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The first two methods used the F objective function, while the third method used the relaxed formulation objective function (F p).
The numerical approach is based on this relaxed formulation thus making it mesh-independent.
A relaxed formulation of this problem is introduced, which allows for composite materials as admissible designs.
We show that the relaxed formulation is obtained by replacing the set of characteristic functions by its convex envelope.
Then, by means of gradient Young measures, we obtain a relaxed formulation of the problem in which the original cost density is replaced by its constrained quasi-convexification.
In addition to a marked performance advantage of the relaxed formulation for 12 IDs and somewhat superior performance of the relaxed formulation for 8 IDs, a significant change in performance is observed when the sensing radius R is 1.1 or greater.
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It is worth noting that variables x i s and z ij s can be relaxed in Formulation 1c -(1e) and the convexity constraint (1f) suffice to guarantee their integrality in any optimal solution to the problem.
By introducing the confidence level and the preference level of decision maker, we obtain a relaxed robust deterministic formulation of the stochastic problem.
By combining both problem formulations (relaxed and MINLP), MPeSS is able to arrive to near-globally optimal values in approximately 47% of the runs.
It is possible to relax the ML formulation to a semidefinite programming (SDP) problem in order to provide a high-fidelity approximate solution that can be obtained in a globally optimum fashion with reduced computational efforts.
However, in the current bi-level formulation, this restriction is relaxed.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com