a maximal (alpha, k)-clique is a clique in which every node has at most k negative neighbors and at least inverted right perpendicular alpha kinverted left perpendicular positive neighbors (alpha >= 1). We show that the problem of enumerating all maximal (alpha, k)-cliques in a signed network is NP-hard. To enumerate all maximal (alpha, k)-cliques efficiently, we first develop an elegant signed network reduction technique to significantly prune the signed network. Then, we present an efficient branch and bound enumeration algorithm with several carefully-designed pruning rules to enumerate all maximal (alpha, k)-cliques in the reduced signed network. In addition, we also propose an efficient algorithm with three novel upper-bounding techniques to find the maximum (alpha, k)-clique in a signed network. The results of extensive experiments on five large real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.
In reality, the machine might become unavailable due to machine breakdowns or various inevitable reasons, and machine might have different capability to processing job. Motivated by this, we consider the problem of sc...
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In reality, the machine might become unavailable due to machine breakdowns or various inevitable reasons, and machine might have different capability to processing job. Motivated by this, we consider the problem of scheduling n non-preemptive and independent jobs on m identical machines incorporating machine availability and eligibility constraints while minimizing the maximum lateness. Each machine is capable of processing at specific availability intervals. We develop a branch and bound algorithm applying several immediate selection rules for solving this scheduling problem.
This research focuses on finding the best transfer schemes in metro networks. Using sample-based time-invariant link travel times to capture the uncertainty of a realistic network, a two-stage stochastic integer progr...
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This research focuses on finding the best transfer schemes in metro networks. Using sample-based time-invariant link travel times to capture the uncertainty of a realistic network, a two-stage stochastic integer programming model with the minimized expected travel time and penalty value incurred by transfer activities is formulated. The first stage aims to find a sequence of potential transfer nodes (stations) that can compose a feasible path from origins to destinations in the transfer activity network, and the second stage provides the least time paths passing by the generated transfer stations in the first stage for evaluating the given transfer schemes and then outputs the best routing information. To solve our proposed model, an efficient hybrid algorithm, in which the label correcting algorithm is embedded into a branch and bound searching framework, is presented to find the optimal solutions of the considered problem. Finally, the numerical experiments are implemented in different scales of metro networks. The computational results demonstrate the effectiveness and performance of the proposed approaches even for the large-scale Beijing metro network. (C) 2015 Elsevier Ltd. All rights reserved.
Lagrangian bounds, i.e. bounds computed by Lagrangian relaxation, have been used successfully in branch and boundbound methods for solving certain classes of nonconvex optimization problems by reducing the duality ga...
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Lagrangian bounds, i.e. bounds computed by Lagrangian relaxation, have been used successfully in branch and boundbound methods for solving certain classes of nonconvex optimization problems by reducing the duality gap. We discuss this method for the class of partly linear and partly convex optimization problems and, incidentally, point out incorrect results in the recent literature on this subject.
The purpose of this paper is to propose a practical branch and bound algorithm for solving a class of long-short portfolio optimization problem with concave and d.c. transaction cost and complementarity conditions on ...
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The purpose of this paper is to propose a practical branch and bound algorithm for solving a class of long-short portfolio optimization problem with concave and d.c. transaction cost and complementarity conditions on the variables. We will show that this algorithm can solve a problem of practical size and that the long-short strategy leads to a portfolio with significantly better risk-return structure compared with standard purchase only portfolio both in terms of ex-ante and ex-post performance.
We consider linear fractional programming problems in a form of which the linear fractional program and its stochastic and distributionally robust counterparts with finite support are special cases. We introduce a nov...
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We consider linear fractional programming problems in a form of which the linear fractional program and its stochastic and distributionally robust counterparts with finite support are special cases. We introduce a novel reformulation that involves differences of square terms in the constraint, subsequently using a piecewise linear approximation for the concave part. Using the resulting second order cone programs (SOCPs), we develop a solution algorithm in the branch and bound framework. Our method iteratively refines the piecewise linear approximations by dividing hyper-rectangles and solves SOCPs to obtain lower bounds for the sub-hyper-rectangles. We derive a bound on the optimality gap as a function of the approximation errors at the iterate and prove that the number of iterations to attain an epsilon-optimal solution is in the order of O(root epsilon). Numerical experiments show that the proposed algorithm scales better than state-of-the-art linear-programming-based algorithms and commercial solvers to solve linear fractional programs. Specifically, the proposed algorithm achieves two or more digits of accuracy in significantly less time than the time required by the known algorithms on medium to larger size problem instances. Experimental results with Wasserstein ambiguity sets reveal that our reformulation-based approach solves small size distributionally robust linear fractional programs, with the cardinality of support up to 25.
