Multi-Objective Optimization of Modified Cycloidal-Toothed Gerotor Pumps by Genetic Algorithm

2019 ◽  
Author(s):  
Andrew J. Robison ◽  
Andrea Vacca
Keyword(s):  
Contact Stress ◽  
Performance Metrics ◽  
Radius Of Curvature ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Flow Ripple ◽  
Multi Objective ◽  
Profile Type ◽  
Radial Gap

Abstract Cycloidal-toothed gerotors are formed by the combination of epicycloid and a hypocyloid arcs that use the pitch circles as their base circles. They are a common profile type used in industry likely because they can be generated by simple parametric equations. One of the problems with the cycloidal-toothed profile type is that the radius of curvature of both the inner and outer gear are zero when the gears contact at the pitch point which can lead to high contact stress. A gear generation algorithm has been developed that modifies the hypocycloid tooth form to eliminate contact in regions with very low radii of curvature that is yet to be described in scientific literature. Seven performance metrics are developed to evaluate size, flow ripple, adhesive wear, contact stress, radial gap leakage, lateral gap leakage, and inlet throttling that are used as objective functions in a multi-objective optimization. The pump geometry is optimized by applying the NSGA-II algorithm with a population size of 1000 for 500 generations to produce a pareto front, and the results are compared to two cycloidal-toothed gerotors used in the automotive industry. Two designs were found that significantly reduce the contact stress in the profiles while giving the same performance in the other six objective functions in comparison to the profiles used in industry. Another two designs are found that can significantly reduce several objective functions if the size of the pump can be increased slightly.

Kinematic Multi-Objective Optimization of Circular-Toothed Gerotor Pumps by Genetic Algorithm

2017 ◽  
Author(s):  
Andrew J. Robison ◽  
Andrea Vacca
Keyword(s):  
Genetic Algorithm ◽  
Design Method ◽  
Third Party ◽  
Low Flow ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Generation Algorithm ◽  
Multi Objective ◽  
Pareto Curve

A gerotor gear generation algorithm has been developed that evaluates key performance objective functions to be minimized or maximized, and then an optimization algorithm is applied to determine the best design. Because of their popularity, circular-toothed gerotors are the focus of this study, and future work can extend this procedure to other gear forms. Parametric equations defining the circular-toothed gear set have been derived and implemented. Two objective functions were used in this kinematic optimization: maximize the ratio of displacement to pump radius, which is a measure of compactness, and minimize the kinematic flow ripple, which can have a negative effect on system dynamics and could be a major source of noise. Designs were constrained to ensure drivability, so the need for additional synchronization gearing is eliminated. The NSGA-II genetic algorithm was then applied to the gear generation algorithm in modeFRONTIER, a commercial software that integrates multi-objective optimization with third-party engineering software. A clear Pareto front was identified, and a multi-criteria decision-making genetic algorithm was used to select three optimal designs with varying priorities of compactness vs low flow variation. In addition, three pumps used in industry were scaled and evaluated with the gear generation algorithm for comparison. The scaled industry pumps were all close to the Pareto curve, but the optimized designs offer a slight kinematic advantage, which demonstrates the usefulness of the proposed gerotor design method.

Multi-Objective Evolutionary Algorithms

2016 ◽  
pp. 301-345
Author(s):  
A. K. Nandi ◽  
K. Deb
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Optimization Problem ◽  
Performance Metrics ◽  
Research Work ◽  
Primary Objective ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Mould Material ◽  
Multi Objective

The primary objective in designing appropriate particle reinforced polyurethane composite which will be used as a mould material in soft tooling process is to minimize the cycle time of soft tooling process by providing faster cooling rate during solidification of wax/plastic component. This chapter exemplifies an effective approach to design particle reinforced mould materials by solving the inherent multi-objective optimization problem associated with soft tooling process using evolutionary algorithms. In this chapter, first a brief introduction of multi-objective optimization problem with the key issues is presented. Then, after a short overview on the working procedure of genetic algorithm, a well- established multi-objective evolutionary algorithm, namely NSGA-II along with various performance metrics are described. The inherent multi-objective problem in soft tooling process is demonstrated and subsequently solved using an elitist non-dominated sorting genetic algorithm, NSGA-II. Multi-objective optimization results obtained using NSGA-II are analyzed statistically and validated with real industrial application. Finally the fundamental results of this approach are summarized and various perspectives to the industries along with scopes for future research work are pointed out.

scholarly journals MULTI-OBJECTIVE OPTIMIZATION OF REINFORCED CONCRETE FRAMES USING NSGA-II ALGORITHM

2016 ◽  
Vol 8 (4) ◽  
pp. 157-164 ◽  
Author(s):  
Mehdi Babaei ◽  
Masoud Mollayi
Keyword(s):  
Genetic Algorithm ◽  
Reinforced Concrete ◽  
Steel Structures ◽  
American Concrete Institute ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Design Variables ◽  
Pareto Fronts

