scholarly journals A Branch-and-Bound Algorithm for Polymatrix Games ϵ-Proper Nash Equilibria Computation

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 365
Author(s):  
Slim Belhaiza
Keyword(s):  
Branch And Bound ◽  
Nash Equilibria ◽  
Decision Makers ◽  
Experimental Results ◽  
Branch And Bound Algorithm ◽  
Linear Programs ◽  
Polymatrix Games

When several Nash equilibria exist in the game, decision-makers need to refine their choices based on some refinement concepts. To this aim, the notion of a ϵ-proper equilibria set for polymatrix games is used to develop 0–1 mixed linear programs and compute ϵ-proper Nash equilibria. A Branch-and-Bound exact arithmetics algorithm is proposed. Experimental results are provided on polymatrix games randomly generated with different sizes and densities.

Two-Agent Advertisement Scheduling on Physical Books to Maximize the Total Profit

2019 ◽  
Vol 36 (03) ◽  
pp. 1950014 ◽  
Author(s):  
Kuen-Fang Jea ◽  
Jen-Ya Wang ◽  
Chih-Wei Hsu
Keyword(s):  
Branch And Bound ◽  
Upper Bound ◽  
Execution Time ◽  
Harry Potter ◽  
Experimental Results ◽  
Branch And Bound Algorithm ◽  
Scheduling Problem ◽  
Online Search ◽  
Dragon’S Blood ◽  
Total Profit

Most of us may have had the experience of forgetting some term from a physical book when the term appears in neither the table of contents nor the index. Unfortunately, we must search for it page by page. In one edition of the popular physical book “Harry Potter and the Sorcerer’s Stone”, for example, the term “dragon’s blood” only appears on pages 81 and 175, so browsing through the whole book to find it would be inevitable. In this study, a mechanism is provided to carry out an online search on physical books. To financially support this mechanism, we can put online advertisements with different offers on these physical books. An advertisement scheduling problem (ASP) is therefore formulated to maximize the total profit. To obtain the optimal schedules, we propose a branch-and-bound algorithm equipped with an upper bound. Experimental results show that the proposed upper bound performs well and completes the search in only 4% of the execution time of an ordinary branch-and-bound algorithm.

scholarly journals A Novel Optimization Method for Nonconvex Quadratically Constrained Quadratic Programs

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Hongwei Jiao ◽  
Yong-Qiang Chen ◽  
Wei-Xin Cheng
Keyword(s):  
Branch And Bound ◽  
Computational Efficiency ◽  
Numerical Experiments ◽  
Optimization Method ◽  
Global Optimum ◽  
Branch And Bound Algorithm ◽  
Linear Programs ◽  
Quadratic Programs ◽  
Optimum Point ◽  
Quadratically Constrained

This paper presents a novel optimization method for effectively solving nonconvex quadratically constrained quadratic programs (NQCQP) problem. By applying a novel parametric linearizing approach, the initial NQCQP problem and its subproblems can be transformed into a sequence of parametric linear programs relaxation problems. To enhance the computational efficiency of the presented algorithm, a cutting down approach is combined in the branch and bound algorithm. By computing a series of parametric linear programs problems, the presented algorithm converges to the global optimum point of the NQCQP problem. At last, numerical experiments demonstrate the performance and computational superiority of the presented algorithm.

scholarly journals Linear programs with an additional separable concave constraint

2004 ◽  
Vol 8 (3) ◽  
pp. 155-174 ◽  
Author(s):  
Takahito Kuno ◽  
Jianming Shi
Keyword(s):  
Local Search ◽  
Branch And Bound ◽  
Special Class ◽  
Concave Function ◽  
Concave Minimization ◽  
Simplex Algorithm ◽  
Direct Application ◽  
Special Structure ◽  
Branch And Bound Algorithm ◽  
Linear Programs

In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland's branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we solve the problem alternating local search and branch-and-bound. In the indirect application, we carry out the bounding operation using a parametric right-hand-side simplex algorithm.

