scholarly journals An enumerative algorithm for non-linear multi-level integer programming problem

2009 ◽  
Vol 19 (2) ◽  
pp. 263-279 ◽  
Author(s):  
Ritu Narang ◽  
S.R. Arora
Keyword(s):  
Programming Problem ◽  
Optimization Problems ◽  
Feasible Region ◽  
Integer Programming Problem ◽  
The Third ◽  
Level Problem ◽  
Enumerative Algorithm ◽  
Indefinite Quadratic ◽  
Feasible Solutions ◽  
Optimum Solution

In this paper a multilevel programming problem, that is, three level programming problem is considered. It involves three optimization problems where the constraint region of the first level problem is implicitly determined by two other optimization problems. The objective function of the first level is indefinite quadratic, the second one is linear and the third one is linear fractional. The feasible region is a convex polyhedron. Considering the relationship between feasible solutions to the problem and bases of the coefficient sub-matrix associated to the variables of the third level, an enumerative algorithm is proposed, which finds an optimum solution to the given problem. It is illustrated with the help of an example. .

Multiobjective Programming

2014 ◽  
pp. 1585-1604
Author(s):  
Minghe Sun
Keyword(s):  
Programming Problem ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Objective Functions ◽  
Solution Quality ◽  
Solution Methods ◽  
Multiobjective Programming Problem ◽  
Feasible Solutions ◽  
Multiobjective Programming Problems

Optimization problems with multiple criteria measuring solution quality can be modeled as multiobjective programming problems. Because the objective functions are usually in conflict, there is not a single feasible solution that can optimize all objective functions simultaneously. An optimal solution is one that is most preferred by the decision maker (DM) among all feasible solutions. An optimal solution must be nondominated but a multiobjective programming problem may have, possibly infinitely, many nondominated solutions. Therefore, tradeoffs must be made in searching for an optimal solution. Hence, the DM's preference information is elicited and used when a multiobjective programming problem is solved. The model, concepts and definitions of multiobjective programming are presented and solution methods are briefly discussed. Examples are used to demonstrate the concepts and solution methods. Graphics are used in these examples to facilitate understanding.

scholarly journals Application of Heuristic and Metaheuristic Algorithms in Solving Constrained Weber Problem with Feasible Region Bounded by Arcs

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Igor Stojanović ◽  
Ivona Brajević ◽  
Predrag S. Stanimirović ◽  
Lev A. Kazakovtsev ◽  
Zoran Zdravev
Keyword(s):  
Heuristic Algorithm ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Facility Location Problem ◽  
Metaheuristic Algorithms ◽  
Feasible Region ◽  
Weber Problem ◽  
Bee Colony ◽  
Feasible Solutions ◽  
Weiszfeld Procedure

The continuous planar facility location problem with the connected region of feasible solutions bounded by arcs is a particular case of the constrained Weber problem. This problem is a continuous optimization problem which has a nonconvex feasible set of constraints. This paper suggests appropriate modifications of four metaheuristic algorithms which are defined with the aim of solving this type of nonconvex optimization problems. Also, a comparison of these algorithms to each other as well as to the heuristic algorithm is presented. The artificial bee colony algorithm, firefly algorithm, and their recently proposed improved versions for constrained optimization are appropriately modified and applied to the case study. The heuristic algorithm based on modified Weiszfeld procedure is also implemented for the purpose of comparison with the metaheuristic approaches. Obtained numerical results show that metaheuristic algorithms can be successfully applied to solve the instances of this problem of up to 500 constraints. Among these four algorithms, the improved version of artificial bee algorithm is the most efficient with respect to the quality of the solution, robustness, and the computational efficiency.

