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Furthermore, estimation of distribution algorithm is used to deal with the upper level problem.
The upper level problem is to maximize the consumer surplus of all demand scenarios with budget constraint.
In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the upper level problem.
Three different approaches, based on two different evolutionary algorithms and discrete variable relaxation, are devised and compared to tackle the upper level problem.
At the upper level problem, the system performance index is defined as the sum of total travel times and investment costs of link capacity expansions.
The lower level sub-model is the traffic network user equilibrium (UE) formulation for a given network design strategy determined by the upper level problem.
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The upper-level problem of the NDPRD is established as one of multi-objective optimization.
For the fixed mode-share model, the upper-level problem minimizes the total travel time of both cyclists and motorists.
In the upper-level problem, the costs of expansion are uncertain by adding random variables to the cost function coefficients.
Furthermore, we consider the set Y (3.2) as a new constraint set for the upper-level problem [6].
This is because the upper-level problem does not require the gradient of the problem to be optimized.
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