A BRANCH-AND-BOUND ALGORITHM FOR FINDING ALL OPTIMAL SOLUTIONS OF THE ASSIGNMENT PROBLEM

2007 ◽  
Vol 24 (06) ◽  
pp. 831-839 ◽  
Author(s):  
ZHUO FU ◽  
RICHARD EGLESE ◽  
MIKE WRIGHT
Keyword(s):  
Decision Making ◽  
Branch And Bound ◽  
Assignment Problem ◽  
Experimental Results ◽  
Branch And Bound Algorithm ◽  
Optimization Models ◽  
Component Part ◽  
Optimal Solutions ◽  
Linear Assignment Problem ◽  
Linear Assignment

Alternative optimal solutions can give more choice for practical decision making. Therefore, the provision of methods for finding alternative optimal solutions is an important component part of the solution techniques for optimization models. The aim of this paper is to present a branch-and-bound algorithm for finding all optimal solutions of the linear assignment problem. Numerical experimental results are also given.

DO INHERENTLY SEQUENTIAL BRANCH-AND-BOUND ALGORITHMS EXIST?

1994 ◽  
Vol 04 (01n02) ◽  
pp. 3-13 ◽  
Author(s):  
JENS CLAUSEN ◽  
JESPER LARSSON TRÄFF
Keyword(s):  
Branch And Bound ◽  
Graph Partitioning ◽  
Optimization Problems ◽  
Parallel Implementation ◽  
Meaningful Work ◽  
Experimental Results ◽  
Branch And Bound Algorithm ◽  
Branch And Bound Algorithms ◽  
Graph Partitioning Problem ◽  
Partitioning Problem

In the construction of algorithms for [Formula: see text] optimization problems the Branch-and-Bound paradigm is an essential tool. Furthermore, Branch-and-Bound algorithms are traditionally regarded as well suited for parallel implementation due to the subdivision of the problem considered into essentially independent subproblems. In this paper we present experimental results for a Branch-and-Bound algorithm for the Graph Partitioning Problem showing that the traditional parallelization of a Branch-and-Bound algorithm does not always lead to an efficient parallel algorithm. The main reason seems to be lack of meaningful work, i.e. concurrent existence of subproblems which have to be solved to ensure optimality of the solution. We support this claim with experimental results.

Unit Commitment Solution by Branch and Bound Algorithm

2020 ◽  
Author(s):  
Bishaljit Paul ◽  
Sushovan Goswami ◽  
Dipu Mistry ◽  
Chandan Kumar Chanda
Keyword(s):  
Branch And Bound ◽  
Unit Commitment ◽  
Branch And Bound Algorithm

scholarly journals Identification of mechanical properties of arteries with certification of global optimality

2021 ◽  
Author(s):  
Jan-Lucas Gade ◽  
Carl-Johan Thore ◽  
Jonas Stålhand
Keyword(s):  
Global Solution ◽  
Branch And Bound ◽  
Clinical Data ◽  
Minimization Problem ◽  
Branch And Bound Algorithm ◽  
Stationary Points ◽  
Model Parameters ◽  
Global Optimality ◽  
Clinical Value ◽  
Non Linear

AbstractIn this study, we consider identification of parameters in a non-linear continuum-mechanical model of arteries by fitting the models response to clinical data. The fitting of the model is formulated as a constrained non-linear, non-convex least-squares minimization problem. The model parameters are directly related to the underlying physiology of arteries, and correctly identified they can be of great clinical value. The non-convexity of the minimization problem implies that incorrect parameter values, corresponding to local minima or stationary points may be found, however. Therefore, we investigate the feasibility of using a branch-and-bound algorithm to identify the parameters to global optimality. The algorithm is tested on three clinical data sets, in each case using four increasingly larger regions around a candidate global solution in the parameter space. In all cases, the candidate global solution is found already in the initialization phase when solving the original non-convex minimization problem from multiple starting points, and the remaining time is spent on increasing the lower bound on the optimal value. Although the branch-and-bound algorithm is parallelized, the overall procedure is in general very time-consuming.

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