Network For Programming Problems Research Articles

Noticeability Versus Impact in Traffic Signal Tampering

This paper investigates the vulnerability of urban traffic networks to cyber-attacks on traffic lights. We model traffic signal tampering as a bi-objective optimization problem that simultaneously seeks to reduce vehicular throughput in the network over time (maximize impact) while introducing minimal changes to network signal timings (minimize noticeability). We represent the Spatio-temporal traffic dynamics as a static network flow problem on a time-expanded graph. This allows us to reduce the (non-convex) attack problem to a tractable form, which can be solved using traditional techniques used to solve linear network programming problems. We show that minor but objective adjustments in the signal timings over time can severely impact traffic conditions at the network level. We investigate network vulnerability by examining the concavity of the Pareto-optimal frontier obtained by solving the bi-objective attack problem. Numerical experiments are carried to illustrate the types of insights that can be extracted from the Pareto-optimal frontier. For instance, our experiments suggest that the vulnerability of a traffic network to signal tampering is independent of the demand levels.

Optimizing the Pilot Testing of ERP Systems

In the creation of ERP systems, it is important to plan the pilot testing. In pilot projects (also known as experimental projects), the main functions of the system are tested by a limited set of advanced users. In planning the pilot testing, the key is to determine its extent. With too little testing, fundamental functions of the system may not be checked, and the probability of detecting significant errors only at complete rollout will be high. With excessive testing, the work required in the pilot project will be considerably increased, and the required speed and flexibility will not be attained in testing the basic functions. The effectiveness of pilot testing will be no better than the effectiveness of full-scale introduction. A mathematical formulation of the determination of the optimal extent of pilot testing is developed on the basis of the generation of a portfolio of IT services and their scheduling in the creation of the ERP system for a large steel company. The solution of this problem takes the form of a set of services that must be verified and the relations between them, within the specified constraint on the resources devoted to testing, such that optimal results are obtained. The solution is obtained by network programming, based on a structurally similar network representation of the relevant criteria and constraints. A solution procedure is outlined, along with an example of its use. In this procedure, dichotomous programming is used to solve individual problems. The approximate solutions obtained may be improved by solving a double network-programming problem. The branch and bound method may be used to find the global optimum of the initial problem. In that approach, the boundaries are values of the target functions for the approximate solutions. Generalization of this problem is based on the preferences of IT-service users regarding the quality of verification of different relations between the services. Those preferences may be taken into account by weighting the corresponding relationships. That leaves the basic solution procedure unchanged.

ABOUT ONE INVERSE PROBLEM OF THE LINEAR-FRACTIONAL PROGRAMMING ON GENERALIZED NETWORK

For the one linear-fractional network programming problem with additional constraints of general kind and with inexact data we constructed a mathematical model for calculation of the new parameters of the restrictions for which the infeasible solution becomes feasible solution. For the selected feasible solution of this problem we minimally changed the parameters in the numerator of the linear-fractional objective function in order that the selected feasible solution has become an optimal. The measure proximity vectors estimated are using the norm l1. That has allowed to remain within the framework of linear programming in solving of inverse problems.

Combination of genetic network programming and knapsack problem to support record clustering on distributed databases

This research involves implementation of genetic network programming (GNP) and standard dynamic programming to solve the knapsack problem (KP) as a decision support system for record clustering in distributed databases. Fragment allocation with storage capacity limitation problem is a background of the proposed method. The problem of storage capacity is to distribute sets of fragments into several sites (clusters). Total amount of fragments in each site must not exceed the capacity of site, while the distribution process must keep the relation (similarity) between fragments within each site. The objective is to distribute big data to certain sites with the limited amount of capacities by considering the similarity of distributed data in each site. To solve this problem, GNP is used to extract rules from big data by considering characteristics (value ranges) of each attribute in a dataset. The proposed method also provides partial random rule extraction method in GNP to discover frequent patterns in a database for improving the clustering algorithm, especially for large data problems. The concept of KP is applied to the storage capacity problem and standard dynamic programming is used to distribute rules to each site by considering similarity (value) and data amount (weight) related to each rule to match the site capacities. From the simulation results, it is clarified that the proposed method shows some advantages over the conventional clustering algorithms, therefore, the proposed method provides a new clustering method with an additional storage capacity problem.

A branch‐and‐bound algorithm for representative integer efficient solutions in multiple objective network programming problems

AbstractIn many applications of multiple objective network programming (MONP) problems, only integer solutions are acceptable as the final optimal solution. Representative efficient solutions are usually obtained by sampling the efficient set through the solution of augmented weighted Tchebycheff network programs. Because such efficient solutions are usually not integer solutions, a branch‐and‐bound (BB) algorithm is developed to find integer efficient solutions. The purpose of the BB algorithm is to support interactive procedures by generating representative integer efficient solutions. To be computationally efficient, the algorithm takes advantage of the network structure as much as possible. An algorithm, used in the BB algorithm and performed on the key tree, is developed to construct feasible solutions from infeasible solutions and basic solutions from nonbasic solutions when bounds on branching variables change. The BB algorithm finds basic and nonbasic or supported and unsupported integer efficient solutions as long as they are optimal. Details of the algorithm are presented, an example is provided and computational results are reported. Computational results show that the BB algorithm performs well. Although the BB algorithm is developed for the purpose of generating integer efficient solutions for MONP problems, it can also solve more general integer network flow problems with linear side constraints. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013

Reliability-aware Algorithms of Multipoint Relay with Application Analysis in the Flooding Broadcast of Link-16

The multipoint relay (MPR) flooding broadcast in Link-16 is a multi-objective network programming problem with multi-constraints. Trying to obtain the fewest nodes in MPR set and the maximum reliability is seldom considered in existing flooding broadcast algorithms under the multiple QoS (Quality of Service) constraints. According to the different objectives considered preferentially, two reliability-aware heuristic algorithms of flooding broadcast RA-MPR-N and RA-MPR-R are proposed in this paper. Comparing with the paired-slot flooding relay, RA-MPR-N selects as few neighbor nodes as possible to cover all two-hop nodes, while RA-MPR-R guarantees the maximum reliability. Both theoretical analysis and simulation show that the number of nodes in MPR set obtained by RA-MPR-N and the average reliability obtained by RA-MPR-R are satisfactory.

