-First of all, my apologies if you receive duplicated this message, I
sent it 2 days ago, but due to the length of the text it was sent to the
moderator of the list.-
Hi Mohammed,
I should have mentioned this option, the linear combination of criteria
is naturally the obvious solution when the multiobjective problem is
approached for the first time.
To define a ranking procedure for the solutions can reduce the
multiobjective problem to a single objective problem, but it has many
drawbacks:
- An arbitrary vector of weights must be defined. Who should define that
weights? each user? the routing machine? How do you measure that travel
time is for example w_i more or less important than the economic cost,
or the CO2 emissions? In the majority of the cases these weights would
be totally arbitrary and will not reflect the user preferences.
- The linear combination function would add different measures, in our
case we are adding euros + minutes, or euros + meters + minutes, and the
resulting value would not have much sense. Moreover, if you are adding
meters and euro cents for example, the first criterion (or metric) is
going to be several orders of magnitude greater than the second, i.e. if
you are adding a solution path with 150000 meters that costs you 900
euro cents (150km and 9 euros), when you add both magnitudes the second
one will become quite irrelevant, and solution paths that minimize the
distance are always preferred.
- To avoid the second problem, you can normalize all the criteria to be
expressed in a scale from 0 to 100, from the minimum value for that
criterion (optimum) to the worst possible one, but this would still be a
bad solution to model the user preferences.
Thanks anyway for you answer Mohammed, it helped me to further develop
the purpose of multiobjective graph search algorithms.
In summary, routing on road maps with a single criterion have been
practically solved, it is enough to see that OSRM calculates an optimum
route in the order of milliseconds, and my guess is that other variants
like routing with multiple criteria or dynamic costs (like traffic
information) will be soon included in routing services. (if they are not
yet).
Best regards,
Francisco J.
Message: 2
Date: Thu, 9 Apr 2015 19:16:18 +0100
From: Mohammed Ayoub NEGGAZ <[email protected]
<mailto:[email protected]>>
To: Mailing list to discuss Project OSRM
<[email protected] <mailto:[email protected]>>
Subject: Re: [OSRM-talk] OSRM-talk Digest, Vol 27, Issue 12
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Hi Francis,
I'm working on the dynamic case of the problem but I think I
might help you.
What if you create a formula for your critera for example, for
the costs
that you gave you can define :
weight = (Travel Time * TT_Weight) + (Cost * C_Weight) where TT_ and
C_Weight are factors and weight will allways give a scalar.
If we are interrested in travel time we define TT_Weight = 2 <
C_Weight = 4
and then
A= (60 min, 30€) = 60*2 + 30*4 = 240
B= (65 min, 25€) = 65*2 + 25*4 = 230
C= (85 min, 20€) = 85*2 + 20*4 = 250
D= (90 min, 15€) = 90*2 = 15*4 = 240
The algorithm can respond with B which (he thinks) the best
route if we
prefere spending less than arriving in time.
With this modelization, you need to define a static vector of
weights (on
for each property) and therefore you can use CH with Bi-Dijkstra
provided
by OSRM.
I wish this can help you.
Good luck in your work.
With respect,
2015-04-09 17:28 GMT+01:00 Francis <[email protected]
<mailto:[email protected]>>:
> Hi Romain,
>
> I would also be pretty interested in a bicriteria (or
multicriteria) OSRM
> version. What bicriteria algorithm would you like to use?
> Let me first introduce myself. I'm involved in a SmartCities
European
> Project in my city and we would like to provide routes that
consider the
> minimization of multiple criteria simultaneously, like travel
time,
> economic cost or CO2 emissions. I'm about to finish my phD in
> Multiobjective Shortest Path Problems and I'd love to apply
some of the
> algorithms I have developed to that project. I do believe
OSRM may be a
> great starting point for such a service.
> I have started recently to inspect the source code. Let me
point out some
> of the issues concerning an OSRM service that minimizes
simultaneously more
> than one criterion:
> - Multiple lua profiles could be necessary (one for each
criterion).
> - Edge weights are no longer a scalar value, but a vector of
n dimensions
> (n- number of criteria).
> - The preprocessing of the input graph and the routing algorithm
> (Contraction Hierarchies and bidirectional Dijkstra) must be
adapted to the
> Multicriteria case, specifically, the preprocessing process
were shortcuts
> are added as well as the search process were bidirectional
Dijkstra's
> algorithm is employed to find the shortest path.
> - Since the concept of optimum does not apply to Bicriteria or
> Multicriteria search, the new multiobjective algorithm would
return a set
> of solutions, typically the set of Pareto or non-dominated
solutions.
> - Unless the two considered criteria are highly correlated
(like travel
> time and distance, for example), the number of Pareto
solutions is usually
> big (hundreds, thounsands...), so in order to make it
practical for the
> user to choose one of the alternatives, something else from
Multicriteria
> Decision Making would be necessary (Goal Programming,
Compromise Search,
> tighten the concept of dominance...).
> - The frontend receives and paints several routes.
>
> I'm not sure how this would be interesting for the rest of
the community,
> but I'd like to show an example of why this could be pretty
useful.
> Let me assume we are considering two criteria, travel time
and the
> economic cost of the route (gas + tolls), and there are four
possible
> routes:
> A= (60 min, 30€)
> B= (65 min, 25€)
> C= (85 min, 20€)
> D= (90 min, 15€)
> where (x,y) = (travel time, economic cost)
>
> With the current version of OSRM we obtain solution A, since
it is the
> fastest of all. If we load an economic cost profile in OSRM,
that labels
> each edge with the economic cost of traversing that edge, we
obtain
> solution D, since it is the cheapest. What about if the user
wants a
> solution with better trade-off? B and C would be good
solutions too.
> I think an OSRM version providing the extreme solutions for
each criterion
> (fastest-A and most-economical-D in this case) and a small
set of solutions
> with "good" trade-off between both criteria would be a very
interesting
> feature for the project, although I'm not sure how this could
be included,
> since it would involve many changes and the performance in
continental maps
> is unknown.
>
> Sorry for such a long mail.
>
> PS: If someone is interested these are some academic
references of papers
> dealing with this problem:
> Preprocessing a multicriteria algorithm for routing:
>
http://i11www.iti.uni-karlsruhe.de/extra/publications/dw-pps-09.pdf
> Algorithm that extends A* to the Multiobjective case, keeping
the same
> theoretical properties than A*:
> http://dl.acm.org/citation.cfm?doid=1754399.1754400
> Parallelization of that algorithm:
> http://algo2.iti.kit.edu/documents/Sanders%202013/ipdps.pdf
>
> Best regards,
> Francisco J.
>
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