Consistent Neighborhood Search for Combinatorial Optimization

Algorithm 1

CNS.

Initialization: generate an initial solution 𝑠, set 𝑠^∗=𝑠 and 𝑓^∗=𝑓(𝑠);

While a stopping time condition is not met and 𝑓^∗>0 , do

 1. initialize the value of the best move: set 𝑔=+∞;

 2. generate the best move: for each non assigned variable 𝑠_𝑖 and each value 𝑑_𝑗∈𝐷_𝑖, test move 𝑚=(𝑠_𝑖,𝑑_𝑗) on 𝑠 as follows:

   (a) assignment phase: give value 𝑑_𝑗 to variable 𝑠_𝑖 and compute the associated set 𝐶(𝑚) of conflicting variables;

   (b) reassignment phase (optional): for each variable 𝑠_𝑟 of 𝐶(𝑚), if it is possible to assign another admissible value to 𝑠_𝑟

   without augmenting the number of violations, do it and remove 𝑠_𝑟 from 𝐶(𝑚);

   (c) let 𝑠^cand be the so obtained candidate neighbor solution (which might be non feasible at this stage);

   (d) update the best candidate move: if |𝐶(𝑚)|<𝑔, set 𝑠′=𝑠^cand and 𝑔=|𝐶(𝑚)|;

 3. repairing phase on the best move: remove the value of the 𝑔 conflicting variables of 𝑠′ and let 𝑠 be the

  resulting new current solution;

 4. update the record: if 𝑓(𝑠)<𝑓^∗, set 𝑠^∗=𝑠 and 𝑓^∗=𝑓(𝑠)

Output: solution 𝑠^∗ (which is a complete feasible solution if 𝑓^∗=0);