scholarly journals A New Multi-Objective Bayesian Optimization Formulation With the Acquisition Function for Convergence and Diversity

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Leshi Shu ◽  
Ping Jiang ◽  
Xinyu Shao ◽  
Yan Wang
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Bayesian Optimization ◽  
Optimization Approach ◽  
Exploration And Exploitation ◽  
Pareto Solutions ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Optimization Formulation

Abstract Bayesian optimization is a metamodel-based global optimization approach that can balance between exploration and exploitation. It has been widely used to solve single-objective optimization problems. In engineering design, making trade-offs between multiple conflicting objectives is common. In this work, a multi-objective Bayesian optimization approach is proposed to obtain the Pareto solutions. A novel acquisition function is proposed to determine the next sample point, which helps improve the diversity and convergence of the Pareto solutions. The proposed approach is compared with some state-of-the-art metamodel-based multi-objective optimization approaches with four numerical examples and one engineering case. The results show that the proposed approach can obtain satisfactory Pareto solutions with significantly reduced computational cost.

scholarly journals Shape Design Optimization of a Robot Arm Using a Surrogate-Based Evolutionary Approach

2020 ◽  
Vol 10 (7) ◽  
pp. 2223 ◽  
Author(s):  
J. C. Hsiao ◽  
Kumar Shivam ◽  
C. L. Chou ◽  
T. Y. Kam
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Shape Design ◽  
Optimization Approach ◽  
Robot Arm ◽  
Shape Design Optimization ◽  
Robot Arms ◽  
Conflicting Objectives ◽  
Computer Aided

In the design optimization of robot arms, the use of simulation technologies for modeling and optimizing the objective functions is still challenging. The difficulty is not only associated with the large computational cost of high-fidelity structural simulations but also linked to the reasonable compromise between the multiple conflicting objectives of robot arms. In this paper we propose a surrogate-based evolutionary optimization (SBEO) method via a global optimization approach, which incorporates the response surface method (RSM) and multi-objective evolutionary algorithm by decomposition (the differential evolution (DE ) variant) (MOEA/D-DE) to tackle the shape design optimization problem of robot arms for achieving high speed performance. The computer-aided engineering (CAE) tools such as CAE solvers, computer-aided design (CAD) Inventor, and finite element method (FEM) ANSYS are first used to produce the design and assess the performance of the robot arm. The surrogate model constructed on the basis of Box–Behnken design is then used in the MOEA/D-DE, which includes the process of selection, recombination, and mutation, to optimize the robot arm. The performance of the optimized robot arm is compared with the baseline one to validate the correctness and effectiveness of the proposed method. The results obtained for the adopted example show that the proposed method can not only significantly improve the robot arm performance and save computational cost but may also be deployed to solve other complex design optimization problems.

scholarly journals Comparative Study of Knee-Based Algorithms for Many-Objective Optimization Problems

2018 ◽  
Vol 12 (1) ◽  
pp. 7-16
Author(s):  
Saad M. Alzahrani ◽  
Naruemon Wattanapongsakorn
Keyword(s):  
Optimization Problems ◽  
Benchmark Problems ◽  
Multi Objective Optimization ◽  
Trade Off ◽  
Knee Region ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Small Set ◽  
Optimum Solution

Nowadays, most real-world optimization problems consist of many and often conflicting objectives to be optimized simultaneously. Although, many current Multi-Objective optimization algorithms can efficiently solve problems with 3 or less objectives, their performance deteriorates proportionally with the increasing of the objectives number. Furthermore, in many situations the decision maker (DM) is not interested in all trade-off solutions obtained but rather interested in a single optimum solution or a small set of those trade-offs. Therefore, determining an optimum solution or a small set of trade-off solutions is a difficult task. However, an interesting method for finding such solutions is identifying solutions in the Knee region. Solutions in the Knee region can be considered the best obtained solution in the obtained trade-off set especially if there is no preference or equally important objectives. In this paper, a pruning strategy was used to find solutions in the Knee region of Pareto optimal fronts for some benchmark problems obtained by NSGA-II, MOEA/D-DE and a promising new Multi-Objective optimization algorithm NSGA-III. Lastly, those knee solutions found were compared and evaluated using a generational distance performance metric, computation time and a statistical one-way ANOVA test.