In recent decades, the use of genetic algorithm (GA) for optimization of structures has been highly attractive in the study of concrete and steel structures aiming at weight optimization. However, it has been challenging for multi-objective optimization to determine the trade-off between objective functions and to obtain the Pareto-front for reinforced concrete (RC) and steel structures. Among different methods introduced for multi-objective optimization based on genetic algorithms, Non-Dominated Sorting Genetic Algorithm II (NSGA II) is one of the most popular algorithms. In this paper, multi-objective optimization of RC moment resisting frame structures considering two objective functions of cost and displacement are introduced and examined. Three design models are optimized using the NSGA-II algorithm. Evaluation of optimal solutions and the algorithm process are discussed in details. Sections of beams and columns are considered as design variables and the specifications of the American Concrete Institute (ACI) are employed as the design constraints. Pareto-fronts for the objective space have been obtained for RC frame models of four, eight and twelve floors. The results indicate smooth Pareto-fronts and prove the speed and accuracy of the method.

Multi-Objective Evolutionary Algorithms

2017 ◽  
pp. 185-229
Author(s):  
A. K. Nandi ◽  
K. Deb
Keyword(s):  
Genetic Algorithm ◽  
Evolutionary Algorithms ◽  
Optimization Problem ◽  
Performance Metrics ◽  
Research Work ◽  
Primary Objective ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Mould Material ◽  
Multi Objective

The primary objective in designing appropriate particle reinforced polyurethane composite which will be used as a mould material in soft tooling process is to minimize the cycle time of soft tooling process by providing faster cooling rate during solidification of wax/plastic component. This chapter exemplifies an effective approach to design particle reinforced mould materials by solving the inherent multi-objective optimization problem associated with soft tooling process using evolutionary algorithms. In this chapter, first a brief introduction of multi-objective optimization problem with the key issues is presented. Then, after a short overview on the working procedure of genetic algorithm, a well- established multi-objective evolutionary algorithm, namely NSGA-II along with various performance metrics are described. The inherent multi-objective problem in soft tooling process is demonstrated and subsequently solved using an elitist non-dominated sorting genetic algorithm, NSGA-II. Multi-objective optimization results obtained using NSGA-II are analyzed statistically and validated with real industrial application. Finally the fundamental results of this approach are summarized and various perspectives to the industries along with scopes for future research work are pointed out.

scholarly journals LAND-USE PLANNING FOR SUSTAINABLE URBAN DEVELOPMENT IN AFRICA: A SPATIAL AND MULTI-OBJECTIVE OPTIMIZATION APPROACH

2019 ◽  
Vol 45 (5) ◽  
pp. 1-15 ◽  
Author(s):  
Alex Lubida ◽  
Mozafar Veysipanah ◽  
Petter Pilesjo ◽  
Ali Mansourian
Keyword(s):  
Land Use ◽  
Land Use Planning ◽  
Geographical Information ◽  
Sustainable Urban Development ◽  
Optimization Approach ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
The City

Land-use planning, which requires finding a balance among different conflicting social, economic and environment factors, is a complex task needed everywhere, including Africa. One example is the city of Zanzibar in Tanzania, which is under special consideration for land-use revision. From one side, the city has high potentials for tourist industry and at the other side there are major challenges with the city structure and poor accessibilities. In order to prepare a proper land-use plan for the city, a variety of influencing conflicting factors needs to be considered and satisfied. This can be regarded as a common problem in many African cities, which are under development. This paper aims to address the problem by proposing and demonstrating the use of Geographical Information System (GIS) and multi-objective optimization for land-use planning, in Zanzibar as a case study. The measures which have been taken by Zanzibar government to address the development challenges through the Zanzibar Strategy for Growth and Reduction of Poverty (ZSGRP) were identified by studying related documents and interviewing experts. Based on these, two objective functions were developed for land-use planning. Optimum base land-use plans were developed and mapped by optimizing the objective functions using the NSGA-II algorithm. The results show that the proposed approach and outputs can considerably facilitate land-use planning in Zanzibar. Similar approaches are highly recommended for other cities in Africa which are under development.

scholarly journals A New Evolutionary Approach to Optimal Sensor Placement in Water Distribution Networks

Water ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 1625
Author(s):  
Andrea Ponti ◽  
Antonio Candelieri ◽  
Francesco Archetti
Keyword(s):  
Water Distribution ◽  
Sensor Placement ◽  
Distribution Networks ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Genetic Operators ◽  
Placement Problem ◽  
Nsga Ii ◽  
Multi Objective ◽  
Dynamic Representation

The sensor placement problem is modeled as a multi-objective optimization problem with Boolean decision variables. A new multi objective evolutionary algorithm (MOEA) is proposed for approximating and analyzing the set of Pareto optimal solutions. The evaluation of the objective functions requires the execution of a hydraulic simulation model of the network. To organize the simulation results a data structure is proposed which enables the dynamic representation of a sensor placement and its fitness as a heatmap. This allows the definition of information spaces, in which the fitness of a placement can be represented as a matrix or, in probabilistic terms as a histogram. The key element in the new algorithm is this probabilistic representation which is embedded in a space endowed with a metric based on a specific notion of distance. Among several distances between probability distributions the Wasserstein (WST) distance has been selected: WST has enabled to derive new genetic operators, indicators of the quality of the Pareto set and criteria to choose among the Pareto solutions. The new algorithm has been tested on a benchmark water distribution network with two objective functions showing an improvement over NSGA-II, in particular for low generation counts, making it a good candidate for expensive black-box multi-objective optimization

