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

Algorithm 3

The modified VNS algorithm for the 𝑝-median problem.

Function pmp_search (𝑝, 𝐶₁)

(1)   (𝑓₁, 𝐶^′₁) = localsearch (𝐶₁); 𝑓₁⋅ count =1; 𝐶₂= changecluster (𝐶^′₁, 𝑓₁· count);

(2)   for 𝑖=2 to REPEAT do

(3)    (𝑓_𝑖, 𝐶^′_𝑖) = localsearch (𝐶_𝑖);

(4)    if 𝑓_𝑖⋅ objv < 𝑓_𝑖−1⋅ objv and 𝑓_𝑖⋅ maxlength <= 𝐿 then

(5)       𝑓_𝑖⋅ count =1;𝐶_𝑖+1= changecluster (𝐶^′_𝑖, 𝑓_𝑖⋅ count);

(6)    else

(7)        𝑓_𝑖⋅ count∶=𝑓_𝑖⋅ count +1;

(8)        if 𝑓_𝑖⋅ count = RESTART then

(9)         𝐶_𝑖+1= initcluster;

(10)         else

(11)         if rand < Pc then

(12)          𝐶_𝑖+1= changecluster (𝐶^′_𝑖, 𝑓_𝑖⋅ count);

(13)       else

(14)          𝐶_𝑖+1= changecluster (𝐶_𝑖, 𝑓_𝑖⋅ count));

(15)   min = 𝐦𝐢𝐧_𝑖{𝑓_𝑖⋅objv}

(16)   return (𝑓_min, 𝐶^′_min).

end pmp_search