The portfolio rebalancing with transaction costs plays an important role in both theoretical analyses and commercial applications. This paper studies a standard portfolio problem that is subject to an additional ortho...
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The portfolio rebalancing with transaction costs plays an important role in both theoretical analyses and commercial applications. This paper studies a standard portfolio problem that is subject to an additional orthogonality constraint guaranteeing that buying and selling a same security do not occur at the same time point. Incorporating the orthogonality constraint into the portfolio problem leads to a quadratic programming problem with linear complementarity constraints. We derive an enhanced simultaneous diagonalization based second order cone programming (ESDSOCP) relaxation by taking advantage of the feature that the objective and constraint matrices are commutative. The ESDSOCP relaxation has lower computational complexity than the semi-definite programming (SDP) relaxation, and it is proved to be as tight as the SDP relaxation. It is worth noting that the original simultaneous diagonalization based second order cone programming relaxation (SDSOCP) is only guaranteed to be as tight as the SDP relaxation on condition that the objective matrix is positive definite. Note that the objective matrix in this paper is positive semidefinite (while not positive definite), thus the ESDSOCP relaxation outperforms the original SDSOCP relaxation. We further design a branch and bound algorithm based on the ESDSOCP relaxation to find the global optimal solution and computational results illustrate the effectiveness of the proposed algorithm.
This paper considers Capacitated Vehicle Routing Problem (CVRP) in an imprecise and random environment. The deterministic version of the problem deals with finding a set of routes in such a way that the demand of all ...
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This paper considers Capacitated Vehicle Routing Problem (CVRP) in an imprecise and random environment. The deterministic version of the problem deals with finding a set of routes in such a way that the demand of all the customers present in the network are satisfied and the cost incurred in performing these operations comes out to be a minimum. In practical life situations, problems are not always defined in crisp form. Phenomena like randomness and impreciseness are quite natural to arise in real life. This work presents CVRP in such a mixed environment, such type of CVRP may be called as Fuzzy Stochastic Capacitated Vehicle Routing Problem. In this work, the demands of the customers are assumed to be stochastic and are revealed only when a vehicle arrives at the customer location. Moreover, the edge weights represent time required to traverse the edge and hence are both imprecise and random in nature. Factors like traffic conditions, weather conditions, are responsible for the random nature of the edge weights and the varying speed of the vehicle is responsible for impreciseness. Thus, the work presents CVRP with stochastic demands and stochastic and imprecise travel times. In this paper, an expectation-based approach has been used to deal with the randomness of edge weights. A two-stage model is used to solve the problem where the first stage corresponds to finding an optimal tour and recourse actions are planned in the second stage. A procedure based on branch and bound algorithm has been used to find minimum cost route. A small numerical example is presented to explain the working of the method proposed and the proposed solution approach is further tested on modified fuzzy versions of some benchmarks datasets.
Boolean network is a modeling tool that describes a dynamic system with binary variables and their logical transition formulas. Recent studies in precision medicine use a Boolean network to discover critical genetic a...
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Boolean network is a modeling tool that describes a dynamic system with binary variables and their logical transition formulas. Recent studies in precision medicine use a Boolean network to discover critical genetic alterations that may lead to cancer or target genes for effective therapies to individuals. In this paper, we study a logical inference problem in a Boolean network to find all such critical genetic alterations in a minimal (parsimonious) way. We propose a bilevel integer programming model to find a single minimal genetic alteration. Using the bilevel integer programming model, we develop a branch and bound algorithm that effectively finds all of the minimal alterations. Through a computational study with eleven Boolean networks from the literature, we show that the proposed algorithm finds solutions much faster than the state-of-the-art algorithms in large data sets. (C) 2021 Elsevier B.V. All rights reserved.
There are substantial number of exact and heuristic solution methods proposed for solving the facilities location problems. This paper develops an algorithm to solve the capacitated, multi-commodity, multiperiod (dyna...
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There are substantial number of exact and heuristic solution methods proposed for solving the facilities location problems. This paper develops an algorithm to solve the capacitated, multi-commodity, multiperiod (dynamic), multi-stage facility location problem. The literature on such composite facility location problem is still sparse, The proposed algorithm consists of two parts: in the first part branch and bound is used to generate a list of candidate solutions for each period and then dynamic programming is used to find the optimal sequence of configurations over the multi-period planning horizon. bounds commonly known in the location literature as delta and omega are used extensively to effectively reduce the total number of transshipment subproblems needed to be solved. The proposed algorithm is particularly effective when the facility reopening and closing costs are relatively significant in the multi-period problem. An example problem is included to illustrate the proposed solution procedure.
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