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I can name the problem as "Multiple Traveling Salesman Problem with Mutual Nodes". I have a group of people from different locations in a city. They want to plan a tour to see specific shops. How can I solve this problem? How can I model the problem to use meta-heuristic algorithms such as GA or ACO?

Ebola
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    What have you tried? You need to include a minimal working example. – Thomas Wagenaar Jun 18 '17 at 18:55
  • @ThomasW the problem is I haven't found any paper or research or similar project to do this task. Usually meta-heuristic approaches are used to solve such problems. But there is a problem with using these approaches. The planned tour which consists of different routes for different users is a single solution for the problem (in GA, it is a chromosome). How can we form this one single solution and how can we apply the evolution operators to evolve the solutions toward better answers? The same is happening with ACO. how can we form the solutions? – Ebola Jun 21 '17 at 21:09

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I am going to assume the problem is as below;

  • Each person may want to go any set of cities from the big map.

  • Two or more people can be in same city at the same time

  • Two or more people can use the same edge at the same time.

For Genetic Algorithm, each Chromosome will look like this;

route for person 1|route for person 2|route for person 3..

An example generation can be;

Chromosome1= 2,6,7,1|4,7,2|3,5,6
Chromosome2= 6,7,2,1|2,4,7|3,5,6

You will need to apply crossover and mutation operations for each route separately. You can use crossover methods like PMX (Partial-mapped Crossover) for permutation representations. You can use operations like random swap, insert, scramble for mutation.

For Ant Colony Optimization, each ant will need to build solutions for every person in each iteration. Also, different pheromone values should be stored for each person's route. Because, even if they have common locations(for example both of them have cities 2 and 3), that doesn't mean the edge between these cities should have same desirability (the edge between 2 and 3 may be suitable for person1 but it can be undesirable for person2).

So, I think it will be best to find routes for each person separately. Because there can not be a information exchange between solutions for each person's routes.

HK1911
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  • Your answer was very helpful however I think it is better to consider all tours together, because the sum of all tours length must be minimized and beside that, it should manage the sequence of POIs to visit. – Ebola Jul 12 '17 at 20:20