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Because boundedly rational user equilibrium (BRUE) always has a set of solutions instead of a unique one, from a static network equilibrium viewpoint, under BRUE there is no guarantee of attainability of any specific target flow by implementing tolls.
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It might have a set of solutions or have no solution.
Hence, instead of having one solution we have a set of solutions that cannot be compared to each other.
At the end, the tester has a set of possible solutions and can either prioritize one objective, by choosing solutions in the extreme points of the fronts or choose solutions with smaller ED values, according to the testing goals and resources.
The above problem usually has a set of Pareto-optimal solutions, whose projections compose the complete Pareto front.
then the boundary value problem (4.13), (4.14) has a set of linearly independent solutions in the form of the series (4.18).
After this procedure, all the RefSet members have a set of offspring solutions around them covering different distances and directions.
We did this because we need to have a set of optimal solutions as a reference for comparison, and we hoped that all the test data had the similar memory consumption so that their performance was comparable.
The data have been used to retrieve the dust optical thickness τ, single scattering albedo w and asymmetry factor g. The fitting of the spectra by a radiative transfer code has revealed a set of solutions which could be constrained by Mie modeling of the parameters τ, w, and g for a gamma particle size distribution.
Finally, we have a set of non-dominant solutions that forms the first boundary of solutions.
The obtained self-consistent equations for the mean HS fraction n H and distortion ξ have a set of non-trivial solutions determined by different relations between the characteristic parameters of short- and long-range interactions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com