Question

I’m using a genetic algorithm (GA) to optimise a traveling salesman problem (TSP). My problem is how I calculate the fitness of an individual.
Obviously solutions with shorter routes are fitter but how exactly do I assign a fitness value without knowing what the shortest possible route and longest possible route is to determine where my solution fits in that range?

Answer 1

Having fitness equals to path length is fine. Keep in mind that in genetic algorithms the fitness is only used for selecting individuals: consequently with usual selection procedures the scale does not matter, only the rank does.

Examples of implementation:

• http://www.codeproject.com/Articles/1403/Genetic-Algorithms-and-the-Traveling-Salesman-Prob
• http://khayyam.developpez.com/articles/algo/voyageur-de-commerce/genetique/ (use Google translate)
• http://www.lalena.com/ai/tsp/
• http://www.mathworks.com/matlabcentral/fileexchange/13680

More subtleties (2001 – Swarm Intelligence – Kennedy & Eberhart – page 249):

Pablo Moscato is a South American researcher who has pioneered the
study of memetic algorithms (e.g., Moscato, 1989). He and Michael
Norman, who is now in Scotland at the University of Edinburgh, began
working together in the 1980s at Caltech. In a recent paper they
describe the use of a memetic algorithm for optimization of a
traveling salesman problem (TSP) (Moscato and Norman, 1992). Recall
that the TSP requires finding the shortest path through a number of
cities, passing through each one only once. The problem has a rich
history in applied mathematics, as it is very hard to solve,
especially when the number of cities is large. TSP is an NP-hard
problem, which suggests that if a way is found to solve it, then a
large number of other problems will also have been solved. Moscato and
Norman use an algorithm with both cooperation and competition among
agents in the population, and implement a hybrid version of simulated
annealing for local search.

A population of individuals—these
researchers usually use a population size of 16—searches the problem
space, which is defined by permutations of the cities, called “tours.”
The population is conceptualized as a ring, where each individual is
attached to its two immediately adjacent neighbors, with whom it
competes in the search; individuals are also connected to others on
the far side of the ring, with whom they cooperate. Each individual in
the population comprises a tour of the cities. Competition is seen as
“challenge” and “battles” between pairs of individuals, where the tour
lengths of an individual and its neighbor are compared and a
probability threshold is set based on the difference. The difference
between the tours’ lengths affects the steepness of the sshaped curve;
when the difference is small or the temperature is cool, the
probability distribution becomes nearly uniform, and when the
difference in lengths between the two tours is great, the probability
is increased that tour 1 will be deleted and replaced with a copy of
tour 0.

Cooperation is used to let more successful individuals “mate”
with one another, rather than with less-fit members of the population.
The same rule that is used in deciding competitive interactions is
used to assess the desirability of partners for crossover, which is
implemented just as it is in GA. One individual “proposes” to another,
and if the proposition is accepted, that is, if the stochastic
decision favors their interaction, then the crossover operator is
implemented. Thus the next generation is created.