Mixture Surrogate Models for Multi- Objective Optimization

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Shailesh S. Kadre ◽  
Vipin K. Tripathi
Keyword(s):  
Finite Element ◽  
Optimization Problems ◽  
Surrogate Models ◽  
Optimization Techniques ◽  
Optimization Process ◽  
Multiple Model ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Costly Function ◽  
Selection Of

Multi-objective optimization problems (MOOP) involve minimization of more than one objective functions and all of them are to be simultaneously minimized. The solution of these problems involves a large number of iterations. The multi- objective optimization problems related structural optimization of complex engineering structures is usually solved with finite element analysis (FEA). The solution time required to solve these FEA based solutions are very high. So surrogate models or meta- models are used to approximate the finite element solution during the optimization process. These surrogate assisted multi- objective optimization techniques are very commonly used in the current literature. These optimization techniques use evolutionary algorithm and it is very difficult to guarantee the convergence of the final solution, especially in the cases where the budget of costly function evaluations is low. In such cases, it is required to increase the efficiency of surrogate models in terms of accuracy and total efforts required to find the final solutions.In this paper, an advanced surrogate assisted multi- objective optimization algorithm (ASMO) is developed. This algorithm can handle linear, equality and non- linear constraints and can be applied to both benchmark and engineering application problems. This algorithm does not require any prior knowledge for the selection of surrogate models. During the optimization process, best single and mixture surrogate models are automatically selected. The advanced surrogate models are created by MATSuMoTo, the MATLAB based tool box. These mixture models are built by Dempster- Shafer theory (DST). This theory has a capacity to handle multiple model characteristics for the selection of best models. By adopting this strategy, it is ensured that most accurate surrogate models are selected. There can be different kind of surrogate models for objective and constraint functions. Multi-objective optimization of machine tool spindle is studied as the test problem for this algorithm and it is observed that the proposed strategy is able to find the non- dominated solutions with minimum number of costly function evaluations. The developed method can be applied to other benchmark and engineering applications.

Efficient Computation of Probabilistic Dominance in Multi-objective Optimization

2021 ◽  
Vol 1 (4) ◽  
pp. 1-26
Author(s):  
Faramarz Khosravi ◽  
Alexander Rass ◽  
Jürgen Teich
Keyword(s):  
Optimization Problems ◽  
Statistical Tests ◽  
Optimization Techniques ◽  
Simultaneous Optimization ◽  
Sampled Data ◽  
Efficient Computation ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Conflicting Objectives ◽  
Comparison Operator

Real-world problems typically require the simultaneous optimization of multiple, often conflicting objectives. Many of these multi-objective optimization problems are characterized by wide ranges of uncertainties in their decision variables or objective functions. To cope with such uncertainties, stochastic and robust optimization techniques are widely studied aiming to distinguish candidate solutions with uncertain objectives specified by confidence intervals, probability distributions, sampled data, or uncertainty sets. In this scope, this article first introduces a novel empirical approach for the comparison of candidate solutions with uncertain objectives that can follow arbitrary distributions. The comparison is performed through accurate and efficient calculations of the probability that one solution dominates the other in terms of each uncertain objective. Second, such an operator can be flexibly used and combined with many existing multi-objective optimization frameworks and techniques by just substituting their standard comparison operator, thus easily enabling the Pareto front optimization of problems with multiple uncertain objectives. Third, a new benchmark for evaluating uncertainty-aware optimization techniques is introduced by incorporating different types of uncertainties into a well-known benchmark for multi-objective optimization problems. Fourth, the new comparison operator and benchmark suite are integrated into an existing multi-objective optimization framework that features a selection of multi-objective optimization problems and algorithms. Fifth, the efficiency in terms of performance and execution time of the proposed comparison operator is evaluated on the introduced uncertainty benchmark. Finally, statistical tests are applied giving evidence of the superiority of the new comparison operator in terms of \epsilon -dominance and attainment surfaces in comparison to previously proposed approaches.

scholarly journals A Decomposition-Based Interactive Method for Multi-Objective Evolutionary Algorithm

2012 ◽  
Author(s):  
Nguye Long ◽  
Bui Thu Lam
Keyword(s):  
Optimization Problems ◽  
Decision Makers ◽  
Optimization Process ◽  
Multi Objective Optimization ◽  
Interactive Method ◽  
Multi Objective ◽  
Pareto Optimal Set ◽  
Single Solution ◽  
Optimal Set

