Multi-Objective Optimization With Multiple Spatially Distributed Surrogates

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Kalyan Shankar Bhattacharjee ◽  
Hemant Kumar Singh ◽  
Tapabrata Ray
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
A Priori ◽  
Search Space ◽  
Nsga Ii ◽  
Multi Objective ◽  
Engineering Design Optimization ◽  
Spatially Distributed ◽  
Computationally Expensive

In engineering design optimization, evaluation of a single solution (design) often requires running one or more computationally expensive simulations. Surrogate assisted optimization (SAO) approaches have long been used for solving such problems, in which approximations/surrogates are used in lieu of computationally expensive simulations during the course of search. Existing SAO approaches often use the same type of approximation model to represent all objectives and constraints in all regions of the search space. The selection of a type of surrogate model over another is nontrivial and an a priori choice limits flexibility in representation. In this paper, we introduce a multi-objective evolutionary algorithm (EA) with multiple adaptive spatially distributed surrogates. Instead of a single global surrogate, local surrogates of multiple types are constructed in the neighborhood of each offspring solution and a multi-objective search is conducted using the best surrogate for each objective and constraint function. The proposed approach offers flexibility of representation by capitalizing on the benefits offered by various types of surrogates in different regions of the search space. The approach is also immune to illvalidation since approximated and truly evaluated solutions are not ranked together. The performance of the proposed surrogate assisted multi-objective algorithm (SAMO) is compared with baseline nondominated sorting genetic algorithm II (NSGA-II) and NSGA-II embedded with global and local surrogates of various types. The performance of the proposed approach is quantitatively assessed using several engineering design optimization problems. The numerical experiments demonstrate competence and consistency of SAMO.

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.

A rank-based constraint handling technique for engineering design optimization problems solved by genetic algorithms

2017 ◽  
Vol 187 ◽  
pp. 77-87 ◽  
Author(s):  
Rafael de Paula Garcia ◽  
Beatriz Souza Leite Pires de Lima ◽  
Afonso Celso de Castro Lemonge ◽  
Breno Pinheiro Jacob
Keyword(s):  
Genetic Algorithms ◽  
Design Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Constraint Handling ◽  
Engineering Design Optimization ◽  
Handling Technique

Adaptive Particle Swarm Optimization with Dynamic Population and its Application to Constrained Engineering Design Optimization

2012 ◽  
Vol 538-541 ◽  
pp. 3074-3078
Author(s):  
Yi Liu ◽  
Cai Hong Mu ◽  
Wei Dong Kou ◽  
Jing Liu
Keyword(s):  
Particle Swarm Optimization ◽  
Design Optimization ◽  
Population Size ◽  
Engineering Design ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Swarm Optimization ◽  
Adaptive Particle Swarm Optimization ◽  
Engineering Design Optimization ◽  
Dynamic Population

This paper presents a variant of the particle swarm optimization (PSO) that we call the adaptive particle swarm optimization with dynamic population (DP-APSO), which adopts a novel dynamic population (DP) strategy whereby the population size of swarm can vary with the evolutionary process. The DP strategy enables the population size to increase when the swarm converges and decrease when the swarm disperses. Experiments were conducted on two well-studied constrained engineering design optimization problems. The results demonstrate better performance of the DP-APSO in solving these engineering design optimization problems when compared with two other evolutionary computation algorithms.

An Approach to Identify Six Sigma Robust Solutions of Multi/Many-Objective Engineering Design Optimization Problems

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Tapabrata Ray ◽  
Md Asafuddoula ◽  
Hemant Kumar Singh ◽  
Khairul Alam
Keyword(s):  
Design Optimization ◽  
Engineering Design ◽  
Optimization Problems ◽  
Product Family ◽  
Latin Hypercube Sampling ◽  
General Aviation ◽  
Design Variables ◽  
Engineering Design Optimization ◽  
The Face ◽  
And Performance

In order to be practical, solutions of engineering design optimization problems must be robust, i.e., competent and reliable in the face of uncertainties. While such uncertainties can emerge from a number of sources (imprecise variable values, errors in performance estimates, varying environmental conditions, etc.), this study focuses on problems where uncertainties emanate from the design variables. While approaches to identify robust optimal solutions of single and multi-objective optimization problems have been proposed in the past, we introduce a practical approach that is capable of solving robust optimization problems involving many objectives building on authors’ previous work. Two formulations of robustness have been considered in this paper, (a) feasibility robustness (FR), i.e., robustness against design failure and (b) feasibility and performance robustness (FPR), i.e., robustness against design failure and variation in performance. In order to solve such formulations, a decomposition based evolutionary algorithm (DBEA) relying on a generational model is proposed in this study. The algorithm is capable of identifying a set of uniformly distributed nondominated solutions with different sigma levels (feasibility and performance) simultaneously in a single run. Computational benefits offered by using polynomial chaos (PC) in conjunction with Latin hypercube sampling (LHS) for estimating expected mean and variance of the objective/constraint functions has also been studied in this paper. Last, the idea of redesign for robustness has been explored, wherein selective component(s) of an existing design are altered to improve its robustness. The performance of the strategies have been illustrated using two practical design optimization problems, namely, vehicle crash-worthiness optimization problem (VCOP) and a general aviation aircraft (GAA) product family design problem.

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