genetic algorithm for tsp in optimizing cnc tool...

International Journal of Engineering Technology, Management and Applied Sciences

www.ijetmas.com February 2017, Volume 5, Issue 2, ISSN 2349-4476

139

Raja Chınna Karuppanan B,Saravanan M

Genetic Algorithm for TSP in Optimizing CNC Tool Path

Raja Chınna Karuppanan B,

Anna Unıversıty,Chennaı,Indıa.

Saravanan M,

Anna Unıversıty,Chennaı,Indıa

.

ABSTRACT

The optimization of CNC machining parameters is a major researcharea in which more number of research works

are done. The tool path is considered to be the most important element in CNC Machining operations. The various Tool

movement activities are studied for further improvements. Finding the optimum tool pathof a CNC Machine is

analogous to Traveling salesman problem.Evolutionary Algorithms are adapted for solving this problem. The GA is one

among the popular algorithms applied to find the best solutions for this problem.The solution found by genetic

algorithm is self evolved. This paper details the application of MATLAB in solving the TSP using Genetic Algorithm.

Keywords:CNC, Tool path ,Machiningparameters ,Optimization, TSP , Genetic Algorithm , Matlab, Tool Box,Energy

1 INTRODUCTION

The problem of finding the minimum distance travelled by the cutting tool in a Computer Numerically

controlled machine is very important for the minimization of the cost. The complexity of the problem

increases with the number of axis and the number of tool destinations. The nodes are the points where the tool

stops for an operation or exit to travel to the next entry point. These locations in CNC machiningoperations

are determined by the work piece and the type of machining required. The near best tool path is found by

searching solutions in an exhaustive search space. These problems are known as TravelingSalesman Problem

(TSP).

The Traveling salesman problem is a combinatorial problem in which a salesmanis given a tour programto

visit a number of cities within a geographical boundary.The tour map contains a number of

locationsdepending upon the itinerary. It's the job of the salesman to visit each of these locations to make a

sale.Before settingoff on the journey the sales man has to plan a route such that the total tour time is

minimized. It is impossible to find the best route manually if there are more number of locations.The number

of possibleroutes are a factorial of the number of locations to be visited.

For example, if the number of locations to be visited are 10, then thefactorial of 10 is 3628800 which means

the number of possible routes are 36,28,800.Finding the best route among these 36,28,800 routes is beyond

the imagination of a human. If even one city is added to the tour the difficulty of a solution becomes

manifold. For the 11 locations the possible number of routes are 3,99,16,800. The number of new routes

increased by 3,62,88,000. Finding the shortestroute is impractical even by the present day‟s state of art

computing techniques.

2 FINDING THE SOLUTION FOR TSP

It may not be practically possible to find the best solution for a problem like this.There are algorithms which

discover close to optimum solutions. Genetic Algorithm,Simulated annealing algorithm,Tabusearch,Ant

Colony algorithm,Artificial Neural Network (ANN) ,Fuzzy logic approach ,Branch and Bound method are the

commonly used algorithms for TSP problems.



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These algorithms are capable of finding a 'good-enough' solution to the Traveling salesman problem quickly.

The Genetic Algorithmapproach is selected for our study due to the ease ofprogramming, robustness and

versatility.

2.1 Genetic Algorithm

Genetic algorithms are part of evolutionary computing, which is a rapidly growing area of artificial

intelligence. Genetic algorithms are biological basedand inspired by Darwin's theory about evolution in which

solution to a problem is evolved. Fig.1 shows the flow chart of a simple GA.

Fig.1

The traditional way of presenting an algorithm for the TSP problem is not done with GA due to the reason that

every city must be unique in a gene and shall not be duplicated. A valid solution would need to represent a

route where every location is included at least once. The coding shall be such that the route does not contain a

single location more than once, or missed out a location completely.For a gene presentation, a sequential

representation is used where the cities are listed in the order in which they are visited. It's common way for

TSP Genome.

