An automated reference point-like approach for multicriteria shortest path problems

Abstract

In this paper we introduce a method of analysis for the automated ordering and selection of solutions of a multicriteria shortest path model. The method is based on a reference point approach,where the paths in a specific priority region are ranked by non-decreasing order of a Chebyshev metric.In order to list paths according with this objective function a labelling algorithm is proposed. The developed method is applied in a video-traffic routing context. Computational results are presented and analysed, for randomly generated networks of significant dimension.

A bicriteria routing model for multi-fibre WDM networks

“…This leads to the use, at this step, of a reference-point based procedure of the type proposed in [18], by considering as reference point the 'left bottom corner' of S (this point coincides with the optimal point if S = A).…”

“…Note that in this context, the computational efficiency is a major factor taking into account the automated nature of the routing mechanism, requiring a solution in a very short-time period, a factor which becomes critical in networks of higher dimension. Nevertheless a 'pure' reference-point approach, as the one in [18] might be more advantageous in a routing model where more than two criteria were used since it is not critically sensitive to the different number of criteria unlike the present approach. This sensitivity of the present approach to the number of criteria stems from the fact that this type of method has the disadvantage of finding, in some cases, solution(s) outside the currently searched priority region before all solutions inside this region have been calculated, taking into consideration that solutions are found along the dashed lines illustrated in Fig.…”

Stochastic hierarchical multiobjective routing model in MPLS networks with two service classes: an experimental study on imprecision and uncertainty issues

“…Noting that the model is supposed to be applied in an automated manner and following our previous experience in this area [5], we have developed a solution selection procedure based on the definition of dynamic preference thresholds in the o.f. space, combined with the use of reference points, inspired by the methodology described in [22]. This corresponds to imbedding the preferences of a 'virtual decision maker' in the form of a specific, problem-oriented, procedure of selection of non-dominated solutions.…”

Hierarchical multiobjective routing model in Multiprotocol Label Switching networks with two service classes – a Pareto archive strategy

“…The approach chosen to select the "best" solution in the best possible priority region is based on the calculation of a Chebyshev distance to a reference point, as described in Clímaco et al (2006). Note that this operation is more time-consuming than simply choosing the first solution found in the best possible priority region.…”

“…The weights in the weighted Chebyshev distance are w i|R = 1 Mi|R−mi|R , which allow the Chebyshev metrics w i|R C i ( ) − C * i|R to be dimension free and proportional to the size of the rectangular region. A weighted Chebyshev norm was used because this variant of the Chebyshev metric is the more adequate to the adopted reference point based technique (see details in Clímaco et al (2006)), which is based on the search and selection of nondominated solutions in the rectangular preference regions. In fact, the use of the weights (as defined in the method) makes the contour of the rectangle a isocost Chebyshev line for each particular region.…”