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Methodology/Algorithm

We begin the solution procedure with the construction of a random permutation. The

random permutation is then stored in a list called the tabu list as a reference for the bestinitial solution and its fitness value was calculated. In optimization problems the fitness

of an individual is usually measured in terms of the objective function value of the

solution it represents. Thus for the !"#$% an individual corresponding to a solution with

a low cost is said to be of high fitness. The number of iterations was initialized before

performing the tabu search. The datasets used determine the optimum number of

iterations that should be performed respective to each dataset. The reason behind this is to

reduce the time and program memory wastage. "or small size datasets% the solution with

the highest fitness value can be obtained within a few iterations. In this project% the

procedures of the code were separated into two levels.

In #evel &ne% random permutations with values representing an individual facility

were generated as candidates. The candidates were then chec'ed to ensure that there is no

clash with the permutations contained in the tabu list to avoid repetition. If it is% a random

permutation would be generated again until there is no clash occurring with the tabu list.

If there isn(t% the tabu list is updated with the addition of the generated permutation. )e*t%

the fitness values for the candidates were calculated. The candidate with the best fitness

value would replace the one contained in the array for the best solution found.

In #evel Two% the number of iterations was initialized again to obtain an optimum

number of iterations. +owever% the number of iterations in this level would be much

lesser than that in #evel &ne. )e*t% the best solution was e*tracted from the candidates in

#evel &ne. A second tabu list was initiated. The modifications were done in this level

where two points were selected randomly. The position of the facilities from the e*tracted

solution indicated by the points were swapped with each other. Then% the new

arrangement was chec'ed again to ensure there was no repetition. The fitness value for

the modified candidates were subse,uently calculated. The second tabu list was then

updated when there is no clash occurring. The best solution from each iteration is placed

into a matri* until all iterations are complete. Then% the best solution from this matri* is

compared to the best solution from #evel &ne. +ence% the best solution was obtained.

7/25/2019 Methodology of Modified Tabu Search Algorithm

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-ode

Input A !"#$ instance of size n

&utpur A modified arrangement which has the minimum cost among all permutation

. &btain initial facility arrangement and corresponding fitness value

0. Initiate first tabu list

#evel

1. 2enerate first tabu list

3. while 45ma*imum iterations6 begin

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7. 2enerate new facilities arrangement as candidate

8. -hec' if any candidate clashes with the first tabu list

9. -alculate fitness value for candidates arrangement

:. The best solution for #evel is obtained

;. end*tract the best solution from #evel

3. elect two points

7. wap the facilities indicated by the two points

8. -hec' if any modified candidate clashes with second tabu list

9. -alculate fitness value for modified candidates arrangement

:. elect best solution from #evel 0

;. -ompare best solution from #evel 0 with best solution from #evel

0=. end