Multi-objectivity has existed in many real-world optimization problems. In most multi-objective cases, objectives are often conflicting, there is no single solution being optimal with regards to all objectives. These problems are called Multi-objective Optimization Problems (MOPs). To date, there have been al large number of methods for solving MOPs including evolutionary methods (namly Multi-objective Evolutionary Algorithms MOEAs). With the use of a population of solutions for searching. MOEAs are naturally suitable for approximating optimal solutions (called the Pareto Optimal Set (POS) or the efficient set). There has been a popular trend in MOEAs considering the role of Decision Makers (DMs) during the optimization process (known as the human-in-loop) for checking, analyzing the results and giving the preference to guide the optimization process. This is call the interactive method.

scholarly journals An Overview of Few Nature Inspired Optimization Techniques and Its Reliability Applications

2020 ◽  
Vol 5 (4) ◽  
pp. 732-743
Author(s):  
Nitin Uniyal ◽  
Sangeeta Pant ◽  
Anuj Kumar
Keyword(s):  
Optimization Problems ◽  
Optimization Techniques ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Research Fields ◽  
Research Problems ◽  
Nature Inspired Algorithms ◽  
New Algorithms ◽  
Single Objective

Optimization has been a hot topic due to its inevitably in the development of new algorithms in almost every applied branch of Mathematics. Despite the broadness of optimization techniques in research fields, there is always an open scope of further refinement. We present here an overview of nature-inspired optimization with a subtle background of fundamentals and classification and their reliability applications. An attempt has been made to exhibit the contrast nature of multi objective optimization as compared to single objective optimization. Though there are various techniques to achieve the optimality in optimization problems but nature inspired algorithms have proved to be very efficient and gained special attention in modern research problems. The purpose of this article is to furnish the foundation of few nature inspired optimization techniques and their reliability applications to an interested researcher.

A Manufacturing Oriented Single Point Search Hyper-Heuristic Scheme for Multi-Objective Optimization

2017 ◽  
Author(s):  
Pei Cao ◽  
Zhaoyan Fan ◽  
Robert Gao ◽  
Jiong Tang
Keyword(s):  
Simulated Annealing Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Single Point ◽  
Optimization Techniques ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Practical Applications ◽  
Multi Objective ◽  
Point Search

Multi-objective optimization problems are frequently encountered in engineering analyses. Optimization techniques in practical applications are devised and evaluated mostly for specific problems, and thus may not be generally applicable when applications vary. In this study we formulate a probability matching based hyper-heuristic scheme, then propose four low-level heuristics which can work coherently with the single point search algorithm MOSA/R (Multi-Objective Simulated Annealing Algorithm based on Re-pick) towards multi-objective optimization problems of various properties, namely DTLZ and UF test instances. Making use of the domination amount, crowding distance and hypervolume calculations, the hyper-heuristic scheme could meet different optimization requirements. The approach developed (MOSA/R-HH) exhibits better and more robust performance compared to AMOSA, NSGA-II and MOEA/D as illustrated in the numerical tests. The outcome of this research may potentially benefit various design and manufacturing practices.

scholarly journals An Improved Multi-Objective Workflow Scheduling Using NSPSO With Fuzzy Rules

2021 ◽  
Author(s):  
SOMA PRATHIBHA ◽  
B. Latha ◽  
V. Vijaykumar
Keyword(s):  
Optimization Problems ◽  
Optimization Techniques ◽  
Energy Reduction ◽  
Workflow Scheduling ◽  
Biological Applications ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Learning Capabilities ◽  
Workload Allocation ◽  
Different Dimensions

Abstract Lot of scientific problems in various domains from modelling sky as mosaics to understand Genome sequencing in biological applications are modelled as workflows with large number of interconnected tasks. Particle Swarm Optimization (PSO) based metaheuristics are currently used to address many optimization problems as they are simple to implement and able to produce quickly optimal or sub-optimal solutions based on learning capabilities. Even though many works are cited in the literature on workflow scheduling, most of the existing works are focused on reducing the makespan alone. Moreover, energy efficiency is considered only in few works included in the literature. Constraints about the dynamic workload allocation are not introduced in the existing systems. Moreover, the optimization techniques used in the existing systems have improved the QoS with little scalability in the cloud environment since they consider only the infrastructure as the service model.In this work a new algorithm has been proposed based on the proposal of a new Multi-Objective Optimization model called F-NSPSO using NSPSO Meta-Heuristic s. This method allows the user to choose a suitable configuration dynamically. An average of above 15% in the energy reduction for the proposed system over simple DVFS was achieved for all types of workflow applications with different dimensions. Similarly when compared to NSPSO an energy reduction of at least 10% has been observed for F-NSPSO for all three types of workflow applications. Compared to NSPSO algorithm F-NSPSO algorithm shows at least 13%, 12% and 21% improvement in average makespan for Montage, Cybershake and Epigenomics workflow applications respectively.

