tion Problem
The final decision about the optimum route is approached as an optimization problem. The optimum path is the one that takes the traveller from his/her initial location to the target destination, subject to the traveller’s constraints. To determine the optimum route, two factors are considered. The first is the monetary allowance for the trip, which would include the cash to be spent on gas, toll roads, and parking, among others. The other factor is the traveller’s desired journey time. The TCTP module takes advantage of these factors to explore routing options that are optimum
in a broad sense as they go beyond the shortest distance and the shortest time in defining optimality. Due to the doctrine’s influence, the optimum route might not prove to be the one with the shortest trip time or the shortest distance.
S
Toronto
(a) Road network map covering the area of interest taken.
London a b 2 1 12 5 3 4 z c f e g 6 10 7 8 9 11 j n o q h r i k m l p Toronto x
(b) A schematic graph corresponding to the road network of interest.
Figure 5.5: Mapping a satellite map to graph based on the area of interest.
The decision aid unit in the TCTP module has two types of input: 1) The trav- eller’s constraints (i.e., trip-time and trip-monetary constraints) and 2) the cost of
each road segment, ξi. The decision is to find the optimum route, rOpt, that minimizes
the cost, ξr, subject to the traveller’s temporal, τr, and monetary, ψ, constraints. The
trip is formulated as a graph-based combinatorial problem. Road segments, Lr, are
previously specified by the ATIS. Each li ∈ Lr has a cost value, ξi, that is computed
by the doctrine-based recommendation unit.
The problem of finding the best route can now be stated as follows: given a graph G = (V, E), where V is the set of nodes (vertices) in the graph, and E denotes the edges in the graph, find the route with minimum cost. The graph represents an area of interest, R(stri, ftri), that includes the starting point, stri, and the destination point,
ftri, of the trip. The ATIS defines the area of interest prior to the trip planning to
limit the search space, as shown Figure 5.5. The goal is to find the best route, rOpt,
with minimum cost value, ξr. Travellers are using vehicles for their commute from one
point to another. The trip-planning problem with preferences windows is formulated as follows: rOpt = min X ∀i,j∈E ξrij xij (5.2) Subject to: X j xij − X j xji = 1 if i is a starting node −1 if i is a destination node 0 otherwise , ∀i (5.3) X i,j∈A tij xij 6 τk (5.4) X i,j∈A mij xij 6 ψk (5.5) xij ∈ {0, 1} (5.6) where ξr = Recommendation value,
E = Set of nodes in the net, τ = Temporal constraint,
ψ = Monetary constraint window, tij = Travel time over the segment ij ,
mij = Cost of travel over the segment ij ,
k = Trip query index,
xij is the decision variable representing the road segments and is defined as
xij =
(
1 if the road segment is selected
0 otherwise (5.7)
The Constraint in Equation 5.3 stipulates that the driver leaves the starting point and eventually arrives at the end point and never uses the same road segment twice. The inequality in Equation 5.4 states that the trip time is never more than τ , as indicated at the query time k. The inequality in Equation 5.5 ensures that the total cost of the road segment does not exceed ψ at query time k. The last constraint in Equation 5.6 is the integrity constraint. Finally, this problem can be solved as a binary integer problem.
The objective function in Equation 5.2 is a cost function that is computed based on the chosen doctrine. Each doctrine can be viewed as an independent soft objec- tive. In terms of hard objectives, the formulation will have to accommodate more constraints corresponding to the desired hard demands. If the optimization function was infeasible, the optimization problem becomes an unconstrained routing problem that can be solved using Dijkstra’s algorithm. Next, two measures of assessment that can be used to compare the module’s trip suggestions with the preferences of the travellers are defined.
Doctrine Satisfaction Index
The TCTP module provides travellers with individualized routes reflecting their pref- erences. For the travellers to be able to understand the quality of the suggested route, the TCTP module associate each route with a doctrine satisfaction index. Further- more, the doctrine satisfaction index can be used within the TMP framework to order the different routes according to their corresponding doctrine satisfaction index.
For traveler tri, the minimum trip cost value, ξr, for the optimal route, rOpt, is
used to compute the doctrine satisfaction index, DSi. For each road segment li, li ∈
Lr, there is ξi, where ξr =
P
∀li∈Lrξi. Furthermore, ∀ li ∈ Lr, there is a known trip
distance |li|. DSi is defined as follows:
|Lr| = X ∀li∈Lr |li| (5.8) DSi = X ∀li∈Lr ξi∗ |li| |Lr| . (5.9)
Correspondingly, road doctrine satisfaction index DSr can be categorized into four
levels:
D
Sr∈ {Highly satisfied, Satisfied, Marginally satisfied, Unsatisfied} .
(5.10)An example of the computation of the route doctrine satisfaction index DSr is shown
in Figure 5.6. The satisfaction levels are mapped to the three membership functions of the road recommendation unit. For instance, if DSi is computed to be 0.2, then
i S D
Marginally
Satisfied Unsatisfied Highly Satisfied Satisfied
Figure 5.6: Doctrine satisfaction index computation process.
Safety-Risk Exposure Index
Additionally, for the safety doctrine, a trip safety-risk exposure index is provided. Travellers who choose to use this doctrine will be provided with figures and numbers reflecting their safety-risk exposure during the trip. The safety-risk index is computed cumulatively throughout the trip. It is possible that after a repetitive exposure to a low-risk activity, the overall safety risk can be assessed as a medium cumulative risk.