A linear programming based algorithm to solve a class of optimization problems with a multi-linear objective function and affine constraints

2018 ◽  
Vol 89 ◽  
pp. 17-30 ◽  
Author(s):  
Hadi Charkhgard ◽  
Martin Savelsbergh ◽  
Masoud Talebian
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Optimization Problems ◽  
Linear Objective Function ◽  
Affine Constraints

scholarly journals Modeling of Gauss Elimination Technique and AHA Simplex Algorithm for Multi-objective Linear Programming Problems

2020 ◽  
pp. 1-14
Author(s):  
Sanjay Jain ◽  
Adarsh Mangal
Keyword(s):  
Linear Programming ◽  
Numerical Solution ◽  
Objective Function ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Simplex Algorithm ◽  
Multi Objective ◽  
Linear Objective Function ◽  
Gauss Elimination ◽  
Linear Programming Problems

In this research paper, an effort has been made to solve each linear objective function involved in the Multi-objective Linear Programming Problem (MOLPP) under consideration by AHA simplex algorithm and then the MOLPP is converted into a single LPP by using various techniques and then the solution of LPP thus formed is recovered by Gauss elimination technique. MOLPP is concerned with the linear programming problems of maximizing or minimizing, the linear objective function having more than one objective along with subject to a set of constraints having linear inequalities in nature. Modeling of Gauss elimination technique of inequalities is derived for numerical solution of linear programming problem by using concept of bounds. The method is quite useful because the calculations involved are simple as compared to other existing methods and takes least time. The same has been illustrated by a numerical example for each technique discussed here.

SIMULATION OBJECTIVES OF FUZZY LINEAR PROGRAMMING WITH AN α-LEVEL METHOD OF λ-CONTINUE

2019 ◽  
Vol 6 (2) ◽  
pp. 71-76
Author(s):  
Alevtina Jur'evna Shatalova ◽  
Konstantin Andreevich Lebedev Konstantin Andreevich
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Investment Project ◽  
Fuzzy Linear Programming ◽  
Distribution Law ◽  
Linear Optimization Problems ◽  
Level Method

The article describes an approach that allows to formally describe the arising uncertainties in linear optimization problems. The generalized parametric alpha-level method of lambda-continuation of the fuzzy linear programming problem is considered. The model offers two methods that take into account the expansion of the binary fuzzy ratio (“strong” and “weak”). After the condition is formed taking into account the incoming quantities in the form of fuzzy numbers (the objective function and the system of constraints), the optimal solution (the value of the objective function) for each alpha and lambda is calculated using the simplex method implemented in Mathcad. On its basis, a mathematical model is built that will take into account the random values of alpha and lambda with a uniform distribution law. The paper presents a description of the simulation study, which confirms the conclusions about the possibilities of the method. Using the proposed theory, the decision-maker receives more information showing the behavior of the system with small changes in the input parameters to make more informed conclusions about the choice of financing of an investment project. The developed method of simulation of fuzzy estimation can be applied to other economic models with the appropriate necessary modification, for example, to assess the creditworthiness of the enterprise.

A PENALTY METHOD FOR SOLVING BILEVEL LINEAR FRACTIONAL/LINEAR PROGRAMMING PROBLEMS

2004 ◽  
Vol 21 (02) ◽  
pp. 207-224 ◽  
Author(s):  
HERMINIA I. CALVETE ◽  
CARMEN GALÉ
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimization Approach ◽  
Fractional Linear Programming ◽  
Linear Programming Problems ◽  
Level Problem ◽  
The Relationship ◽  
Planning Problems

Bilevel programming involves two optimization problems where the constraint region of the first-level problem is implicitly determined by another optimization problem. This model has been applied to decentralized planning problems involving a decision process with a hierarchical structure. In this paper, we consider the bilevel linear fractional/linear programming problem, in which the objective function of the first-level is linear fractional, the objective function of the second level is linear, and the common constraint region is a polyhedron. For this problem, taking into account the relationship between the optimization problem of the second level and its dual, a global optimization approach is proposed that uses an exact penalty function based on the duality gap of the second-level problem.

scholarly journals Hypergraph Optimization Problems: Why is the Objective Function Linear?