Improving Multi-Objective Genetic Algorithm Efficiency for Computational Expensive Problems Adopting Online Variable-Fidelity Metamodel

2018 ◽  
Author(s):  
Leshi Shu ◽  
Ping Jiang ◽  
Qi Zhou ◽  
Xiangzheng Meng ◽  
Yahui Zhang
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Simulation Models ◽  
Pareto Solutions ◽  
Multi Objective ◽  
Algorithm Efficiency ◽  
Multi Objective Genetic Algorithm ◽  
Computation Process ◽  
Practical Engineering ◽  
Variable Fidelity

Multi-objective genetic algorithms (MOGAs) are effective ways for obtaining Pareto solutions of multi-objective optimization problems. However, the high computational cost of MOGAs limits their applications to practical engineering optimization problems involving computational expensive simulations. To address this issue, a variable-fidelity metamodel (VFM) assisted MOGA approach is proposed, in which VFM is embedded in the computation process of MOGA to replace expensive simulation models. The VFM is updated in the optimization process considering the cost of simulation models with different fidelity and the effects of the VFM uncertainty. A numerical example and an engineering case are used to demonstrate the applicability and efficiency of the proposed approach. The results show that the proposed approach can obtain Pareto solutions with high quality and it outperforms the other three existing approaches in terms of computational efficiency.

scholarly journals Lost in Optimization of Water Distribution Systems: Better Call Bayes

2022 ◽  
Author(s):  
Antonio Candelieri ◽  
Andrea Ponti ◽  
Ilaria Giordani ◽  
Francesco Archetti
Keyword(s):  
Distribution Systems ◽  
Water Distribution ◽  
Probabilistic Models ◽  
Optimization Problems ◽  
Simulation Optimization ◽  
Water Distribution Systems ◽  
Bayesian Optimization ◽  
Optimization Approach ◽  
Hydraulic Simulation ◽  
Multi Objective

The main goal of this paper is to show that Bayesian optimization could be regarded as a general framework for the data driven modelling and solution of problems arising in water distribution systems. Hydraulic simulation, both scenario based, and Monte Carlo is a key tool in modelling in water distribution systems. The related optimization problems fall in a simulation/optimization framework in which objectives and constraints are often black-box. Bayesian Optimization (BO) is characterized by a surrogate model, usually a Gaussian process, but also a random forest and increasingly neural networks and an acquisition function which drives the search for new evaluation points. These modelling options make BO nonparametric, robust, flexible and sample efficient particularly suitable for simulation/optimization problems. A defining characteristic of BO is its versatility and flexibility, given for instance by different probabilistic models, in particular different kernels, different acquisition functions. These characteristics of the Bayesian optimization approach are exemplified by the two problems: cost/energy optimization in pump scheduling and optimal sensor placement for early detection on contaminant intrusion. Different surrogate models have been used both in explicit and implicit control schemes. Showing that BO can drive the process of learning control rules directly from operational data. BO can also be extended to multi-objective optimization. Two algorithms have been proposed for multi-objective detection problem using two different acquisition functions.

scholarly journals A Comparison of Genetic Representations and Initialisation Methods for the Multi-objective Shortest Path Problem on Multigraphs

2021 ◽  
Vol 2 (3) ◽  
Author(s):  
Lilla Beke ◽  
Michal Weiszer ◽  
Jun Chen
Keyword(s):  
Shortest Path ◽  
Time Budget ◽  
Exact Algorithm ◽  
Simple Graph ◽  
Shortest Path Problem ◽  
Future Application ◽  
Multi Objective ◽  
Trade Offs ◽  
Conflicting Objectives ◽  
Problem Instances

