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.

scholarly journals A Lagrange Relaxation Method for Solving Weapon-Target Assignment Problem

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Mingfang Ni ◽  
Zhanke Yu ◽  
Feng Ma ◽  
Xinrong Wu
Keyword(s):  
Operations Research ◽  
Relaxation Method ◽  
Nonlinear Integer Programming ◽  
Heuristic Methods ◽  
Integer Programming Problem ◽  
Optimal Solutions ◽  
Lagrange Relaxation ◽  
Relaxation Problem ◽  
Target Assignment ◽  
Np Complete

We study the weapon-target assignment (WTA) problem which has wide applications in the area of defense-related operations research. This problem calls for finding a proper assignment of weapons to targets such that the total expected damaged value of the targets to be maximized. The WTA problem can be formulated as a nonlinear integer programming problem which is known to be NP-complete. There does not exist any exact method for the WTA problem even small size problems, although several heuristic methods have been proposed. In this paper, Lagrange relaxation method is proposed for the WTA problem. The method is an iterative approach which is to decompose the Lagrange relaxation into two subproblems, and each subproblem can be easy to solve to optimality based on its specific features. Then, we use the optimal solutions of the two subproblems to update Lagrange multipliers and solve the Lagrange relaxation problem iteratively. Our computational efforts signify that the proposed method is very effective and can find high quality solutions for the WTA problem in reasonable amount of time.

A Hybrid Approach of Heuristic and Neural Network for Packing Problems

1994 ◽  
Author(s):  
Zuo Dai ◽  
Jianzhong Cha
Keyword(s):  
Neural Network ◽  
Large Scale ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Hybrid Approach ◽  
Two Dimensions ◽  
Packing Problems ◽  
Combinatorial Optimization Problems ◽  
Complete Problems ◽  
Np Complete

Abstract Artificial Neural Networks, particularly the Hopfield-Tank network, have been effectively applied to the solution of a variety of tasks formulated as large scale combinatorial optimization problems, such as Travelling Salesman Problem and N Queens Problem [1]. The problem of optimally packing a set of geometries into a space with finite dimensions arises frequently in many applications and is far difficult than general NP-complete problems listed in [2]. Until now within accepted time limit, it can only be solved with heuristic methods for very simple cases (e.g. 2D layout). In this paper we propose a heuristic-based Hopfield neural network designed to solve the rectangular packing problems in two dimensions, which is still NP-complete [3]. By comparing the adequacy and efficiency of the results with that obtained by several other exact and heuristic approaches, it has been concluded that the proposed method has great potential in solving 2D packing problems.

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 Estimates of objective function minimum for solving linear fractional unconstrained combinatorial optimization problems on arrangements

2021 ◽  
pp. 32-36
Author(s):  
Tetiana Barbolina
Keyword(s):  
Combinatorial Optimization ◽  
Objective Function ◽  
Numerical Experiments ◽  
Polynomial Algorithm ◽  
Optimization Problems ◽  
Finite Sequence ◽  
Feasible Set ◽  
Combinatorial Optimization Problems ◽  
Unconstrained Problems

The paper is devoted to the study of one class of Euclidean combinatorial optimization problems — combinatorial optimization problems on the general set of arrangements with linear fractional objective function and without additional (non-combinatorial) constraints. The paper substantiates the improvement of the polynomial algorithm for solving the specified class of problems. This algorithm foresees solving a finite sequence of linear unconstrained problems of combinatorial optimization on arrangements. The modification of the algorithm is based on the use of estimates of the objective function on the feasible set. This allows to exclude some of the problems from consideration and reduce the number of problems to be solved. The numerical experiments confirm the practical efficiency of the proposed approach.

Multi-objective parameter optimization of the HYPE model using shuffled frog-leaping algorithm

2021 ◽  
Author(s):  
Xinyu Li ◽  
Prajna Kasargodu Anebgailu ◽  
Jörg Dietrich
Keyword(s):  
Optimization Problems ◽  
Population Based ◽  
Optimization Techniques ◽  
Model Parameters ◽  
Hydrological Models ◽  
Watershed Model ◽  
Shuffled Frog Leaping Algorithm ◽  
Multi Objective ◽  
Combinatorial Optimization Problems ◽  
Shuffled Frog Leaping

<p>The calibration of hydrological models using bio-inspired meta-heuristic optimization techniques has been extensively tested to find the optimal parameters for hydrological models. Shuffled frog-leaping algorithm (SFLA) is a population-based cooperative search technique containing virtual interactive frogs distributed into multiple memeplexes. The frogs search locally in each memeplex and are periodically shuffled into new memeplexes to ensure global exploration. Though it is developed for discrete optimization, it can be used to solve multi-objective combinatorial optimization problems as well.</p><p>In this study, a hydrological catchment model, Hydrological Predictions for the Environment (HYPE) is calibrated for streamflow and nitrate concentration in the catchment using SFLA. HYPE is a semi-distributed watershed model that simulates runoff and other hydrological processes based on physical as well as conceptual laws. SFLA with 200 runtimes and 5 memeplexes containing 10 frogs each is used to calibrate 22 model parameters. It is compared with manual calibration and Differential Evolution Markov Chain (DEMC) method from the HYPE-tool. The preliminary results of the statistical performance measures for streamflow calibration show that SFLA has the fastest convergence speed and higher stability when compared with the DEMC method. NSE of 0.68 and PBIAS of 7.72 are recorded for the best run of SFLA during the calibration of streamflow. In comparison, the HYPE-tool DEMC produced the best NSE of 0.45 and a PBIAS of -3.37 while the manual calibration resulted in NSE of 0.64 and PBIAS of 2.01.</p>

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.

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