Applicability of existing continuous methods in determining the Pareto set for nonlinear, mixed-integer multicriteria optimization problems

2000 ◽  
Author(s):  
Indraneel Das
Keyword(s):  
Multicriteria Optimization ◽  
Optimization Problems ◽  
Pareto Set ◽  
Mixed Integer ◽  
Continuous Methods

scholarly journals A Multi-Objective Approach toward Optimal Design of Sustainable Integrated Biodiesel/Diesel Supply Chain Based on First- and Second-Generation Feedstock with Solid Waste Use

Energies ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2261
Author(s):  
Evgeniy Ganev ◽  
Boyan Ivanov ◽  
Natasha Vaklieva-Bancheva ◽  
Elisaveta Kirilova ◽  
Yunzile Dzhelil
Keyword(s):  
Supply Chain ◽  
Optimal Design ◽  
Solid Waste ◽  
Second Generation ◽  
Agricultural Land ◽  
Optimization Problems ◽  
Biodiesel Production ◽  
Mixed Integer ◽  
Economic Criterion ◽  
Multi Objective

This study proposes a multi-objective approach for the optimal design of a sustainable Integrated Biodiesel/Diesel Supply Chain (IBDSC) based on first- (sunflower and rapeseed) and second-generation (waste cooking oil and animal fat) feedstocks with solid waste use. It includes mixed-integer linear programming (MILP) models of the economic, environmental and social impact of IBDSC, and respective criteria defined in terms of costs. The purpose is to obtain the optimal number, sizes and locations of bio-refineries and solid waste plants; the areas and amounts of feedstocks needed for biodiesel production; and the transportation mode. The approach is applied on a real case study in which the territory of Bulgaria with its 27 districts is considered. Optimization problems are formulated for a 5-year period using either environmental or economic criteria and the remainder are defined as constraints. The obtained results show that in the case of the economic criterion, 14% of the agricultural land should be used for sunflower and 2% for rapeseed cultivation, while for the environmental case, 12% should be used for rapeseed and 3% for sunflower. In this case, the price of biodiesel is 14% higher, and the generated pollutants are 6.6% lower. The optimal transport for both cases is rail.

Optimization of Real Power Loss and Voltage Stability Index for Distribution Systems with Distributed Generation

2017 ◽  
Vol 33 ◽  
pp. 100-114 ◽  
Author(s):  
Mostafa Elshahed ◽  
Mahmoud Dawod ◽  
Zeinab H. Osman
Keyword(s):  
Genetic Algorithm ◽  
Distributed Generation ◽  
Distribution Systems ◽  
Voltage Stability ◽  
Reactive Power ◽  
Optimization Problems ◽  
Stability Index ◽  
Mixed Integer ◽  
Voltage Profile ◽  
Voltage Stability Index

Integrating Distributed Generation (DG) units into distribution systems can have an impact on the voltage profile, power flow, power losses, and voltage stability. In this paper, a new methodology for DG location and sizing are developed to minimize system losses and maximize voltage stability index (VSI). A proper allocation of DG has to be determined using the fuzzy ranking method to verify best compromised solutions and achieve maximum benefits. Synchronous machines are utilized and its power factor is optimally determined via genetic optimization to inject reactive power to decrease system losses and improve voltage profile and VSI. The Augmented Lagrangian Genetic Algorithm with nonlinear mixed-integer variables and Non-dominated Sorting Genetic Algorithm have been implemented to solve both single/multi-objective function optimization problems. For proposed methodology effectiveness verification, it is tested on 33-bus and 69-bus radial distribution systems then compared with previous works.

scholarly journals Partially distributed outer approximation

2021 ◽  
Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Outer Approximation ◽  
Mixed Integer ◽  
Global Optimality ◽  
Integer Optimization ◽  
Global Minimizers ◽  
Outer Approximation Method ◽  
Coupling Constraints ◽  
Outer Approximation Algorithm

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

An Augmented Lagrange Multiplier Based Method for Mixed Integer Discrete Continuous Optimization and its Applications to Mechanical Design

