Tracing the Envelope of the Objective-Space in Multi-Objective Topology Optimization

2011 ◽  
Author(s):  
Inna Turevsky ◽  
Krishnan Suresh
Keyword(s):  
Topology Optimization ◽  
Eigenvalue Problems ◽  
Optimization Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Topological Sensitivity ◽  
Numerical Examples ◽  
Multi Objective ◽  
Objective Space

In multi-objective problems, one is often interested in generating the envelope of the objective-space, where the envelope is, in general, a superset of pareto-optimal solutions. In this paper, we propose a method for tracing the envelope of multi-objective topology optimization problems, and generating the corresponding topologies. The proposed method exploits the concept of topological sensitivity, and is applied to bi-objective optimization, namely eigenvalue-volume, eigenvalue-eigenvalue and compliance-eigenvalue problems. The robustness and efficiency of the method is illustrated through numerical examples.

Tracing Pareto-Optimal Frontiers in Topology Optimization

2010 ◽  
Author(s):  
Krishnan Suresh
Keyword(s):  
Fixed Point ◽  
Topology Optimization ◽  
Iteration Scheme ◽  
Stochastic Method ◽  
Pareto Optimal ◽  
Topological Sensitivity ◽  
Fixed Point Iteration ◽  
Numerical Examples ◽  
Multi Objective ◽  
Sensitivity Field

In multi-objective topology optimization, a design is defined to be “pareto-optimal” if no other design exists that is better with respect to one objective, and as good with respect to others. This unfortunately suggests that unless other ‘better’ designs are found, one cannot declare a particular topology to be pareto-optimal. In this paper, we first show that a topology can be guaranteed to be (locally) pareto-optimal if certain inherent properties associated with the topological sensitivity field are satisfied, i.e., no further comparison is necessary. This, in turn, leads to a deterministic, i.e., non-stochastic, method for directly tracing pareto-optimal frontiers using the classic fixed-point iteration scheme. The proposed method can generate the full set of pareto-optimal topologies in a single-run, and is therefore both efficient and predictable, as illustrated through numerical examples.

Evaluating the ε-Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions

2005 ◽  
Vol 13 (4) ◽  
pp. 501-525 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Manikanth Mohan ◽  
Shikhar Mishra
Keyword(s):  
Steady State ◽  
Evolutionary Algorithm ◽  
Optimization Problems ◽  
Computational Time ◽  
Test Problems ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Nsga Ii ◽  
Multi Objective

Since the suggestion of a computing procedure of multiple Pareto-optimal solutions in multi-objective optimization problems in the early Nineties, researchers have been on the look out for a procedure which is computationally fast and simultaneously capable of finding a well-converged and well-distributed set of solutions. Most multi-objective evolutionary algorithms (MOEAs) developed in the past decade are either good for achieving a well-distributed solutions at the expense of a large computational effort or computationally fast at the expense of achieving a not-so-good distribution of solutions. For example, although the Strength Pareto Evolutionary Algorithm or SPEA (Zitzler and Thiele, 1999) produces a much better distribution compared to the elitist non-dominated sorting GA or NSGA-II (Deb et al., 2002a), the computational time needed to run SPEA is much greater. In this paper, we evaluate a recently-proposed steady-state MOEA (Deb et al., 2003) which was developed based on the ε-dominance concept introduced earlier (Laumanns et al., 2002) and using efficient parent and archive update strategies for achieving a well-distributed and well-converged set of solutions quickly. Based on an extensive comparative study with four other state-of-the-art MOEAs on a number of two, three, and four objective test problems, it is observed that the steady-state MOEA is a good compromise in terms of convergence near to the Pareto-optimal front, diversity of solutions, and computational time. Moreover, the ε-MOEA is a step closer towards making MOEAs pragmatic, particularly allowing a decision-maker to control the achievable accuracy in the obtained Pareto-optimal solutions.

Solving Two Multi-Objective Optimization Problems Using Evolutionary Algorithm

2011 ◽  
pp. 218-233 ◽  
Author(s):  
Ruhul A. Sarker ◽  
Hussein A. Abbass ◽  
Charles S. Newton
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Benchmark Problems ◽  
Pareto Optimal ◽  
Multi Criteria Decision Making ◽  
Pareto Optimal Solutions ◽  
Assessment Methodology ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Multi Objective

Being capable of finding a set of pareto-optimal solutions in a single run is a necessary feature for multi-criteria decision making, Evolutionary algorithms (EAs) have attracted many researchers and practitioners to address the solution of Multi-objective Optimization Problems (MOPs). In a previous work, we developed a Pareto Differential Evolution (PDE) algorithm to handle multi-objective optimization problems. Despite the overwhelming number of Multi-objective Evolutionary Algorithms (MEAs) in the literature, little work has been done to identify the best MEA using an appropriate assessment methodology. In this chapter, we compare our algorithm with twelve other well-known MEAs, using a popular assessment methodology, by solving two benchmark problems. The comparison shows the superiority of our algorithm over others.

Solving Expensive Multi-Objective Optimization Problems by Kriging Model with Multi-Point Updating Strategy

2014 ◽  
Vol 685 ◽  
pp. 667-670 ◽  
Author(s):  
Ding Han ◽  
Jian Rong Zheng
Keyword(s):  
Optimization Problem ◽  
Optimization Problems ◽  
Average Distance ◽  
Kriging Model ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Good Convergence ◽  
Multi Objective

A method which utilizes Kriging model and a multi-point updating strategy is put forward for solving expensive multi-objective optimization problems. Assisted by a defined cheaper multi-objective optimization problem and a maximum average distance criterion, multiple updating points can be found. The proposed method is tested on two numerical functions and a ten-bar truss problem, the results show that the proposed method is efficient in obtaining Pareto optimal solutions with good convergence and diversity when the same computation resource is used comparing with two other methods.

scholarly journals Single- and Multi-Objective Optimization of a Dual-Chamber Microbial Fuel Cell Operating in Continuous-Flow Mode at Steady State

Processes ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 839
Author(s):  
Ibrahim M. Abu-Reesh
Keyword(s):  
Flow Rate ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Multi Objective Optimization ◽  
Dual Chamber ◽  
Worst Case ◽  
Multi Objective ◽  
Model Based ◽  
Conflicting Objectives

Microbial fuel cells (MFCs) are a promising technology for bioenergy generation and wastewater treatment. Various parameters affect the performance of dual-chamber MFCs, such as substrate flow rate and concentration. Performance can be assessed by power density ( PD ), current density ( CD ) production, or substrate removal efficiency ( SRE ). In this study, a mathematical model-based optimization was used to optimize the performance of an MFC using single- and multi-objective optimization (MOO) methods. Matlab’s fmincon and fminimax functions were used to solve the nonlinear constrained equations for the single- and multi-objective optimization, respectively. The fminimax method minimizes the worst-case of the two conflicting objective functions. The single-objective optimization revealed that the maximum PD ,   CD , and SRE were 2.04 W/m2, 11.08 A/m2, and 73.6%, respectively. The substrate concentration and flow rate significantly impacted the performance of the MFC. Pareto-optimal solutions were generated using the weighted sum method for maximizing the two conflicting objectives of PD and CD in addition to PD and SRE   simultaneously. The fminimax method for maximizing PD and CD showed that the compromise solution was to operate the MFC at maximum PD conditions. The model-based optimization proved to be a fast and low-cost optimization method for MFCs and it provided a better understanding of the factors affecting an MFC’s performance. The MOO provided Pareto-optimal solutions with multiple choices for practical applications depending on the purpose of using the MFCs.

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