An Embedded Multi-Phase Tactic of Scheduling Autoimmunization for Complex Correlated Production System

2010 ◽  
Vol 439-440 ◽  
pp. 505-509 ◽  
Author(s):  
Ya Bo Luo ◽  
Ming Chun Tang
Keyword(s):  
Optimization Problem ◽  
Job Shop ◽  
Optimization Problems ◽  
Scheduling System ◽  
Design Variables ◽  
Complex Optimization ◽  
Feasible Solutions ◽  
Optimum Solution ◽  
Multi Phase ◽  
Machine Allocation

The schedule for job shop system involving the complex correlated constraints is a complex combinatorial optimization problem, for which currently there is no a methodology claiming to have capability to find the optimum solution. Current research concentrate on the search of acceptable feasible solutions. This research proposes an embedded multi-phase methodology to find the acceptable feasible solutions in a higher efficiency. The thinking of the methodology is to decompose the complex optimization problem into two sub problems of the operation sequence and the machine allocation to lower the complexity of the scheduling system and improve the searching efficiency. The two sub problems are solved orderly respectively, and the results of the first sub problem are embedded into the second sub problem as the original values of design variables. Thus these two sub optimization problems are integrated into a searching loop to ensure the feasibility of solution and improve the searching efficiency in the complex correlated system.

scholarly journals Optimization In A Finite-Dimensional Euclide Space

2020 ◽  
Vol 7 (1) ◽  
pp. 20-28
Author(s):  
A.I. Kosolap ◽  
Keyword(s):  
Euclidean Space ◽  
Objective Function ◽  
Optimization Model ◽  
Optimization Problems ◽  
Complexity Class ◽  
Feasible Region ◽  
Complexity Classes ◽  
The Third ◽  
Primal Dual ◽  
Multimodal Problems

In this paper, optimization models in Euclidean space are divided into four complexity classes. Ef-fective algorithms have been developed to solve the problems of the first two classes of complexity. These are the primal-dual interior-point methods. Discrete and combinatorial optimization problems of the third complexity class are recommended to be converted to the fourth complexity class with continuous change of variables. Effective algorithms have not been developed for problems of the third and fourth complexity classes, with the exception of a narrow class of problems that are unimodal. The general optimization problem is formulated as a minimum (maximum) objective function in the presence of constraints. The complexity of the problem depends on the structure of the objective function and its feasible region. If the functions that determine the optimization model are quadratic or polynomial, then semidefinite programming can be used to obtain estimates of so-lutions in such problems. Effective methods have been developed for semidefinite optimization problems. Sometimes it’s enough to develop an algorithm without building a mathematical model. We see such an example when sorting an array of numbers. Effective algorithms have been devel-oped to solve this problem. In the work for sorting problems, an optimization model is constructed, and it coincides with the model of the assignment problem. It follows from this that the sorting problem is unimodal. Effective algorithms have not been developed to solve multimodal problems. The paper proposes a simple and effective algorithm for the optimal allocation of resources in mul-tiprocessor systems. This problem is multimodal. In the general case, for solving multimodal prob-lems, a method of exact quadratic regularization is proposed. This method has proven its compara-tive effectiveness in solving many test problems of various dimensions. Keywords: Euclidean space, optimization, unimodal problems, multimodal problems, complexity classes, numerical methods.

scholarly journals An improved ant system algorithm for maximizing system reliability in the compatible module

2019 ◽  
Vol 9 (4) ◽  
pp. 3232
Author(s):  
Mana Sopa ◽  
Niwat Angkawisittpan
Keyword(s):  
System Reliability ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Neighborhood Search ◽  
Data Sets ◽  
Integer Programming Problem ◽  
Ant System ◽  
Binary Integer Programming ◽  
Compatible Module ◽  
Feasible Solutions

This paper presents an improved Ant System (AS) algorithm called AS-2Swap for solving one of the reliability optimization problems. The objective is to selection a compatible module in order to maximize the system reliability and subject to budget constraints. This problem is NP-hard and formulated as a binary integer-programming problem with a nonlinear objective function. The proposed algorithm is based on the original AS algorithm and the improvement, focused on choosing the feasible solutions, neighborhood search with Swap technique for each loop of finding the solution. The implementation was tested by the five groups of data sets from the existing meta-heuristic found in the literature. The computational results show that the proposed algorithm can find the global optimal solution and is more accurate for larger problems.

