scholarly journals Identifying a Global Optimizer with Filled Function for Nonlinear Integer Programming

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Wei-Xiang Wang ◽  
You-Lin Shang ◽  
Lian-Sheng Zhang
Keyword(s):  
Integer Programming ◽  
Initial Point ◽  
Local Minimizer ◽  
Nonlinear Integer Programming ◽  
Test Problems ◽  
Integer Programming Problem ◽  
Filled Function ◽  
Global Optimizer ◽  
Filling Phase ◽  
Two Phases

This paper presents a filled function method for finding a global optimizer of integer programming problem. The method contains two phases: the local minimization phase and the filling phase. The goal of the former phase is to identify a local minimizer of the objective function, while the filling phase aims to search for a better initial point for the first phase with the aid of the filled function. A two-parameter filled function is proposed, and its properties are investigated. A corresponding filled function algorithm is established. Numerical experiments on several test problems are performed, and preliminary computational results are reported.

scholarly journals Global Minimization of Nonsmooth Constrained Global Optimization with Filled Function

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Wei-xiang Wang ◽  
You-lin Shang ◽  
Ying Zhang
Keyword(s):  
Original Problem ◽  
Initial Point ◽  
Solution Algorithm ◽  
Global Minimization ◽  
Second Phase ◽  
Constrained Global Optimization ◽  
Filled Function ◽  
Minimization Problems ◽  
Global Optimizer ◽  
Two Phases

A novel filled function is constructed to locate a global optimizer or an approximate global optimizer of smooth or nonsmooth constrained global minimization problems. The constructed filled function contains only one parameter which can be easily adjusted during the minimization. The theoretical properties of the filled function are discussed and a corresponding solution algorithm is proposed. The solution algorithm comprises two phases: local minimization and filling. The first phase minimizes the original problem and obtains one of its local optimizers, while the second phase minimizes the constructed filled function and identifies a better initial point for the first phase. Some preliminary numerical results are also reported.

scholarly journals Planning of Aircraft Fleet Maintenance Teams

Aerospace ◽  
2021 ◽  
Vol 8 (5) ◽  
pp. 140
Author(s):  
Duarte P. Pereira ◽  
Isaias L. R. Gomes ◽  
Rui Melicio ◽  
Victor M. F. Mendes
Keyword(s):  
Information System ◽  
Integer Programming ◽  
Positive Integer ◽  
Programming Problem ◽  
Nonlinear Integer Programming ◽  
Mathematical Programming Problem ◽  
Aircraft Maintenance ◽  
Integer Programming Problem ◽  
Integer Variables ◽  
Support Information

This paper addresses a support information system for the planning of aircraft maintenance teams, assisting maintenance managers in delivering an aircraft on time. The developed planning of aircraft maintenance teams is a computer application based on a mathematical programming problem written as a minimization one. The initial decision variables are positive integer variables specifying the allocation of available technicians by skills to maintenance teams. The objective function is a nonlinear function balancing the time spent and costs incurred with aircraft fleet maintenance. The data involve technicians’ skills, hours of work to perform maintenance tasks, costs related to facilities, and the aircraft downtime cost. The realism of this planning entails random possibilities associated with maintenance workload data, and the inference by a procedure of Monte Carlo simulation provides a proper set of workloads, instead of going through all the possibilities. The based formalization is a nonlinear integer programming problem, converted into an equivalent pure linear integer programming problem, using a transformation from initial positive integer variables to Boolean ones. A case study addresses the use of this support information system to plan a team for aircraft maintenance of three lines under the uncertainty of workloads, and a discussion of results shows the serviceableness of the proposed support information system.

scholarly journals A filled function method for constrained nonlinear integer programming

2008 ◽  
Vol 4 (2) ◽  
pp. 353-362 ◽  
Author(s):  
Yongjian Yang ◽  
◽  
Zhiyou Wu ◽  
Fusheng Bai ◽  
◽  
...  
Keyword(s):  
Integer Programming ◽  
Function Method ◽  
Nonlinear Integer Programming ◽  
Filled Function ◽  
Filled Function Method

scholarly journals Weapon Target Assignment

2021 ◽  
Author(s):  
Mohammad Babul Hasan ◽  
Yaindrila Barua
Keyword(s):  
Integer Programming ◽  
Objective Function ◽  
Optimization Problems ◽  
Optimization Techniques ◽  
Nonlinear Integer Programming ◽  
Integer Programming Problem ◽  
Combinatorial Optimization Problems ◽  
Target Assignment ◽  
Minimum Number ◽  
Np Complete

This chapter is mainly based on an important sector of operation research-weapon’s assignment (WTA) problem which is a well-known application of optimization techniques. While we discuss about WTA, we need some common terms to be discussed first. In this section, we first introduce WTA problem and then we present some prerequisites such as optimization model, its classification, LP, NLP, SP and their classifications, and applications of SP. We also discuss some relevant software tools we use to optimize the problems. The weapon target assignment problem (WTA) is a class of combinatorial optimization problems present in the fields of optimization and operations research. It consists of finding an optimal assignment of a set of weapons of various types to a set of targets in order to maximize the total expected damage done to the opponent. The WTA problem can be formulated as a nonlinear integer programming problem and is known to be NP-complete. There are constraints on weapons available of various types and on the minimum number of weapons by type to be assigned to various targets. The constraints are linear, and the objective function is nonlinear. The objective function is formulated in terms of probability of damage of various targets weighted by their military value.

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