A Literature Review: Solving Constrained Non-Linear Bi-Level Optimization Problems With Classical Methods

2019 ◽  
Author(s):  
Arpan Biswas ◽  
Christopher Hoyle
Keyword(s):  
Literature Review ◽  
Optimization Problems ◽  
Classical Method ◽  
Optimization Methods ◽  
Function Evaluation ◽  
Practical Applications ◽  
Design Variables ◽  
Non Linear ◽  
Upper Level ◽  
Work Done

Abstract Bi-level optimization is an emerging scope of research which consists of two optimization problems, where the lower-level optimization problem is nested into the upper-level problem as a constraint. Bi-level programming has gained much attention recently for practical applications. Bi-level Programming Problems (BLPP) can be solved with classical and heuristic optimization methods. However, applying heuristic methods, though easier to formulate for realistic complex design, are likely to be too computationally expensive for solving bi-level problems, especially when the problem has high function evaluation cost associated with handling large number of constraint functions. Thus, classical approaches are investigated in this paper. As we present, there appears to be no universally best classical method for solving any kind of NP-hard BLPP problem in terms of accuracy to finding true optimal solutions and minimal computational costs. This could cause a dilemma to the researcher in choosing an appropriate classical approach to solve a BLPP in different domains and levels of complexities. Therefore, this motivates us to provide a detailed literature review and a comparative study of the work done to date on applying different classical approaches in solving constrained non-linear, bi-level optimization problems considering continuous design variables and no discontinuity in functions.

Multi Objective Design Optimization of Two Bar Truss Using NSGA II and TOPSIS

2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Objective Functions ◽  
Nsga Ii ◽  
Multi Objective ◽  
Total Displacement ◽  
Design Variables ◽  
Conflicting Objectives

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.

scholarly journals Parallelization of computational algorithms for optimization problems with high time consumption

2018 ◽  
Vol 157 ◽  
pp. 02054 ◽  
Author(s):  
Milan Vaško ◽  
Marián Handrik ◽  
Alžbeta Sapietová ◽  
Jana Handriková
Keyword(s):  
Computational Models ◽  
Optimization Problems ◽  
Optimization Algorithms ◽  
Fe Analysis ◽  
Function Evaluation ◽  
Computational Algorithms ◽  
Distributed Computing Systems ◽  
Computing Systems ◽  
Time Consumption ◽  
Design Variables

The paper presents an analysis of the use of optimization algorithms in parallel solutions and distributed computing systems. The primary goal is to use evolutionary algorithms and their implementation into parallel calculations. Parallelization of computational algorithms is suitable for the following cases - computational models with a large number of design variables or cases where the objective function evaluation is time consuming (FE analysis). As the software platform for application of distributed optimization algorithms is using MATLAB and BOINC software package.

A Geometry Based Method of Integrated Engineering Analysis and Optimization

1991 ◽  
Author(s):  
Ronald M. Dolin ◽  
Robert J. Bernhard
Keyword(s):  
Data Structure ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Engineering Analysis ◽  
Design Variables ◽  
Engineering Environment ◽  
Specification Analysis

Abstract An integrated geometry based method of analysis and optimization is presented. The significance of geometry based analysis and optimization methods are discussed. A hierarchical integer based data structure, used to define and manipulate geometry, is presented. Many features of the integer based data structure are given. Shapes are shown to represent the fundamental geometry. Variables of shapes are constrained and related to each other so that a reduced set of design variables result. These design variables are used to pose both analysis and optimization problems. Heuristics are used to simplify the integrated geometry specification, analysis and optimization procedures. The resulting engineering environment concurrently poses analysis and optimization problems during geometry generation, leading to an integrated geometry based method of analysis and optimization.

Design Optimization of Valveless DTH Pneumatic Hammers by a Weighted Pseudo-Gradient Search Method

1998 ◽  
Vol 120 (4) ◽  
pp. 687-694 ◽  
Author(s):  
L. E. Chiang ◽  
E. B. Stamm
Keyword(s):  
Dynamic Model ◽  
Linear Equations ◽  
Optimization Methods ◽  
Optimization Method ◽  
Design Variables ◽  
Standard Procedures ◽  
Non Linear ◽  
Predicted Values ◽  
Gradient Search Method ◽  
Non Linear Equations

A design methodology for Down-The-Hole (DTH) pneumatic hammers used for rock drilling is proposed which renders an optimal design for a given set of constraints. A generic non-linear dynamic model developed by the authors is used to compute the hammer performance. This model consists of a set of six differential equations plus a set of twenty non-linear polynomial equations. In addition there are parameter range restrictions given by fabrication and operational standard procedures. In any given application, magnitudes such as power, impact energy, frequency, efficiency and mass flow may be sought for optimality. However these magnitudes must be computed by integration after solving the dynamic model over an entire cycle, thus traditional optimization methods for non-linear equations that are based in gradient information are not suitable. Hence a method that uses secant information is used to approximate the gradient of the space of design variables. Several prototypes using this optimization method have been designed and field tested. The results are in agreement with predicted values.

scholarly journals A Review of Deterministic Optimization Methods in Engineering and Management

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Hua Lin ◽  
Jung-Fa Tsai ◽  
Chian-Son Yu
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Mixed Integer Nonlinear Programming ◽  
Mixed Integer ◽  
Deterministic Optimization ◽  
Practical Applications ◽  
Signomial Programming ◽  
Deterministic Methods ◽  
Integer Nonlinear Programming

With the increasing reliance on modeling optimization problems in practical applications, a number of theoretical and algorithmic contributions of optimization have been proposed. The approaches developed for treating optimization problems can be classified into deterministic and heuristic. This paper aims to introduce recent advances in deterministic methods for solving signomial programming problems and mixed-integer nonlinear programming problems. A number of important applications in engineering and management are also reviewed to reveal the usefulness of the optimization methods.

