An Information-Theoretic Entropy Metric for Assessing Multi-Objective Optimization Solution Set Quality

2003 ◽  
Vol 125 (4) ◽  
pp. 655-663 ◽  
Author(s):  
Ali Farhang-Mehr ◽  
Shapour Azarm
Keyword(s):  
Evolutionary Algorithms ◽  
Pareto Frontier ◽  
Optimization Techniques ◽  
Solution Set ◽  
Multi Objective Optimization ◽  
Information Theoretic ◽  
Multi Objective ◽  
Speed Reducer ◽  
Quantitative Basis

An entropy-based metric is presented that can be used for assessing the quality of a solution set as obtained from multi-objective optimization techniques. This metric quantifies the “goodness” of a set of solutions in terms of distribution quality over the Pareto frontier. The metric can be used to compare the performance of different multi-objective optimization techniques. In particular, the metric can be used in analysis of multi-objective evolutionary algorithms, wherein the capabilities of such techniques to produce and maintain diversity among different solution points are desired to be compared on a quantitative basis. An engineering test example, the multi-objective design optimization of a speed-reducer, is provided to demonstrate an application of the proposed entropy metric.

On the Entropy of Multi-Objective Design Optimization Solution Sets

2002 ◽  
Author(s):  
Ali Farhang-Mehr ◽  
Shapour Azarm
Keyword(s):  
Design Optimization ◽  
Optimization Technique ◽  
Optimization Techniques ◽  
Pareto Optimal ◽  
Multi Objective Optimization ◽  
Solution Sets ◽  
Multi Objective ◽  
Speed Reducer ◽  
Quantitative Basis ◽  
Multiobjective Design

In this paper, an entropy-based metric is presented for quality assessment of non-dominated solution sets obtained from a multiobjective optimization technique. This metric quantifies the ‘goodness’ of a solution set in terms of its distribution quality over the Pareto-optimal frontier. Therefore, it can be useful in comparison studies of different multi-objective optimization techniques, such as Multi-Objective Genetic Algorithms (MOGAs), wherein the capabilities of such techniques to produce and maintain diversity among different solution points are desired to be compared on a quantitative basis. An engineering test example, the multiobjective design optimization of a speed-reducer, is presented in order to demonstrate an application of the proposed entropy metric.

IMPROVING THE PERFORMANCE OF MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS USING THE ISLAND PARALLEL MODEL

2007 ◽  
Vol 17 (02) ◽  
pp. 127-139 ◽  
Author(s):  
A. MÁRQUEZ ◽  
C. GIL ◽  
R. BAÑOS ◽  
J. GÓMEZ
Keyword(s):  
Parallel Processing ◽  
Evolutionary Algorithms ◽  
Population Size ◽  
Test Problems ◽  
Pareto Optimal ◽  
Parallel Model ◽  
Multi Objective Optimization ◽  
Pareto Optimal Front ◽  
Multi Objective

Recently, the research interest in multi-objective optimization has increased remarkably. Most of the proposed methods use a population of solutions that are simultaneously improved trying to approximate them to the Pareto-optimal front. When the population size increases, the quality of the solutions tends to be better, but the runtime is higher. This paper presents how to apply parallel processing to enhance the convergence to the Pareto-optimal front, without increasing the runtime. In particular, we present an island-based parallelization of five multi-objective evolutionary algorithms: NSGAII, SPEA2, PESA, msPESA, and a new hybrid version we propose. Experimental results in some test problems denote that the quality of the solutions tends to improve when the number of islands increases.

Multi-Objective Optimization Evolutionary Algorithms in Insurance-Linked Derivatives

2007 ◽  
pp. 885-908 ◽  
Author(s):  
M. J. Perez
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Procedure ◽  
Real Data ◽  
Optimization Techniques ◽  
Insurance Companies ◽  
Claim Amount ◽  
Loss Ratio ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Catastrophic Loss

This work addresses a real-world adjustment of economic models where the application of robust and global optimization techniques is required. The problem dealt with is the search for a set of parameters to calculate the reported claim amount. Several functions are proposed to obtain the reported claim amount, and a multi-objective optimization procedure is used to obtain parameters using real data and to decide the best function to approximate the reported claim amount. Using this function, insurance companies negotiate the underlying contract—that is, the catastrophic loss ratio defined from the total reported claim amount. They are associated with catastrophes that occurred during the loss period and declared until the development period expired. The suitability of different techniques coming from evolutionary computation (EC) to solve this problem is explored, contrasting the performance achieved with recent proposals of multi-objective evolutionary algorithms (MOEAs). Results show the advantages of MOEAs in the proposal in terms of effectiveness and completeness in searching for solutions, compared with particular solutions of classical EC approaches (using an aggregation operator) in problems with real data.