Example: [ 12 7 6 10 3 8 4 0 1 2 5 9]

2.1.1 Create a Random Initial Population

Creation of InitialSolutions randomly

Creation of Newer Generation

Evaluation of Fitness of Solutions

Stop

Conditions Met?

Crossover & Mutation



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An initial population is created from a random selection of solutions ,which are known as chromosomes.

2.1.2 Evaluate Fitness

A value for fitness is assigned to each solution (chromosome) depending on how close it is actually in solving

the problem. The answer to the problem is arrived in this way. These "solutions" are part of the possible

characteristics that the system would employ in order to reach the answer.

2.1.3 Reprodution& Mutation

Mutation

The mutation method is applied for shuffling the route, and it does not add or remove a location from

the route, otherwise it would risk creating an invalid solution. If swap mutation is employed the gene

Before mutationis [0 1 2 3 4 5 6 ] . After mutation is after mutation [0 1 3 2 4 5 6 ]. Many methods are

applied for a swapping operation. Random swap is commonly used due to the simplicity.This strategy is

unable to achieve an optimum quickly but it can prevent convergence into a local optimum.The basic idea of

greedy-swap is to randomly select two cities from one chromosome and swap them if the new tour length is

shorter than the old one.

2.1.4 SELECTION

The Routlette rank, roulette cost and tournament and elitism methods are used for the selection of

chromosomes.

Cost Selection

Parents are selected according to their fitness. The better the chromosomes are, the more chances to be

selected they have. In a roulette wheel all chromosomes are placed in the population, the chances of selection

are high accordingly to the fitness .

Rank Selection

The cost selection will have problems when the fitness differ very much. If the best chromosome fitness is

90% of all the roulette wheel then the other chromosomes will have very few chances to be selected. In rank

selection, the ranking is done for the population and then every chromosome receives fitness from this

ranking. The worst will have fitness 1, second worst 2 etc. and the best will get the number of chromosomes in

the population as its rank.

Tournamnet Selection and Elitism

It is a mechanism for choosing individuals from a population. A group of characters selected at random from

the population and the best (normally only one, but possibly more) is chosen. An elitist genetic algorithm is

one that always retains in the population the best individual found so far.Tournamnet Selection is naturally

elitist.The chromosomes with a higher fitness value are more likely to reproduce offspring (which can mutate

after reproduction). The offspring is a product of the father and mother, whose composition consists of a

combination of genes from them. This process is known as "crossing over".

Next Generation

If the new generation contains a solution that produces an output that is close enough or equal to the desired

answer then the problem has been solved. If this is not the case, then the new generation will go through the

same process as their parents did. This will continue until a desired solution is reached.

3 MATLAB

MATLAB, stands for MATrixLABoratory, is a powerful, general-purpose system or environment for

doing mathematics, scientific and engineering calculations. MATLAB is a "High-Performance Numeric

Computation and Visualization Software" package. MATLAB is an interactive system whose basic data is a

matrix that does not require dimensioning.



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Matlab has two toolboxes that contain optimization algorithmsi) Optimization Toolbox ii) Genetic Algorithm

and Direct Search Toolbox. Optimization Toolboxis applied to solve Unconstrained nonlinear, Constrained

nonlinear,Simple convex: LP, QP,Least Squares,Binary Integer Programming, Multiobjective

problems.Genetic Algorithm and Direct Search Toolbox is used to solve generaloptimization problems

Direct search algorithms (directional) for generalized pattern,Genetic algorithm,Simulated annealing and

Threshold acceptanceproblems.There are two methods the Genetic Algorithm is applied in MATLAB

optimization.

3.1 . Calling the Genetic Algorithm Function

The Genetic Algorithm is invoked at the command line, by the function „ga‟with the syntax mentioned

below.

