Boolean Linear Programming Problems Research Articles

Пошук максимальних незалежних множин вершин графа для вдосконалення програмних проєктів

The need is fixed to software project enhancing with seamless integration of technological-descriptive and normative project manage- ment approaches by means of classical Graph Discrete Optimization Problems tailoring for software project management tasks, poorly equipped with best practices within technological approach. Class of software project management tasks is proposed to demonstrate the benefits of such integration. Two Boolean linear programming problems are investigated for searching some maximum size indepen- dent set (Section 1) and an algorithm for searching all possible maximum size independent sets (Section 2). Section 3 presents Problem Statement for searching a given number of non-intersecting independent sets with maximum sum of vertices’ numbers within independent sets. Based on it, Vizing-Plesnevich algorithm is described for coloring the graph vertices with the minimum number of colors. To solve Boolean problems, both specialized mathematical programming language AMPL and corresponding solver program named gu- robi are used. For basic algorithms developed, reference AMPL code versions are given as well as their running results. Illustrative examples of software project enhancing with the algorithms elaborated are considered in Section 4, namely: 25 specialists being conflicted during their previous projects partitioning into coherent conflict-free sub-teams for software projects portfolio; schedule optimization for autonomous testing of reusable components within a critical software system; cores composing for independent teams in a critical software project.

Stability measure of multicriteria integer linear programming problem with a parametric optimality principle

In this paper, we consider a multicriteria integer linear programming problem with a parametric principle of optimality. Parameterization is realized by dividing the set of criteria into several disjoint groups (subsets) of criteria ordered by importance, with Pareto dominance within each group. The introduced parametric principle of optimality made it possible to connect such classical principles of optimality as lexicographic and Pareto ones. For the stability radius, which is the limiting level of perturbations of the parameters of the problem, not causing the appearance of new optimal solutions, the upper and lower estimations are obtained in the case of arbitrary Hölder’s norms in the criterion space and solution space. Some previously known results on the stability of the Boolean linear programming problem are formulated as corollaries.

Eature selection in regression models estimated by OLS as a partial boolean linear programming problem: computational experiments

Eature selection in regression models estimated by OLS as a partial boolean linear programming problem: computational experiments

Scheduling and Power Control for V2V Broadcast Communications With Co-Channel and Adjacent Channel Interference

This paper investigates how to mitigate the impact of both co-channel interference and adjacent channel interference (ACI) on vehicle-to-vehicle (V2V) broadcast communication by scheduling and power control. The optimal joint scheduling and power control problem, with the objective to maximize the number of connected vehicles, is formulated as a mixed integer programming problem with a linear objective and a quadratic constraint. From the joint formulation, we derive (a) the optimal scheduling problem for fixed transmit powers as a Boolean linear programming problem and (b) the optimal power control problem for a fixed schedule as a mixed integer linear programming problem. Optimal schedules and power values can, for smaller-size instances of the problem, be computed by solving first (a) and then (b). To handle larger-size instances of the problem, we propose heuristic scheduling and power control algorithms with reduced computational complexity. Simulation results indicate that the heuristic scheduling algorithm yields significant performance improvements compared to the baseline block-interleaver scheduler and that performance is further improved by the heuristic power control algorithm. Moreover, the heuristic algorithms perform close to the optimal scheme for small instances of the problem.

Modeling Local Scheduler Operation Based on Solution of Nonlinear Boolean Programming Problems

A simulation model of grid system operation is considered, which allows comparing available job scheduling methods. The mathematical description of the characteristics analyzed in the model is given. An example of problem solution based on sample group method is presented. The experimental results are obtained, which demonstrate the advantages of scheduling method based on the solution of Boolean linear programming problems.

Problem Statements for k-Node Shortest Path and k-Node Shortest Cycle in a Complete Graph*

The author formulates mixed Boolean linear programming problems to find the shortest route and the shortest cycle that pass through the given number of nodes in a complete graph. Their special cases provide formulations of problems for finding the shortest Hamiltonian path and the shortest Hamiltonian cycle. The problems include no more than 2n2 variables and no more than (n + 1)2 constraints, where n is the number of nodes of the complete graph.

