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.

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.

Genetic Algorithm and Other Meta-Heuristics

2005 ◽  
pp. 144-173 ◽  
Author(s):  
Bernard K.S. Cheung
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Schema Theory ◽  
Heuristic Methods ◽  
Optimal Solutions ◽  
Corporate Globalization ◽  
Global Optimal ◽  
Mutation And Selection

Genetic algorithms have been applied in solving various types of large-scale, NP-hard optimization problems. Many researchers have been investigating its global convergence properties using Schema Theory, Markov Chain, etc. A more realistic approach, however, is to estimate the probability of success in finding the global optimal solution within a prescribed number of generations under some function landscapes. Further investigation reveals that its inherent weaknesses that affect its performance can be remedied, while its efficiency can be significantly enhanced through the design of an adaptive scheme that integrates the crossover, mutation and selection operations. The advance of Information Technology and the extensive corporate globalization create great challenges for the solution of modern supply chain models that become more and more complex and size formidable. Meta-heuristic methods have to be employed to obtain near optimal solutions. Recently, a genetic algorithm has been reported to solve these problems satisfactorily and there are reasons for this.

Towards Efficient Bounds on Completion Time and Resource Provisioning for Scheduling Workflows on Heterogeneous Processing Systems

2017 ◽  
Vol 9 (3) ◽  
pp. 60-82 ◽  
Author(s):  
D. Sirisha ◽  
G. Vijayakumari
Keyword(s):  
Completion Time ◽  
High Performance ◽  
Turnaround Time ◽  
Resource Provisioning ◽  
Optimal Solutions ◽  
Complete Problem ◽  
Heterogeneous Processing ◽  
Heuristic Scheduling ◽  
Np Complete ◽  
Workflow Tasks

Compute intensive applications featured as workflows necessitate Heterogeneous Processing Systems (HPS) for attaining high performance to minimize the turnaround time. Efficient scheduling of the workflow tasks is paramount to attain higher potentials of HPS and is a challenging NP-Complete problem. In the present work, Branch and Bound (BnB) strategy is applied to optimally schedule the workflow tasks. The proposed bounds are tighter, simpler and less complex than the existing bounds and the upper bound is closer to the exact solution. Moreover, the bounds on the resource provisioning are devised to execute the workflows in the minimum possible time and optimally utilize the resources. The performance of the proposed BnB strategy is evaluated on a suite of benchmark workflows. The experimental results reveal that the proposed BnB strategy improved the optimal solutions compared to the existing heuristic scheduling algorithms for more than 20 percent of the cases and generated better schedules over 7 percent for 82.6 percent of the cases.

Operation Planning of District Heating and Cooling Plants Considering Contract Violation Penalties

2009 ◽  
Vol 13 (3) ◽  
pp. 185-192
Author(s):  
Kosuke Kato ◽  
◽  
Masatoshi Sakawa ◽  
Keiichi Ishimaru ◽  
Satoshi Ushiro ◽  
...  
Keyword(s):  
Cold Water ◽  
District Heating ◽  
Nonlinear Integer Programming ◽  
Planning Problem ◽  
Integer Programming Problem ◽  
Operation Planning ◽  
Urban District ◽  
Water Steam ◽  
Heating And Cooling ◽  
Contract Violation

Urban district heating and cooling (DHC) systems operate large freezers, heat exchangers, and boilers to stably and economically supply hot and cold water, steam, etc., based on customer demand. We formulate an operation-planning problem as a nonlinear integer programming problem for an actual DHC plant. To reflect actual decision making appropriately, we incorporate contract-violation penalties into the running cost consisting of fuel and arrangements expenses. We, then, solve operation-planning problems with and without penalties, demonstrating the effectiveness of taking penalties into consideration.

scholarly journals New Methods for the Construction of Test Cases for Partitioning Heuristics

VLSI Design ◽  
1995 ◽  
Vol 3 (1) ◽  
pp. 93-98 ◽  
Author(s):  
Youssef Saab
Keyword(s):  
Integrated Circuits ◽  
Network Flow ◽  
Test Cases ◽  
Heuristic Methods ◽  
Optimal Solutions ◽  
Clustering Problem ◽  
New Methods ◽  
Fixed Dimension ◽  
Geometric Clustering ◽  
Partitioning Problem

Partitioning is an important problem in the design automation of integrated circuits. This problem in many of its formulation is NP-Hard, and several heuristic methods have been proposed for its solution. To evaluate the effectiveness of the various partitioning heuristics, it is desirable to have test cases with known optimal solutions that are as “random looking” as possible. In this paper, we describe several methods for the construction of such test cases. All our methods except one use the theory of network flow. The remaining method uses a relationship between a partitioning problem and the geometric clustering problem. The latter problem can be solved in polynomial time in any fixed dimension.

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 Two Neighbourhood-based Approaches for the Set Covering Problem

2019 ◽  
Vol 5 (1) ◽  
pp. 1-15
Author(s):  
Eduardo Meca Castro
Keyword(s):  
Set Covering ◽  
Covering Problem ◽  
Heuristic Methods ◽  
Set Covering Problem ◽  
Dispatching Rule ◽  
Average Deviation ◽  
Constructive Heuristic ◽  
Dynamic Dispatching ◽  
Np Complete ◽  
Feasible Solutions

The Set Covering Problem is a well-known NP-complete problem which we address in this work. Due to its combinatorial nature heuristic methods, namely neighbourhood-based meta-heuristics, were used.Based on the well-known algorithms GRASP, Simulated Annealing and Variable Neighbourhood Descend, along with a constructive heuristic based on a dynamic dispatching rule to generate initial feasible solutions, two approaches to the problem were formulated. The performance of both methods was assessed in 42 instances of the problem. Our best approach has an average deviation from the best-known solution of 0.23% and reached 0% for 26 instances under 40 minutes.

Integration of Data Mining and Operations Research

2011 ◽  
pp. 1046-1052
Author(s):  
Stephan Meisel
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Decision Making ◽  
Operations Research ◽  
Secondary Analysis ◽  
The Other ◽  
Optimization Models ◽  
Optimal Solutions ◽  
Number Of Publications ◽  
The One

Basically, Data Mining (DM) and Operations Research (OR) are two paradigms independent of each other. OR aims at optimal solutions of decision problems with respect to a given goal. DM is concerned with secondary analysis of large amounts of data (Hand et al., 2001). However, there are some commonalities. Both paradigms are application focused (Wu et al., 2003; White, 1991). Many Data Mining approaches are within traditional OR domains like logistics, manufacturing, health care or finance. Further, both DM and OR are multidisciplinary. Since its origins, OR has been relying on fields such as mathematics, statistics, economics and computer science. In DM, most of the current textbooks show a strong bias towards one of its founding disciplines, like database management, machine learning or statistics. Being multidisciplinary and application focused, it seems to be a natural step for both paradigms to gain synergies from integration. Thus, recently an increasing number of publications of successful approaches at the intersection of DM and OR can be observed. On the one hand, efficiency of the DM process is increased by use of advanced optimization models and methods originating from OR. On the other hand, effectiveness of decision making is increased by augmentation of traditional OR approaches with DM results. Meisel and Mattfeld (in press) provide a detailed discussion of the synergies of DM and OR.

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