Multi-objective optimization of the cascade parameters of a torque converter based on CFD and a genetic algorithm

2021 ◽  
pp. 095440702098055
Author(s):  
Zilin Ran ◽  
Wenxing Ma ◽  
Chunbao Liu ◽  
Jing Li
Keyword(s):  
Genetic Algorithm ◽  
Flow Field ◽  
Surrogate Model ◽  
High Efficiency ◽  
Cfd Simulation ◽  
Pareto Frontier ◽  
Torque Converter ◽  
Solution Set ◽  
Multi Objective Optimization ◽  
Multi Objective

It is hard to simultaneously improve the peak efficiency (η *) and the width of the high-efficiency region ( Gη) for a hydrodynamic torque converter. A combination of comprehensive CFD simulation and multi-objective optimization was pretested. The elaborate CFD simulation calculation included a reasonable mesh layout, a robust algorithm and a correct turbulence model, whose results were also experimentally verified. In our study, the Kriging surrogate model was first used to construct a nonlinear relationship between the inlet and outlet angle and the economic performance index of the hydrodynamic torque converter. To ensure that the accuracy of the surrogate model meet the requirements, we also used 10 sets of sample points to verify the accuracy of our surrogate model. The accuracy is found to meet the requirements, which shows that the accuracy of the constructed surrogate model is relatively high. We choose to apply the second-generation non-dominant sorting genetic algorithm (NSGA-II) to solve our problem. After solving the Pareto frontier solution set, we obtain a set of global optimal solutions on the Pareto frontier solution set. The optimization results show that the η * is increased by 2.49% and that the Gη is increased by 14.23%. We extracted the flow field structure near the turbine region, characterized the difference between original and optimal model from the flow field perspective, and demonstrated the accuracy of our optimization results. Finally, we used CFD to verify our optimization results, further illustrating the accuracy of the optimization results prediction. Literature research indicates that a large amount of experiments to optimize the η * and the Gη of the hydrodynamic torque converter will bring huge trial cost and time cost. We conclude from our research that the proposed calculation method can solve such problems well.

scholarly journals Multi-Objective Whale Optimization Algorithm for Computation Offloading Optimization in Mobile Edge Computing

Sensors ◽  
2021 ◽  
Vol 21 (8) ◽  
pp. 2628
Author(s):  
Mengxing Huang ◽  
Qianhao Zhai ◽  
Yinjie Chen ◽  
Siling Feng ◽  
Feng Shu
Keyword(s):  
Optimization Algorithm ◽  
Edge Computing ◽  
Solution Set ◽  
Whale Optimization Algorithm ◽  
Computation Offloading ◽  
Mobile Edge Computing ◽  
Multi Objective ◽  
Whale Optimization ◽  
Artificial Immune System Algorithm

Computation offloading is one of the most important problems in edge computing. Devices can transmit computation tasks to servers to be executed through computation offloading. However, not all the computation tasks can be offloaded to servers with the limitation of network conditions. Therefore, it is very important to decide quickly how many tasks should be executed on servers and how many should be executed locally. Only computation tasks that are properly offloaded can improve the Quality of Service (QoS). Some existing methods only focus on a single objection, and of the others some have high computational complexity. There still have no method that could balance the targets and complexity for universal application. In this study, a Multi-Objective Whale Optimization Algorithm (MOWOA) based on time and energy consumption is proposed to solve the optimal offloading mechanism of computation offloading in mobile edge computing. It is the first time that MOWOA has been applied in this area. For improving the quality of the solution set, crowding degrees are introduced and all solutions are sorted by crowding degrees. Additionally, an improved MOWOA (MOWOA2) by using the gravity reference point method is proposed to obtain better diversity of the solution set. Compared with some typical approaches, such as the Grid-Based Evolutionary Algorithm (GrEA), Cluster-Gradient-based Artificial Immune System Algorithm (CGbAIS), Non-dominated Sorting Genetic Algorithm III (NSGA-III), etc., the MOWOA2 performs better in terms of the quality of the final solutions.

Multi-objective optimization of injection-molded plastic parts using entropy weight, random forest, and genetic algorithm methods

2020 ◽  
Vol 40 (4) ◽  
pp. 360-371
Author(s):  
Yanli Cao ◽  
Xiying Fan ◽  
Yonghuan Guo ◽  
Sai Li ◽  
Haiyue Huang
Keyword(s):  
Genetic Algorithm ◽  
Random Forest ◽  
Regression Model ◽  
Process Parameters ◽  
Multi Objective Optimization ◽  
Entropy Weight ◽  
Multi Objective ◽  
Injection Molded ◽  
Plastic Parts

AbstractThe qualities of injection-molded parts are affected by process parameters. Warpage and volume shrinkage are two typical defects. Moreover, insufficient or excessively large clamping force also affects the quality of parts and the cost of the process. An experiment based on the orthogonal design was conducted to minimize the above defects. Moldflow software was used to simulate the injection process of each experiment. The entropy weight was used to determine the weight of each index, the comprehensive evaluation value was calculated, and multi-objective optimization was transformed into single-objective optimization. A regression model was established by the random forest (RF) algorithm. To further illustrate the reliability and accuracy of the model, back-propagation neural network and kriging models were taken as comparative algorithms. The results showed that the error of RF was the smallest and its performance was the best. Finally, genetic algorithm was used to search for the minimum of the regression model established by RF. The optimal parameters were found to improve the quality of plastic parts and reduce the energy consumption. The plastic parts manufactured by the optimal process parameters showed good quality and met the requirements of production.

Sign in / Sign up

Export Citation Format

Share Document