1993 ◽  
Author(s):  
B. K. Kannan ◽  
Steven N. Kramer
Keyword(s):  
Lagrange Multiplier ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Optimization Problems ◽  
Mechanical Design ◽  
Continuous Optimization ◽  
Mixed Integer ◽  
Continuous Variables ◽  
Augmented Lagrange Multiplier

Abstract An algorithm for solving nonlinear optimization problems involving discrete, integer, zero-one and continuous variables is presented. The augmented Lagrange multiplier method combined with Powell’s method and Fletcher & Reeves Conjugate Gradient method are used to solve the optimization problem where penalties are imposed on the constraints for integer / discrete violations. The use of zero-one variables as a tool for conceptual design optimization is also described with an example. Several case studies have been presented to illustrate the practical use of this algorithm. The results obtained are compared with those obtained by the Branch and Bound algorithm. Also, a comparison is made between the use of Powell’s method (zeroth order) and the Conjugate Gradient method (first order) in the solution of these mixed variable optimization problems.

Multirow Intersection Cuts Based on the Infinity Norm

2021 ◽  
Author(s):  
Álinson S. Xavier ◽  
Ricardo Fukasawa ◽  
Laurent Poirrier
Keyword(s):  
Optimization Problems ◽  
Valid Inequalities ◽  
Linear Optimization ◽  
Computational Cost ◽  
General Purpose ◽  
Mixed Integer ◽  
Infinity Norm ◽  
Intersection Cuts ◽  
Linear Optimization Problems ◽  
Mixed Integer Linear Optimization

When generating multirow intersection cuts for mixed-integer linear optimization problems, an important practical question is deciding which intersection cuts to use. Even when restricted to cuts that are facet defining for the corner relaxation, the number of potential candidates is still very large, especially for instances of large size. In this paper, we introduce a subset of intersection cuts based on the infinity norm that is very small, works for relaxations having arbitrary number of rows and, unlike many subclasses studied in the literature, takes into account the entire data from the simplex tableau. We describe an algorithm for generating these inequalities and run extensive computational experiments in order to evaluate their practical effectiveness in real-world instances. We conclude that this subset of inequalities yields, in terms of gap closure, around 50% of the benefits of using all valid inequalities for the corner relaxation simultaneously, but at a small fraction of the computational cost, and with a very small number of cuts. Summary of Contribution: Cutting planes are one of the most important techniques used by modern mixed-integer linear programming solvers when solving a variety of challenging operations research problems. The paper advances the state of the art on general-purpose multirow intersection cuts by proposing a practical and computationally friendly method to generate them.

scholarly journals Mixed integer nonlinear programming (MINLP)-based bandwidth utility function on internet pricing scheme with monitoring and marginal cost

2019 ◽  
Vol 9 (2) ◽  
pp. 1240
Author(s):  
Robinson Sitepu ◽  
Fitri Maya Puspita ◽  
Elika Kurniadi ◽  
Yunita Yunita ◽  
Shintya Apriliyani
Keyword(s):  
Utility Function ◽  
Marginal Cost ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Mixed Integer ◽  
Monitoring Cost ◽  
Internet Pricing ◽  
Pricing Scheme ◽  
Linear Optimization Problems

<span>The development of the internet in this era of globalization has increased fast. The need for internet becomes unlimited. Utility functions as one of measurements in internet usage, were usually associated with a level of satisfaction of users for the use of information services used. There are three internet pricing schemes used, that are flat fee, usage based and two-part tariff schemes by using one of the utility function which is Bandwidth Diminished with Increasing Bandwidth with monitoring cost and marginal cost. Internet pricing scheme will be solved by LINGO 13.0 in form of non-linear optimization problems to get optimal solution. The optimal solution is obtained using the either usage-based pricing scheme model or two-part tariff pricing scheme model for each services offered, if the comparison is with flat-fee pricing scheme. It is the best way for provider to offer network based on usage based scheme. The results show that by applying two part tariff scheme, the providers can maximize its revenue either for homogeneous or heterogeneous consumers.</span>

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