A Modified 𝑝-Median Model for the Emergency Facilities Location Problem and Its Variable Neighbourhood Search-Based Algorithm

Algorithm 1

The basic VNS scheme.

Initialisation. Define the set of neighbourhood structures 𝑁_𝑘, 𝑘=1,…,𝑘_max, that will be

   used in the search; find an initial solution 𝑌₀; set 𝑌←𝑌₀; and choose a stop condition.

Repeat the following until the stop condition is met:

(1) Set 𝑘←1; (2) Until 𝑘=𝑘_max repeat the following steps:

(a) Shaking. Generate a point 𝑌^′ at random from the 𝑘th neighbourhood of 𝑌(𝑌∈𝑁_𝑘(𝑌));

(b) Local search. Apply some local search method with 𝑌^′ as the initial solution;

   denote with 𝑌^′′ the local optimum that is obtained;

(c) Move or not. If 𝑌^′′ is better than Y, move there (𝑌←𝑌^′′), and continue the search

   from 𝑁₁(𝑥) (𝑘←1); otherwise, set 𝑘←𝑘+1;