J. Puerto Albandoz
In this paper we address two different related problems. We first study the problem of finding a simple shortest path in a d-dimensional real space subdivided in several polyhedra endowed with different lp-norms. The second problem that we consider is the Weber problem that results in this subdivision of lp-normed polyhedra. We relate its local optimality condition with Snell's law and provide an extension of this law in our framework space. We propose a solution scheme based on the representation of the problem as a mixed-integer second order cone problem (MISOCP) using an lp-norm modelling approach. We derive two different MISOCPs formulations, theoretically compare the lower bounds provided by their continuous relaxations, and propose a preprocessing scheme to improve their performance. To solve the second problem, we adapt the solution scheme that we developed for the shortest path problem and validate our methodology with extensive computational experiments.
Palabras clave: Geodesic location problems
Programado
Localización (GELOCA4)
13 de junio de 2025 11:00
Sala 3. Maria Rúbies Garrofé