Improved approximation algorithm for k-level UFL with penalties, a simplistic view on randomizing the scaling parameter

The state of the art in approximation algorithms for facility location problems are complicated combinations of various techniques. In particular, the currently best 1.488-approximation algorithm for the uncapacitated facility location (UFL) problem by Shi Li is presented as a result of a non-trivial randomization of a certain scaling parameter in the LP-rounding algorithm by Chudak and Shmoys combined with a primal-dual algorithm of Jain et al. In this paper we first give a simple interpretation of this randomization process in terms of solving an aux- iliary (factor revealing) LP. Then, armed with this simple view point, Abstract. we exercise the randomization on a more complicated algorithm for the k-level version of the problem with penalties in which the planner has the option to pay a penalty instead of connecting chosen clients, which results in an improved approximation algorithm

An Improved Genetic Algorithm for the Multi Level Uncapacitated Facility Location Problem

In this paper, an improved genetic algorithm (GA) for solving the multi-level uncapacitated facility location problem (MLUFLP) is presented. First improvement is achieved by better implementation of dynamic programming, which speeds up the running time of the overall GA implementation. Second improvement is hybridization of the genetic algorithm with the fast local search procedure designed specially for MLUFLP. The experiments were carried out on instances proposed in the literature which are modied standard single level facility location problem instances. Improved genetic algorithm reaches all known optimal and the best solutions from literature, but in much shorter time. Hybridization with local search improves several best-known solutions for large-scale MLUFLP instances, in cases when the optimal is not known. Overall running time of both proposed GA methods is signicantly shorter compared to previous GA approach

Improved Combinatorial Approximation Algorithms for the k-Level Facility Location Problem

In this paper we present improved combinatorial approximation algorithms for the k-level facility location problem. First, by modifying the path reduction developed in [2], we obtain a combinatorial algorithm with a performance factor of 3:27 for any k 2, thus improving the previous bound of 4:56 achieved by a combinatorial algorithm. Then we develop another combinatorial algorithm that has a better performance guarantee and uses the rst algorithm as a subroutine. The latter algorithm can be recursively implemented and achieves a guarantee factor h(k), where h(k) is strictly less than 3:27 for any k and tends to 3:27 as k goes to 1. The values of h(k) can be easily computed with an arbitrary accuracy: h(2) 2:4211, h(3) 2:8446, h(4) 3:0565, h(5) 3:1678 and so on. Thus, for the cases of k = 2 and k = 3 the second combinatorial algorithm ensures an approximation factor substantially better than 3, which is currently the best approximation ratio for the k-level problem provided by the non-combinatorial algorithm due to Aardal, Chudak, and Shmoys [1]

Multi-level Facility Location Problems

We conduct a comprehensive review on multi-level facility location problems which extend several classical facility location problems and can be regarded as a subclass within the well-established field of hierarchical facility location. We first present the main characteristics of these problems and discuss some similarities and differences with related areas. Based on the types of decisions involved in the optimization process, we identify three different categories of multi-level facility location problems. We present overviews of formulations, algorithms and applications, and we trace the historical development of the field