Step 1 . Reset all GA parameters and operators (i.e., selection, crossover, and mutation) to their default settings. Step 2 . Randomly generate a population of chromosomes (candidates or potential solutions) of size
(defulat: 300), with each
chromosome containing
(default: 100) elements, and with each element corresponding to the serial number (ranging from 1 to
) of a specific convenience store (Figure 2(a) ). Step 3 . Assign each chromosome in the initial population a fitness score obtained by the objective function. Step 4 . Repeat Steps 4a–4c until
offspring have been created. Step 4a . Using a roulette wheel sampling mechanism in which selection probability is proportional to the fitness score, randomly select two chromosomes from the population to serveas parents. Note that any chromosome can be selected more than once (i.e., in other iterations). Step 4b . Using a two-point crossover process to exchange elements between parent chromosomes, producing two new offspring with Probability
(default: 0.8) from each pair of parents (Figure 2(b) ). If no crossover occurs, the two new offspring Will be exact copies of their respective parents. To avoid repeats, rearrange parental elements prior to this exchange so that the same elements are moved to the front of each chromosome. Step 4c . Mutate the two offspring for each element at probability
(default: 0.01) and insert the resulting chromosomes into the new population. Step 5 . Replace the current population with the new one.Step 6 . Assign each chromosome in the current population a fitness score obtained by the objective function. Step 7 . Maintain the best chromosome as the approximate global optimal solution for the AED location-allocation problem and its associated fitness score for each generation in the current population. Step 8 . Use the stirring operator to prevent premature convergence. Evolution should be sufficiently stable so that the sum of the difference of best fitness scores over
generations (default: 20) falls below a tolerance value
(default: 10−10 ). In the stirring operator, replace
percent (default: 20%) of the chromosomes in the current population with new and randomly generated chromosomes to trigger searches for additional
generations. Step 9 . If the sum of the difference of best fitness scores in Additional
generations
then Stop the evolution process and return the AED location-allocation solution with the best fitness score else Go to Step 4. end if