1996 ◽  
Vol 3 (50) ◽  
Author(s):  
Aleksandar Pekec
Keyword(s):  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
A Priori ◽  
Point Of View ◽  
Linear Objective Function ◽  
Discrete Structures

Choosing an objective function for an optimization problem is a<br />modeling issue and there is no a-priori reason that the objective function<br />must be linear. Still, it seems that linear 0-1 programming formulations<br />are overwhelmingly used as models for optimization problems<br />over discrete structures. We show that this is not an accident. Under<br />some reasonable conditions (from the modeling point of view), the<br />linear objective function is the only possible one.

Developing Schedule With Linear Programming (Case Study: STTF II Project Komplek Sukamukti Banjaran)

2020 ◽  
Vol 4 (02) ◽  
pp. 34-45
Author(s):  
Naufal Dzikri Afifi ◽  
Ika Arum Puspita ◽  
Mohammad Deni Akbar
Keyword(s):  
Linear Programming ◽  
Objective Function ◽  
Project Scheduling ◽  
Time Limit ◽  
Minimum Time ◽  
Service Cost ◽  
Trade Off ◽  
Overtime Work ◽  
The Cost

Shift to The Front II Komplek Sukamukti Banjaran Project is one of the projects implemented by one of the companies engaged in telecommunications. In its implementation, each project including Shift to The Front II Komplek Sukamukti Banjaran has a time limit specified in the contract. Project scheduling is an important role in predicting both the cost and time in a project. Every project should be able to complete the project before or just in the time specified in the contract. Delay in a project can be anticipated by accelerating the duration of completion by using the crashing method with the application of linear programming. Linear programming will help iteration in the calculation of crashing because if linear programming not used, iteration will be repeated. The objective function in this scheduling is to minimize the cost. This study aims to find a trade-off between the costs and the minimum time expected to complete this project. The acceleration of the duration of this study was carried out using the addition of 4 hours of overtime work, 3 hours of overtime work, 2 hours of overtime work, and 1 hour of overtime work. The normal time for this project is 35 days with a service fee of Rp. 52,335,690. From the results of the crashing analysis, the alternative chosen is to add 1 hour of overtime to 34 days with a total service cost of Rp. 52,375,492. This acceleration will affect the entire project because there are 33 different locations worked on Shift to The Front II and if all these locations can be accelerated then the duration of completion of the entire project will be effective

Scalable Computing Architecture for Time-Dependent Transportation Optimization Problems Based on High-Performance Computing Techniques

2019 ◽  
Vol 2673 (4) ◽  
pp. 205-216 ◽  
Author(s):  
Pengfei (Taylor) Li ◽  
Peirong (Slade) Wang ◽  
Farzana Chowdhury ◽  
Li Zhang
Keyword(s):  
Objective Function ◽  
High Performance Computing ◽  
High Performance ◽  
Optimization Problems ◽  
Dynamic Network ◽  
Alternative Formulation ◽  
High Fidelity ◽  
Objective Functions ◽  
Performance Computing ◽  
Transportation Optimization

Traditional formulations for transportation optimization problems mostly build complicating attributes into constraints while keeping the succinctness of objective functions. A popular solution is the Lagrangian decomposition by relaxing complicating constraints and then solving iteratively. Although this approach is effective for many problems, it generates intractability in other problems. To address this issue, this paper presents an alternative formulation for transportation optimization problems in which the complicating attributes of target problems are partially or entirely built into the objective function instead of into the constraints. Many mathematical complicating constraints in transportation problems can be efficiently modeled in dynamic network loading (DNL) models based on the demand–supply equilibrium, such as the various road or vehicle capacity constraints or “IF–THEN” type constraints. After “pre-building” complicating constraints into the objective functions, the objective function can be approximated well with customized high-fidelity DNL models. Three types of computing benefits can be achieved in the alternative formulation: ( a) the original problem will be kept the same; ( b) computing complexity of the new formulation may be significantly reduced because of the disappearance of hard constraints; ( c) efficiency loss on the objective function side can be mitigated via multiple high-performance computing techniques. Under this new framework, high-fidelity and problem-specific DNL models will be critical to maintain the attributes of original problems. Therefore, the authors’ recent efforts in enhancing the DNL’s fidelity and computing efficiency are also described in the second part of this paper. Finally, a demonstration case study is conducted to validate the new approach.

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