Multi-objective Optimization for Common and Special Components: First Step Toward Network Optimization of Regular and Non-Regular Flights

2015 ◽  
Vol 11 (02) ◽  
pp. 183-199
Author(s):  
Takahiro Jinba ◽  
Hiroto Kitagawa ◽  
Eriko Azuma ◽  
Keiji Sato ◽  
Hiroyuki Sato ◽  
...  
Keyword(s):  
Optimization Method ◽  
High Rate ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Test Bed ◽  
Nsga Ii ◽  
Multi Objective ◽  
The Common ◽  
Airline Company ◽  
Common Components

To optimize the problem composed of (i) the common components which should be optimized from the viewpoint of all objective functions and (ii) the special components which should be optimized from the viewpoint of one of the objective functions, this paper proposes a new multi-objective optimization method which optimizes not only the common components for all objective functions but also the special ones for each objective function. To investigate the effectiveness of the proposed method, this paper tested our method on the test-bed problem which is an extended version of the 0/1 knapsack problem. The intensive experiments have revealed the following implications: (i) Our method finds better solutions which have higher fitness than the conventional method (NSGA-II); (ii) our method can find the solutions that had a large norm (which corresponds to a high profit of an airline company in the flight scheduling problem) with the high rate of the common components; and (iii) since the crowding distance employed in our method contributes to keeping the diversity during the solution search, our method has high exploration capability of solutions.

A Novel Hybrid Multi-Objective Population Migration Algorithm

2015 ◽  
Vol 29 (01) ◽  
pp. 1559001 ◽  
Author(s):  
Aijia Ouyang ◽  
Kenli Li ◽  
Xiongwei Fei ◽  
Xu Zhou ◽  
Mingxing Duan
Keyword(s):  
Optimization Problems ◽  
Population Migration ◽  
Mutation Operator ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
Nsga Ii ◽  
Multi Objective ◽  
Good Point ◽  
Point Set ◽  
Good Point Set

This paper presents a multi-objective co-evolutionary population migration algorithm based on Good Point Set (GPSMCPMA) for multi-objective optimization problems (MOP) in view of the characteristics of MOPs. The algorithm introduces the theory of good point set (GPS) and dynamic mutation operator (DMO) and adopts the entire population co-evolutionary migration, based on the concept of Pareto nondomination and global best experience and guidance. The performance of the algorithm is tested through standard multi-objective functions. The experimental results show that the proposed algorithm performs much better in the convergence, diversity and solution distribution than SPEA2, NSGA-II, MOPSO and MOMASEA. It is a fast and robust multi-objective evolutionary algorithm (MOEA) and is applicable to other MOPs.

scholarly journals A New Approach to Group Multi-Objective Optimization under Imperfect Information and Its Application to Project Portfolio Optimization

2021 ◽  
Vol 11 (10) ◽  
pp. 4575
Author(s):  
Eduardo Fernández ◽  
Nelson Rangel-Valdez ◽  
Laura Cruz-Reyes ◽  
Claudia Gomez-Santillan
Keyword(s):  
Portfolio Optimization ◽  
Imperfect Information ◽  
Model Parameters ◽  
Final Decision ◽  
Project Portfolio ◽  
Objective Functions ◽  
Multi Objective Optimization ◽  
New Approach ◽  
Multi Objective ◽  
Group Member

This paper addresses group multi-objective optimization under a new perspective. For each point in the feasible decision set, satisfaction or dissatisfaction from each group member is determined by a multi-criteria ordinal classification approach, based on comparing solutions with a limiting boundary between classes “unsatisfactory” and “satisfactory”. The whole group satisfaction can be maximized, finding solutions as close as possible to the ideal consensus. The group moderator is in charge of making the final decision, finding the best compromise between the collective satisfaction and dissatisfaction. Imperfect information on values of objective functions, required and available resources, and decision model parameters are handled by using interval numbers. Two different kinds of multi-criteria decision models are considered: (i) an interval outranking approach and (ii) an interval weighted-sum value function. The proposal is more general than other approaches to group multi-objective optimization since (a) some (even all) objective values may be not the same for different DMs; (b) each group member may consider their own set of objective functions and constraints; (c) objective values may be imprecise or uncertain; (d) imperfect information on resources availability and requirements may be handled; (e) each group member may have their own perception about the availability of resources and the requirement of resources per activity. An important application of the new approach is collective multi-objective project portfolio optimization. This is illustrated by solving a real size group many-objective project portfolio optimization problem using evolutionary computation tools.

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