A Multi-Start Biased-Randomized Algorithm for the Capacitated Dispersion Problem

Abstract

The capacitated dispersion problem is a variant of the maximum diversity problem in which a set of elements in a network must be determined. These elements might represent, for instance, facilities in a logistics network or transmission devices in a telecommunication network. Usually, it is considered that each element is limited in its servicing capacity. Hence, given a set of possible locations, the capacitated dispersion problem consists of selecting a subset that maximizes the minimum distance between any pair of elements while reaching an aggregated servicing capacity. Since this servicing capacity is a highly usual constraint in real-world problems, the capacitated dispersion problem is often a more realistic approach than is the traditional maximum diversity problem. Given that the capacitated dispersion problem is an NP-hard problem, whenever large-sized instances are considered, we need to use heuristic-based algorithms to obtain high-quality solutions in reasonable computational times. Accordingly, this work proposes a multi-start biased-randomized algorithm to efficiently solve the capacitated dispersion problem. A series of computational experiments is conducted employing small-, medium-, and large-sized instances. Our results are compared with the best-known solutions reported in the literature, some of which have been proven to be optimal. Our proposed approach is proven to be highly competitive, as it achieves either optimal or near-optimal solutions and outperforms the non-optimal best-known solutions in many cases. Finally, a sensitive analysis considering different levels of the minimum aggregate capacity is performed as well to complete our study.

A Forward–Backward Simheuristic for the Stochastic Capacitated Dispersion Problem

“…This method is able to reach all of the best-known solutions to the CDP established in the literature. Gomez et al [35] proposed a multi-start biased randomized algorithm to efficiently solve the instances in the testbed. Furthermore, Lu et al [11] introduced a solution-based tabu search algorithm, which incorporated a hash-based mechanism to rapidly identify eligible neighboring solutions and employed a streamline calculation strategy to quickly determine the objective function value of a neighboring solution.…”

Optimization of Vehicular Networks in Smart Cities: From Agile Optimization to Learnheuristics and Simheuristics

“…Martí et al [ 81 ] proposed new instances, tested them through computational experiments, and demonstrated how these problems have evolved over time from an operations research standpoint. Moreover, based on other previous works Martí et al [ 82 ] formulated a new MILP model to propose an exact and heuristic approach to solve the CDP and later Gomez et al [ 83 ] proposed a BR algorithm that uses the construction-destruction concept to generate high-quality solutions for the CDP in short computing times.…”

“…We present a case study to show how the CDP described by Gomez et al [ 83 ] can be combined with vehicular networks in real-world scenarios to efficiently allocate facilities in a city. This study aims to maximize the minimum distances between any pair of open facilities where each facility has a known capacity and the total capacity of open facilities must exceed a user-defined threshold.…”

“…According to the traffic data ( , accessed on 26 December 2022), the traffic situation is classified into various states, such as no data, very-fluid, fluid, dense, very-dense, congestion, and cut-off. Here we consider very-fluid, fluid, dense, and very-dense situations and apply different sizes of threshold b to evaluate the performance of Gomez et al [ 83 ] constructive heuristic model in a realistic scenario where the solution is constructed by adding promising elements one by one until the required capacity was reached and compare it to a random scenario where the solution is randomly selected from a list of elements until all the required capacity is covered.…”

“…In this section, we demonstrate the outcome of a real numerical experiment using the constructive heuristic methodology Gomez et al [ 83 ], which we then compared to a random scenario. The experiment was conducted on a standard computer.…”