scholarly journals Adjusting normalization bounds to improve hypervolume based search for expensive multi-objective optimization

2021 ◽  
Author(s):  
Bing Wang ◽  
Hemant Kumar Singh ◽  
Tapabrata Ray
Keyword(s):  
Numerical Experiments ◽  
Optimization Problems ◽  
Surrogate Models ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Promising Candidate ◽  
Multi Objective ◽  
Improved Performance

AbstractWhen solving expensive multi-objective optimization problems, surrogate models are often used to reduce the number of true evaluations. Based on predictions from the surrogate models, promising candidate solutions, also referred to as infill solutions, can be identified for evaluation to expedite the search towards the optimum. This infill process in turn involves optimization of certain criteria derived from the surrogate models. In this study, predicted hypervolume maximization is considered as the infill criterion for expensive multi/many-objective optimization. In particular, we examine the effect of normalization bounds on the performance of the algorithm building on our previous study on bi-objective optimization. We propose a more scalable approach based on “surrogate corner” search that shows improved performance where some of the conventional techniques face challenges. Numerical experiments on a range of benchmark problems with up to 5 objectives demonstrate the efficacy and reliability of the proposed approach.

Collaborative Optimization of Excavator Boom Mechanism Parameters under Multiple Loading Conditions

2013 ◽  
Vol 655-657 ◽  
pp. 390-395
Author(s):  
Guang Qiu Yin ◽  
Shu He Zheng ◽  
Shu Wen Lin
Keyword(s):  
Optimization Problems ◽  
Optimization Technique ◽  
Systems Design ◽  
Optimization Techniques ◽  
Collaborative Optimization ◽  
Multi Objective Optimization ◽  
Design And Optimization ◽  
Multi Objective ◽  
Coupling System ◽  
Multiple Loading

On the base of explaining Multi-Objective Optimization Problems (MOOP) and Collaborative Optimization Techniques (COT), this paper puts forward an original and efficient approach—Collaborative Optimization Technique for Multi-Objective Optimization Problems (COTMOOP)—which combines Collaborative Optimization (CO) techniques and Evolutionary Algorithms (EAs). It has been developed so as to facilitate the organizations and increase the performances of complex coupling systems design and optimization. The newly method has been succeeded in applying to the design and optimization of excavator boom mechanism that is a complex coupling system. The optimal solutions can prove that the approach is efficient and practical.

scholarly journals An Improved Multi-Objective Evolutionary Approach for Aerospace Shell Production Scheduling Problem

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 509
Author(s):  
Qing Wang ◽  
Xiaoshuang Wang ◽  
Haiwei Luo ◽  
Jian Xiong
Keyword(s):  
Evolutionary Algorithm ◽  
Production Scheduling ◽  
Production Line ◽  
Optimization Problems ◽  
Structural Features ◽  
Optimization Process ◽  
Scheduling Problems ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Shell Production

To certain degree, multi-objective optimization problems obey the law of symmetry, for instance, the minimum of one objective function corresponds to the maximum of another objective. To provide effective support for the multi-objective operation of the aerospace product shell production line, this paper studies multi-objective aerospace shell production scheduling problems. Firstly, a multi-objective optimization model for the production scheduling of aerospace product shell production lines is established. In the presented model, the maximum completion time and the cost of production line construction are optimized simultaneously. Secondly, to tackle the characteristics of discreteness, non-convexity and strong NP difficulty of the multi-objective problem, a knowledge-driven multi-objective evolutionary algorithm is designed to solve the problem. In the proposed approach, structural features of the scheduling plan are extracted during the optimization process and used to guide the subsequent optimization process. Finally, a set of test instances is generated to illustrate the addressed problem and test the proposed approach. The experimental results show that the knowledge-driven multi-objective evolutionary algorithm designed in this paper has better performance than the two classic multi-objective optimization methods.

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