AbstractThis paper compares different solution approaches for the multi-objective shortest path problem (MSPP) on multigraphs. Multigraphs as a modelling tool are able to capture different available trade-offs between objectives for a given section of a route. For this reason, they are increasingly popular in modelling transportation problems with multiple conflicting objectives (e.g., travel time and fuel consumption), such as time-dependent vehicle routing, multi-modal transportation planning, energy-efficient driving, and airport operations. The multigraph MSPP is more complex than the NP-hard simple graph MSPP. Therefore, approximate solution methods are often needed to find a good approximation of the true Pareto front in a given time budget. Evolutionary algorithms have been successfully applied for the simple graph MSPP. However, there has been limited investigation of their applications to the multigraph MSPP. Here, we extend the most popular genetic representations to the multigraph case and compare the achieved solution qualities. Two heuristic initialisation methods are also considered to improve the convergence properties of the algorithms. The comparison is based on a diverse set of problem instances, including both bi-objective and triple objective problems. We found that the metaheuristic approach with heuristic initialisation provides good solutions in shorter running times compared to an exact algorithm. The representations were all found to be competitive. The results are encouraging for future application to the time-constrained multigraph MSPP.

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.

Optimal Structural Design of a Heat Sink With Laminar Single-Phase Flow Using Computational Fluid Dynamics-Based Multi-Objective Genetic Algorithm

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Ya Ge ◽  
Feng Shan ◽  
Zhichun Liu ◽  
Wei Liu
Keyword(s):  
Genetic Algorithm ◽  
Heat Sink ◽  
Volumetric Flow Rate ◽  
Pareto Solutions ◽  
Nondominated Solutions ◽  
Multi Objective ◽  
Multi Objective Genetic Algorithm ◽  
Conflicting Objectives ◽  
Order Preference ◽  
General Method

This paper proposes a general method combining evolutionary algorithm and decision-making technique to optimize the structure of a minichannel heat sink (MCHS). Two conflicting objectives, the thermal resistance θ and the pumping power P, are simultaneously considered to assess the performance of the MCHS. In order to achieve the ultimate optimal design, multi-objective genetic algorithm is employed to obtain the nondominated solutions (Pareto solutions), while technique for order preference by similarity to an ideal solution (TOPSIS) is employed to determine which is the best compromise solution. Meanwhile, both the material cost and volumetric flow rate are fixed where this nonlinear problem is solved by applying the penalty function. The results show that θ of Pareto solutions varies from 0.03707 K W−1 to 0.10742 K W−1, while P varies from 0.00307 W to 0.05388 W, respectively. After the TOPSIS selection, it is found that P is significantly reduced without increasing too much θ. As a result, θ and P of the optimal MCHS determined by TOPSIS are 35.82% and 52.55% lower than initial one, respectively.

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 A Distributed Multifactorial Particle Swarm Optimization Approach

2021 ◽  
Author(s):  
Ahlem Aboud ◽  
Nizar Rokbani ◽  
Seyedali Mirjalili ◽  
Abdulrahman M. Qahtani ◽  
Omar Almutiry ◽  
...  
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Beta Function ◽  
Particle Swarm ◽  
Search Space ◽  
Optimization Approach ◽  
Multi Objective Optimization ◽  
Swarm Optimization ◽  
Multi Objective ◽  
New System

<p>Multifactorial Optimization (MFO) and Evolutionary Transfer Optimization (ETO) are new optimization challenging paradigms for which the multi-Objective Particle Swarm Optimization system (MOPSO) may be interesting despite limitations. MOPSO has been widely used in static/dynamic multi-objective optimization problems, while its potentials for multi-task optimization are not completely unveiled. This paper proposes a new Distributed Multifactorial Particle Swarm Optimization algorithm (DMFPSO) for multi-task optimization. This new system has a distributed architecture on a set of sub-swarms that are dynamically constructed based on the number of optimization tasks affected by each particle skill factor. DMFPSO is designed to deal with the issues of handling convergence and diversity concepts separately. DMFPSO uses Beta function to provide two optimized profiles with a dynamic switching behaviour. The first profile, Beta-1, is used for the exploration which aims to explore the search space toward potential solutions, while the second Beta-2 function is used for convergence enhancement. This new system is tested on 36 benchmarks provided by the CEC’2021 Evolutionary Transfer Multi-Objective Optimization Competition. Comparatives with the state-of-the-art methods are done using the Inverted General Distance (IGD) and Mean Inverted General Distance (MIGD) metrics. Based on the MSS metric, this proposal has the best results on most tested problems.</p>

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