Finding integer efficient solutions for multiple objective network programming problems

For many practical multiple objective network programming (MONP) problems, only integer solutions are meaningful and acceptable. Representative efficient solutions are usually generated by solving augmented weighted Tchebycheff network programs (AWTNPs), sub-problems derived from MONP problems. However, efficient solutions generated this way are usually not integer valued. In this study, two algorithms are developed to construct integer efficient solutions starting from fractional efficient solutions. One algorithm finds a single integer efficient solution in the neighborhood of the fractional efficient solution. The other enumerates all integer efficient solutions in the same neighborhood. Theory supporting the proposed algorithms is developed. Two detailed examples are presented to demonstrate the algorithms. Computational results are reported. The best integer efficient solution is very close, if not equal, to the integer optimal solution. The CPU time taken to find integer efficient solutions is negligible, when compared with that taken to solve AWTNPs. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 57(4), 362-375 2011

Warm-Start Routines for Solving Augmented Weighted Tchebycheff Network Programs in Multiple-Objective Network Programming

Three warm-start routines are developed to find initial basic feasible solutions for augmented weighted Tchebycheff network programs, subproblems derived from multiple-objective network-programming problems. In an interactive solution procedure, a series of augmented weighted Tchebycheff network programs need to be solved sequentially to find representative nondominated solutions. To speed up the solution process using the network structure of the problem, these warm-start routines start the solution process of one augmented weighted Tchebycheff network program from the optimal solution of the previous one. All three warm-start routines use the same strategy but different ways of reducing the number of basic flow variables, or equivalently increasing the number of basic nonflow variables to construct a basic solution. These warm-start routines can be used by any interactive procedures to facilitate the solution process of multiple-objective network-programming problems. A detailed example is presented. A computational experiment is conducted to compare the performance of these warm-start routines. A cold-start routine and NETSIDE, specialized software for solving network problems with side constraints, are also used as references in the experiment. These warm-start routines can save substantial computation time.

Procedures for Finding Nondominated Solutions for Multiple Objective Network Programming Problems

Procedures for finding nondominated solutions for multiple objective network programming problems are developed and tested. Nondominated solutions are obtained by solving augmented weighted Tchebycheff network programs. The procedures exploit the network structure of the problem in order to speed up the solution process. To use the network structure as much as possible, a weighted-sum network problem and/or a min-max network problem are solved in order to find a basic solution that is close to the optimal solution of the augmented weighted Tchebycheff network program. Starting from this basic solution, the special simplex method for network problems with side constraints is finally applied to solve the augmented weighted Tchebycheff network program. Computational results show that, for the test problems used in this study, up to 70% of computation time can be saved with the proposed procedures as compared with the sole application of the special simplex method for network problems with side constraints. These procedures can be incorporated into any interactive multiple-objective programming procedure which uses sample nondominated solutions to solve multiple-objective network programming problems.

Introduction to the IBM Optimization Subroutine Library

This essay introduces the IBM Optimization Subroutine Library (OSL) and seven OSL-related papers that appear in this issue. Developed as a result of a partnership between several IBM research and development groups, OSL provides a suite of tools for manipulating the models and solving the resulting minimization and maximization problems of mathematical optimization. The problems that OSL addresses include: linear, quadratic, mixed-integer, and pure network programming problems. OSL includes solvers based on the classical simplex method and on newer interior point methods. Because a user-supplied driver program coordinates the problem solution, and because of the “mix and match” philosophy of OSL, a user may, within rather wide limits, individually tailor a technique to solve a particular problem. We conclude that OSL is something new in optimization software.

An algorithm for solving quadratic network flow problems

We describe a new algorithm for solving separable quadratic cost network programming problems and compare its performance with that of the convex simplex methodfor networks.

Structure of the submarking-reachability problem and network programming

Using a linear programming formulation, a unified treatment of the submarking-reachability problem for both capacitated and uncapacitated marked graphs is presented. In both cases, the problem reduces to that of testing feasibility of the dual transshipment problem of operations research. An algorithm called REACH is presented for the feasibility testing problem; its worst-case time complexity is O(mn), where m and n are, respectively, the number of edges and the number of nodes in the marked graph. The place of this work in the context of general network programming problems is indicated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Complexity of some parametric integer and network programming problems

Two examples of parametric cost programming problems—one in network programming and one in NP-hard 0-1 programming—are given; in each case, the number of breakpoints in the optimal cost curve is exponential in the square root of the number of variables in the problem.

Distributed Solution of Network Programming Problems

A method is presented for the solution of network programming problems through the iterative execution of the same algorithm for each station of the network. At a given station, the algorithm requires data only from adjacent stations of the network. The theory of the method is developed through the use of electrical models of network programming problems. The techniques should be useful for the communications message-routing problem and similar cases in which the disadvantages of relying on a computation performed at a master station must be avoided.

Letter to the Editor—On An Algorithm for Solving Some Network-Programming Problems

The purpose of this note is to call to the attention of the readers of this journal a unified algorithm (essentially, a modification and extension of the Ford-Fulkerson algorithm) for solving a class of minimization problems.