Bilevel competitive facility location and pricing problems

We propose new models for competitive facility location and pricing as bilevel Boolean linear programming problems. We obtain results that characterize the complexity of the problem where a monopolist's profit on each of the markets is defined with a monotone nonincreasing function of the servicing cost. For this problem, we also propose two approximate algorithms based on the ideas of alternating heuristics and local search. We give results of a computational experiment that show a possibility for fast computation of approximate solutions.

Optimal recombination in genetic algorithms for combinatorial optimization problems: Part I

This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We consider efficient reductions of the ORPs, allowing to establish polynomial solvability or NP-hardness of the ORPs, as well as direct proofs of hardness results. Part I presents the basic principles of optimal recombination with a survey of results on Boolean Linear Programming Problems. Part II (to appear in a subsequent issue) is devoted to the ORPs for problems which are naturally formulated in terms of search for an optimal permutation.

Stability and accuracy functions for a multicriteria Boolean linear programming problem with parameterized principle of optimality “from Condorcet to Pareto”

A multicriteria Boolean programming problem with linear cost functions in which initial coefficients of the cost functions are subject to perturbations is considered. For any optimal alternative, with respect to parameterized principle of optimality “from Condorcet to Pareto”, appropriate measures of the quality are introduced. These measures correspond to the so-called stability and accuracy functions defined earlier for optimal solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an optimal alternative preserves its optimality are calculated. To illustrate the way how the stability and accuracy functions can be used as efficient tools for post-optimal analysis, an application from the voting theory is considered.

On Complexity of Optimal Recombination for Binary Representations of Solutions

We consider the optimization problem of finding the best possible offspring as a result of a recombination operator in an evolutionary algorithm, given two parent solutions. The optimal recombination is studied in the case where a vector of binary variables is used as a solution encoding. By means of efficient reductions of the optimal recombination problems (ORPs) we show the polynomial solvability of the ORPs for the maximum weight set packing problem, the minimum weight set partition problem, and for linear Boolean programming problems with at most two variables per inequality, and some other problems. We also identify several NP-hard cases of optimal recombination: the Boolean linear programming problems with three variables per inequality, the knapsack, the set covering, the p-median, and some other problems.

Fuzzy boolean programming problems with fuzzy costs: A general study

This paper deals with boolean linear programming problems involving coefficients in the objective function as fuzzy numbers. In the study of these problems different approaches can be proposed to use ranking fuzzy numbers methods and fuzzy preference relations obtaining auxiliary classical boolean programming problems, and to use the representation theorem obtaining a convex set with extreme points defined by the lower or upper bound of the a-level sets of the fuzzy coefficients, and consequently an auxiliary interval boolean programming problem. In this paper we develop and link the different approaches.

Boolean programming problems with fuzzy constraints

Abstract Boolean linear programming problems for which there exist some lack of precision of vague nature in the constraints are considered. An α-cut-based approach is considered to solve them. Then, an algorithm providing a fuzzy solution is proposed and analyzed. The linking with other known solution methods is also studied.

Weakly determinate problems of Boolean linear programming with a partially specified set of admissible solutions

Weakly determinate problems of Boolean programming comprise those in which the objective function or set of admissible solutions is partially but not completely specified. Using the properties of the monotonic Boolean functions which correspond to the constraints of the Boolean linear programming problems, an approach is given for constructing a complete definition of the partially specified set of admissible solutions, and for finding the optimal solutions in the completed definition. To check that the solutions obtained are admissible, a recognition algorithm for the class of admissible solutions is employed.

Stability of solutions in problems of Boolean linear programming

Bounds on the variation of the input parameters that preserve uniqueness of the optimal solution of the Boolean linear programming problems are determined.

An approach to the construction of approximate solutions of Boolean linear programming problems

An approach to the construction of approximate solutions of Boolean linear programming problems

A computer algorithm for the optimization of discrete-time pulse frequency modulated systems

A computer algorithm is described for the optimization of discrete-time pulse frequency modulated systems with state and control constraints. The algorithm, based on a modified maximum principle [1], leads to the solution of a Boolean linear programming problem, for which many computer codes are available commercially. An application to a time-shared sampled-data control system is presented. Numerical examples are given.