Perspective Reformulations of Semicontinuous Quadratically Constrained Quadratic Programs

2020 ◽  
Author(s):  
Xiaojin Zheng ◽  
Yutong Pan ◽  
Zhaolin Hu
Keyword(s):  
Lower Bounds ◽  
Branch And Bound ◽  
Strong Duality ◽  
Computational Experiments ◽  
Quadratic Programs ◽  
Branch And Bound Algorithms ◽  
Study Perspective ◽  
Lifting Techniques ◽  
Quadratically Constrained

We study perspective reformulations (PRs) of semicontinuous quadratically constrained quadratic programs (SQCQPs) in this paper. Based on perspective functions, we first propose a class of PRs for SQCQPs and discuss how to find the best PR in this class via strong duality and lifting techniques. We then study the properties of the PR class and relate them to alternative formulations that are used to derive lower bounds for SQCQPs. Finally, we embed the PR bounds in branch-and-bound algorithms and conduct computational experiments to illustrate the effectiveness of the proposed approach.

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.

A SIMPLE LOWER BOUND FOR TOTAL COMPLETION TIME MINIMIZATION IN A TWO-MACHINE FLOWSHOP

2005 ◽  
Vol 22 (03) ◽  
pp. 391-407 ◽  
Author(s):  
B. M. T. LIN ◽  
J. M. WU
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Completion Time ◽  
Computational Study ◽  
Total Completion Time ◽  
Optimal Solutions ◽  
Branch And Bound Algorithms ◽  
Time Minimization ◽  
Input Instance

The purpose of this study is to present a simple lower bound to facilitate the development of branch-and-bound algorithms for the minimization of total completion time in a two-machine flowshop. The studied problem is known to be strongly NP-hard. In the literature, several lower bounds have been proposed. The bounding technique addressed in this paper is based upon a concept about rearrangement of the parameters of the input instance. The technique is intrinsically simple for computer implementations. We conduct computational experiments for problems with 10–65 jobs. Numerical results from our computational study indicate that the new scheme is very effective in reducing the execution time needed for composing optimal solutions.

scholarly journals Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs

2017 ◽  
Vol 15 (1) ◽  
pp. 1212-1224 ◽  
Author(s):  
Zhisong Hou ◽  
Hongwei Jiao ◽  
Lei Cai ◽  
Chunyang Bai
Keyword(s):  
Branch And Bound ◽  
Computational Efficiency ◽  
Global Minimum ◽  
Quadratic Function ◽  
Numerical Results ◽  
Linear Programs ◽  
Quadratic Programs ◽  
New Variables ◽  
Quadratically Constrained ◽  
Methods Numerical

Abstract This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound framework without introducing any new variables and constrained functions, which can be easily solved by any effective linear programs algorithms. By subsequently solving a series of linear relaxed programs problems, the proposed algorithm can converge the global minimum of the initial quadratically constrained quadratic programs problem. Compared with the known methods, numerical results demonstrate that the proposed method has higher computational efficiency.

scholarly journals An optimal solution for the budgets assignment problem

2021 ◽  
Author(s):  
Mahdi Jemmali
Keyword(s):  
Experimental Study ◽  
Community Development ◽  
Lower Bounds ◽  
Branch And Bound ◽  
Optimal Solution ◽  
Service Organizations ◽  
Hard Problem ◽  
Branch And Bound Algorithms ◽  
Np Hard Problem ◽  
Developmental Role

Municipalities are service organizations that have a major role in strategic planning and community development that consider the future changes and society developments, by implementing set of projects with pre-allocated budgets. Projects have standards, budgets and constraints that differ from one community to another and from one city to another. Fair distributing of different projects to municipalities, while ensuring the provision of various capabilities to reach developmental role is NP-Hard problem. Assuming that all municipalities have the same strategic characteristics. The problem is as follows: given a set of projects with different budgets, how to distribute all projects to all municipalities with a minimum budget gap between municipalities. To derive equity distribution between municipalities, this paper developed lower bounds and eleven heuristics to be utilized in the branch-and-bound algorithms. The performance of the developed heuristics, lower bounds and the exact solutions are presented in the experimental study.

scholarly journals TEMPLATE REALIZATION OF GENERALIZED BRANCH AND BOUND ALGORITHM

2005 ◽  
Vol 10 (3) ◽  
pp. 217-236 ◽  
Author(s):  
M. Baravykaite ◽  
R. Čiegis ◽  
J. Žilinskas
Keyword(s):  
Global Optimization ◽  
Combinatorial Optimization ◽  
Branch And Bound ◽  
Optimization Algorithms ◽  
Optimization Methods ◽  
Branch And Bound Algorithm ◽  
Computational Experiments ◽  
Branch And Bound Algorithms ◽  
Parallel Branch And Bound

In this work we consider a template for implementation of parallel branch and bound algorithms. The main aim of this package to ease implementation of covering and combinatorial optimization methods for global optimization. Standard parts of global optimization algorithms are implemented in the package and only method specific rules should be implemented by the user. The parallelization part of the tool is described in details. Results of computational experiments are presented and discussed. Straipsnyje pristatyta apibendrinto šaku ir režiu algoritmo šablono realizacija. Irankis skirtas palengvinti nuosekliuju ir lygiagrečiuju optimizacijos uždaviniu programu kūrima. Nuo uždavinio nepriklausančios algoritmo dalys yra idiegtos šablone ir vartotojui reikia sukurti tik nuo uždavinio priklausančiu daliu realizacija. Šablone idiegti keli lygiagretieji algoritmai, paremti tyrimo srities padalinimu tarp procesoriu. Pateikiami skaičiavimo eksperimentu rezultatai.

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