An improved PSO algorithm for solving nonlinear programing problems with constrained conditions

2020 ◽  
pp. 2150001
Author(s):  
Wei-Der Chang
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Optimization Methods ◽  
Pso Algorithm ◽  
Engineering Optimization ◽  
Swarm Optimization ◽  
Design Variables ◽  
Constrained Conditions ◽  
Engineering Optimization Problems

Engineering optimization problems can be always classified into two main categories including the linear programming (LP) and nonlinear programming (NLP) problems. Each programming problem further involves the unconstrained conditions and constrained conditions for design variables of the optimized system. This paper will focus on the issue about the design problem of NLP with the constrained conditions. The employed method for such NLP problems is a variant of particle swarm optimization (PSO), named improved particle swarm optimization (IPSO). The developed IPSO is to modify the velocity updating formula of the algorithm to enhance the search ability for given optimization problems. In this work, many different kinds of physical engineering optimization problems are examined and solved via the proposed IPSO algorithm. Simulation results compared with various optimization methods reported in the literature will show the effectiveness and feasibility for solving NLP problems with the constrained conditions.

scholarly journals Unconstrained numerical optimization using real-coded genetic algorithms: a study case using benchmark functions in R from Scratch

2019 ◽  
Vol 11 (3) ◽  
pp. 1-11
Author(s):  
Omar Andres Carmona Cortes ◽  
Josenildo Costa da Silva
Keyword(s):  
Genetic Algorithms ◽  
Numerical Optimization ◽  
Optimization Problems ◽  
Practical Applications ◽  
R Language ◽  
Mutation Operators ◽  
Design Variables ◽  
Study Case ◽  
Selection Mechanisms ◽  
Real Coded Genetic Algorithms

Unconstrained numerical problems are common in solving practical applications that, due to its nature, are usually devised by several design variables, narrowing the kind of technique or algorithm that can deal with them. An interesting way of tackling this kind of issue is to use an evolutionary algorithm named Genetic Algorithm. In this context, this work is a tutorial on using real-coded genetic algorithms for solving unconstrained numerical optimization problems. We present the theory and the implementation in R language. Five benchmarks functions (Rosenbrock, Griewank, Ackley, Schwefel, and Alpine) are used as a study case. Further, four different crossover operators (simple, arithmetical, non-uniform arithmetical, and Linear), two selection mechanisms (roulette wheel and tournament), and two mutation operators (uniform and non-uniform) are shown. Results indicate that non-uniform mutation and tournament selection tend to present better outcomes.

Structural Optimization Methods for Large Scale Problems: Status and Limitations

2007 ◽  
Author(s):  
Claude Fleury
Keyword(s):  
Large Scale ◽  
Real Life ◽  
Local Stress ◽  
Positive Definite Matrix ◽  
Optimization Methods ◽  
Practical Applications ◽  
Cpu Time ◽  
Active Constraints ◽  
Design Variables ◽  
Numerical Effort

This paper presents results from recent numerical experiments supported by theoretical arguments which indicate where are the limits of current optimization methods when applied to problems involving a large number of design variables as well as a large number of constraints, many of them being active. This is typical of optimal sizing problems with local stress constraints especially when composite materials are employed. It is shown that in both primal and dual methods the CPU time spent in the optimizer is related to the numerical effort needed to invert a symmetric positive definite matrix of size jact, jact being the effective number of active constraints, i.e. constraints associated with positive Lagrange multipliers. This CPU time varies with jact3. When the number m of constraints increases, jact has a tendency to grow, but there is a limit. Indeed another well known theoretical property is that the number of active constraints jact should not exceed the number of free primal variables iact, i.e. the number of variables that do not reach a lower or upper bound. This number iact is itself of course smaller than the real number of design variables n. This leads to the conclusion that for problems with many active constraints the CPU time could grow as fast as n3. With respect to m the increase in CPU time remains approximately linear. Some practical applications to real life industrial problems will be briefly shown: design optimisation of an aircraft composite wing with local buckling constraints and topology optimization of an engine pylon.

scholarly journals Identification of a Non-Linear Landing Gear Model Using Nature-Inspired Optimization

2008 ◽  
Vol 15 (3-4) ◽  
pp. 257-272 ◽  
Author(s):  
Felipe A.C. Viana ◽  
Valder Steffen Jr. ◽  
Marcelo A.X. Zanini ◽  
Sandro A. Magalhães ◽  
Luiz C.S. Góes
Keyword(s):  
Inverse Problem ◽  
Shock Absorber ◽  
Model Updating ◽  
Optimization Technique ◽  
Optimization Methods ◽  
Initial Guess ◽  
Landing Gear ◽  
Design Variables ◽  
Non Linear ◽  
The Difference

This work deals with the application of a nature-inspired optimization technique to solve an inverse problem represented by the identification of an aircraft landing gear model. The model is described in terms of the landing gear geometry, internal volumes and areas, shock absorber travel, tire type, and gas and oil characteristics of the shock absorber. The solution to this inverse problem can be obtained by using classical gradient-based optimization methods. However, this is a difficult task due to the existence of local minima in the design space and the requirement of an initial guess. These aspects have motivated the authors to explore a nature-inspired approach using a method known as LifeCycle Model. In the present formulation two nature-based methods, namely the Genetic Algorithms and the Particle Swarm Optimization were used. An optimization problem is formulated in which the objective function represents the difference between the measured characteristics of the system and its model counterpart. The polytropic coefficient of the gas and the damping parameter of the shock absorber are assumed as being unknown: they are considered as design variables. As an illustration, experimental drop test data, obtained under zero horizontal speed, were used in the non-linear landing gear model updating of a small aircraft.

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