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I have been assigned the following problem as a research topic for summer. However, I have not been able to successfully find related problem, except that it seems to be a combination of travelling salesman with the knapsack, even though I'm not sure if that is the case. The statement is:

  • You are a truck driver who earned a big contract and now you must deliver a lot of packages. There are N packages to be delivered, each one has to be delivered at a certain address (x,y) on the city. Additionally each package i has a weight Wi.

  • For simplicity, suppose the distribution area is rectangular and you always start at the point (0,90).

  • You only have one truck, with limited capacity of 1000 (excluding
    truck weight). The truck base weight is 10.

  • The distances to be travelled are far away, so the distance shall be computer using Haversine distance.

  • The company who contracted you will provide you with enough fuel, so you can make unlimited ammount of travels.

  • However, you must be very careful while delivering the packages since you must deliver every single one of them and, if you choose to pick up a package during a trip, you must deliver it no matter what, you
    can't leave them in the middle of your trip.

  • As you are a bit miserly, you agree on the conditions, but you know
    that if you don't take a close to optimal strategy, your truck can
    wear too much, so you could end leaving the contract incomplete,
    which will get you sued and leave you without truck and money.

  • So, due to your experience, you know that to maximize the chances of survival of your truck, you must minimize the following function:

    http://goo.gl/jQxXzN (sorry, I can't post images because I have not enough reputation).

where m is the number of tripss, n is the number of packages for each trip j, wij is the weight of the i-th gift during the j-th trip, Dist represents Haversine distance between two points, Loc(i) is the location of the i-th gift, Loc(0) and Loc(n) are the (0,90) point (starting point), and wnj (last weight of the trip) is always the truck weight (base weight).

So, basically, those are all the restictions of the research topic I got. I have been thinking maybe some metaheuristics such as ant collony or genetic algorithms could be of help, but I would have to get to know the problem a bit better. Any idea or information (paper, book, etc) is welcomed.

user229044
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addictedtohaskell
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    Congratulations, you've been assigned the problem that UPS and Fed-Ex have been trying to solve for years. Best of luck. – NM Pennypacker Dec 22 '15 at 21:14
  • I think that's a different problem, because they have a fleet of trucks/planes/etc and I have to consider only one. But thanks, I'm gonna need the luck! – addictedtohaskell Dec 22 '15 at 21:27
  • Surely this is some variant of VRP, which should be solvable in the usual way (ILP) – harold Dec 22 '15 at 22:02

1 Answers1

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This sounds like a variation of the Capacitated Vehicle Routing Problem (CRVP), specifically with with single-vehicle and single-depot (however with non-uniform packages). For some reference on this problem, see e.g.:

I think your idea of metaheuristics---ant colony optimisation (ACO) in particular---would be a wise approach. Note that for TSP related problems, generally ACO is to prefer over genetic algorithms (GA).

Possibly the following somewhat well known article (1) can get you started to studying the possible benefits of ACO approach. (2) extends the result from (1). Note that this covers the regular VHP (no capacitated), but it should prove valuable as a starting point, the least giving inspiration.

  1. SavingsAnts for the Vehicle Routing Problem (K. Doerner et al.)
  2. An improved ant colony optimization for vehicle routing problem (Yu Bin et al.)

There also seems to exists literature specifically one the subject of ACO and CVRP, but I cannot comment to the quality of these, but I'll list them for you to inspect by yourself. Note that (3) is an extension from the authors of (1).

  1. Parallel Ant Systems for the Capacitated Vehicle Routing Problem (K. Doerner et al.)
  2. Ant Colony Optimization for Capacitated Vehicle Routing Problem (W.F. Tan et al.)

Sound like an interesting research topic, good luck!

dfrib
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