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I would like to solve a TSP problem with benefit and cost. Let us say A salesman has a set of customers to visit each visit will take cost of moving time from the current location to the location of a customer and as well as visit duration. Meanwhile the benefit is a numeric score that a Salesman will get from visiting a customer. The salesman has a time limitation, hence he should visit a set of customers (not necessary all) that gives him maximum net benefit = score - travel time. The Salesman must return to his initial location in the given time.

A* expands the node with least cost function f(n) = g(n) + h(n) and return the path to the goal which has the lowest cost.

If I can determine the g(n) as the net benefit aforementioned. What is the best way to determine h(n) ?

I know this is a combinatorial problem similar to orienteering problem. Is it possible to solve this problem using A* ? Actually the path does not need to be optimal. I just want to have a path that gives the maximum net benefit (reverse to the cost in A*)

Priska Aprilia
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    [Where should I post questions about algorithms?](http://meta.stackexchange.com/questions/165519/where-should-i-post-questions-about-algorithms-stack-overflow-or-programmers-se): [Programmers](http://programmers.stackexchange.com/) – Rubens Farias Oct 25 '15 at 08:39
  • @RubensFarias when referring other sites, it is often helpful to point that [cross-posting is frowned upon](http://meta.stackexchange.com/tags/cross-posting/info) – gnat Oct 25 '15 at 09:19

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