[xfval]=ga(@fitnessfun, nvars, options)

Where „@fitnessfun‟ is a handle to the Fitness Function.„nvars‟ is the number of independent variables for the

Fitness Function.„options‟ is a structure containing options for the genetic algorithm.The syntax returns the

following things.“fval“ the final Value of the Fitness Function.

_ reason – Reason for which the algorithm terminates.

_ output - Structure containing information about the performance of the algorithm.

_ population – Final population.

_ scores – Final scores.

“options = gaoptimset” command set the options. This returns the structure of options with the default

values for its fields. To edit an option structurewith a different value of an option such as ‟Elite Count‟, we

can use the function

Options= gaoptimst(„Elite Count‟, 1)

This will return an options structure with an „Elite Count‟ of 1 instead if its default value 2.

3.2. Using The Genetic Algorithm Tool

The optimization toolbox includes a graphical user interface. Fig.2 shows the GA Toolbox. .

The genetic algorithm tool is a graphical user interface that enables to use the genetic algorithm without

working at the command line. This will open the gatool window. To use this tool we must first enter the

following information,

“Fitness Function”- The objective function that we want to minimize. The fitness function is entered in

theform of „@fitnessfun‟, where „fitnessfun.m‟ is an M file that computes the fitness function.

“Number of variables “- This is the length of the input vector of the fitness function.

To run the genetic algorithm is run by the „start‟ button. The tool displays the result of the optimization

process in the „Status and Result‟ pane.The „plot‟ pane displays various plots that provide the status of the

genetic algorithmwhile it is running. This data displayed is useful to improve the performance of the

algorithm.



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Fig.2

4 STUDYEXPERIMENT

For the study the problem shown in fig 3 is chosen. The figure shows the drawing of a work piece with

holes to be drilled at different locations.

Fig.3

The aim of the experiment is to reduce the time taken by the Tool to travel between the various drill hole

locations. The number of axis movements are only two namely the x and y axis. Each hole is assigned a

number so that it is refered in the algorithm as a city( Fig .4) Since we are trying to minimize the total

distance that the salesman travels, the fitness function will be the total distance D:

D = d(c𝑛𝑘−1 k, ck+1)

Where city n + 1 = city 1 (the starting city). Xi; yes denote the coordinates of city chi, then the

Fitness function becomes

D = (xi - ax) 2 + (yes – in)

2 -------A



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The shown Expression (A) ensures that each city has visited only once, within the constaints , there are no

sub-tours, i.e., eliminates the possibility that in the solution appears more than one contour. A binary

represntationofsolutions is not suitable for this type of problem, and the solutions are represented as vector or

matrix.

Fig.4

The number of possible solutions are permutation of 1, 2, 3,..., n where n is number of cities.In this problem

it is the number of holes. The Matlabprogramme for the problem is shown in fig4.

5 GA MATLAB IMPLEMENTATION

The parameters shown in the Table 1. Are selected after several experimental runs by applying several

population size , mutation and cross over fractions. The number of Iterations also varied for consistent results.

GA Parameters Le Values

Number of Holes (Cities) 32

No of Generations 16000

Population Size 400

Cross Over fraction 0.5

Mutation fraction .08

Table 1.



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Fig.5

6 RESULTS AND DISCUSSION

The shortest tool path is shown in fig .5. The best result achieved is 36.129 units.Increasing the number

of iterations improved the results. For randomly placed drill holes and profile milling operations the

optimization tool is found to be more effective. The best possible route for minimizing the cost is achieved

by interactive process . The best solution generated by the optimization programme is given as the input for

Generating Gcodes . It is found that the cost of machining can be reduced considering the Toolpath travel

distance. By adding the required constraints and modifying the fitness function the above programme can be

used for optimizing different models like tool wear, tool life , minimum energy requirement, tool selection

etc..

ACKNOWLEDGEMENT

The authors wish to thank the MathworksInc, Lee Jacobson, a Freelance code writer for the support

in code development and Octave.org for the free license software to test the Matlab Codes.

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genetic algorithm for tsp in optimizing cnc tool...

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