# Multi Objective Design Optimization of Machine Elements using Modified NSGA

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#### Multi Objective Design Optimization of Machine Elements using Modified NSGA

Mr.P.Karunakaran

Department of Mechanical Engineering Sri Krishna College of Technology Coimbatore, India

Dr.R.Saravanan, M.E., Ph.D., Department of Mechanical Engineering Sri Krishna College of Technology Coimbatore, India

AbstractThis paper presents the modified Non-dominated Sorting Genetic Algorithm technique for multi objective design optimization of 2-bar truss design and simple gear train. The modified algorithm reduces computational time and effort as compared to original algorithm.

KeywordsDesign; Optimization; Genetic Algorithm; NSGA; 2-bar truss; Simple Gear train

1. INTRODUCTION TO OPTIMIZATION

Achieving products with minimum cost and maximum quality is one of the challenges in industries. Optimization can be defined as the process of finding the conditions that give the maximum or minimum value of a function. In addition to the functional requirement if certain objective function is considered then it is called optimum design. Minimizing the effort required or Maximizing the benefits or Combination of both are the examples of optimization. Optimization techniques are used to find the maximum or minimum value of a function.

x(1) is strictly better than x(2) in at least one objective Examples:

3 dominates 2

3 does not dominate 5

2. OPTIMIZATION TECHNIQUES

1. Genetic / Evolutionary Algorithm (Non-Conventional Method)

Genetic algorithms are a part of evolutionary computing,

which is a rapidly growing area of artificial intelligence. As you can guess, genetic algorithms are inspired by Darwin's theory about evolution. Simply said, solution to a problem solved by genetic algorithms is evolved. Genetic Algorithms mimic the principles of natural genetics.

Genetic operators are reproduction, crossover and mutation. During reproduction, first occurs recombination. Genes from parents form in some way the whole new chromosome. Crossover selects genes from parent chromosomes and creates a new offspring. The simplest way how to do this is to choose randomly some crossover point and everything before this point copy from a first parent and then everything after a crossover point copy from the second parent. After a crossover is performed, mutation takes place. This is to prevent falling all solutions in population into a local optimum of solved problem. Mutation changes randomly the new offspring.

2. Non-dominated Sorting Genetic Algorithm

Relates to the concept of domination x(1) dominates x(2), if

x(1) is no worse than x(2) in all objectives

P=Non-dominated (P) Solutions which are not dominated by any member of the set P

Pareto-Optimal set = Non-dominated(S) A number of solutions are optimal

Elites are preserved, Non-dominated solutions are emphasized and NSGA-II can extract Pareto-optimal frontier

3. TWO-BAR TRUSS DESIGN

The Objective of 2-bar truss design is to minimize the volume and minimize stresses in each of the two members.

Optimized solutions obtained using the NSGA and NSGA-II

NSGA-II solutions range (0.00407 m3, 99755 kPa) and (0.05304 m3, 8439 kPa).

4. GEAR TRAIN DESIGN

The objective of gear train design is to minimize the error between the obtained gear ratio and a required gear ratio of 1/6.931.

Design Variables (x1,x2,x3,x4) = (Td,Tb,Ta,Tf).

Optimized solutions obtained using the NSGA and NSGA-II

NSGA-II solutions range

5. PROPOSED ALGORITHM

The multiple objectives of the design problem will formulated as combined objective function. By minimizing the combined objective function the computational time and effort will be reduced as compared to original algorithm.

Formulation of COF

COF = (OF1/MOF1)*WFN + (OF2/MOF2)*WFN

Where,

COF = Combined Objective Function OF = Objective Function

MOF = Maximum of Objective Function WFN = Weightage for Normalization

6. RESULTS

C Language coding obtained from Kanpur Genetic Algorithms Lab used to solve the design problems. The Optimized results will be compared with NSGA-II results.

7. FUTURE SCOPE

This modified Non-dominated Sorting Genetic Algorithm can be applied to solve complex engineering problems and real time engineering problems in order to obtain optimum results.

8. REFERENCES

1. Kalyanmoy Deb, Amrit Pratap, and Subrajyoti Moitra Mechanical Component Design for Multiple Objectives Using Elitist Non-Dominated Sorting GA Technical Report No. 200002

2. Rajkumar Roy, Srichand Hinduja, Roberto Teti Recent advances in engineering design optimisation: Challenges and future trends 57 (2008) 697715

3. Aimin Zhou, Bo-Yang Qu, Hui Li, Shi-Zheng Zhao, Ponnuthurai Nagaratnam Suganthan , Qingfu Zhang Multiobjective evolutionary algorithms: A survey of the state of the art 1 (2011) 3249

4. Yusliza Yusoff, Mohd Salihin Ngadiman, Azlan Mohd Zain Overview of NSGA-II for Optimizing Machining Process Parameter 15 ( 2011 ) 3978 3983

5. Dongho Jeong, Jongsoo Lee

Electrode design optimization of lithium secondary batteries to enhance adhesion and deformation capabilities 75 (2014) 525

533

6. Biswesh R.Acharya, Chinmaya P.Mohanty, S.S.Mahapatra

Multi-objective Optimization of Electrochemical Machining of Hardened Steel Using NSGA II

51 ( 2013 ) 554 560