scholarly journals Analysis of Nonlinear Bypass Route Computation for Wired and Wireless Network Cooperation Recovery System

2018 ◽  
Vol 2 (3) ◽  
pp. 28 ◽  
Author(s):  
Yu Nakayama ◽  
Kazuki Maruta
Keyword(s):  
Programming Problem ◽  
Wireless Network ◽  
Resource Sharing ◽  
Computation Method ◽  
Integer Programming Problem ◽  
Binary Integer Programming ◽  
Telecommunication Services ◽  
Network Cooperation ◽  
Wireless Links ◽  
Routing Method

It is a significant issue for network carriers to immediately restore telecommunication services when a disaster occurs. A wired and wireless network cooperation (NeCo) system was proposed to address this problem. The goal of the NeCo system is quick and high-throughput recovery of telecommunication services in the disaster area using single-hop wireless links backhauled by wired networks. It establishes wireless bypass routes between widely deployed leaf nodes to relay packets to and from dead nodes whose normal wired communication channels are disrupted. In the previous study, the optimal routes for wireless links were calculated to maximize the expected physical layer throughput by solving a binary integer programming problem. However, the routing method did not consider throughput reduction caused by sharing of wireless resources among dead nodes. Therefore, this paper proposes a nonlinear bypass route computation method considering the wireless resource sharing among dead nodes for the NeCo system. Monte Carlo base approach is applied since the nonlinear programming problem is difficult to solve. The performance of the proposed routing method is evaluated with computer simulations and it was confirmed that bandwidth division loss can be avoided with the proposed method.

scholarly journals A Mixed Integer Programming Poultry Feed Ration Optimisation Problem Using the Bat Algorithm

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Godfrey Chagwiza ◽  
Chipo Chivuraise ◽  
Christopher T. Gadzirayi
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Moringa Oleifera ◽  
Bat Algorithm ◽  
Mixed Integer ◽  
Poultry Feed ◽  
Integer Programming Problem ◽  
Optimum Solution ◽  
Mixed Integer Programming Problem ◽  
Number Of Iterations

In this paper, a feed ration problem is presented as a mixed integer programming problem. An attempt to find the optimal quantities of Moringa oleifera inclusion into the poultry feed ration was done and the problem was solved using the Bat algorithm and the Cplex solver. The study used findings of previous research to investigate the effects of Moringa oleifera inclusion in poultry feed ration. The results show that the farmer is likely to gain US$0.89 more if Moringa oleifera is included in the feed ration. Results also show superiority of the Bat algorithm in terms of execution time and number of iterations required to find the optimum solution as compared with the results obtained by the Cplex solver. Results revealed that there is a significant economic benefit of Moringa oleifera inclusion into the poultry feed ration.

TWO BI-OBJECTIVE OPTIMIZATION MODELS FOR COMPETITIVE LOCATION PROBLEMS

2006 ◽  
Vol 05 (03) ◽  
pp. 531-543 ◽  
Author(s):  
FENGMEI YANG ◽  
GUOWEI HUA ◽  
HIROSHI INOUE ◽  
JIANMING SHI
Keyword(s):  
Integer Programming ◽  
Programming Problem ◽  
Efficient Solutions ◽  
Integer Program ◽  
Location Problems ◽  
Optimization Models ◽  
Competitive Location ◽  
Integer Programming Problem ◽  
Single Objective ◽  
Parametric Integer Programming

This paper deals with two bi-objective models arising from competitive location problems. The first model simultaneously intends to maximize market share and to minimize cost. The second one aims to maximize both profit and the profit margin. We study some of the related properties of the models, examine relations between the models and a single objective parametric integer programming problem, and then show how both bi-objective location problems can be solved through the use of a single objective parametric integer program. Based on this, we propose two methods of obtaining a set of efficient solutions to the problems of fundamental approach. Finally, a numerical example is presented to illustrate the solution techniques.

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