Algorithm 1. High-level pseudo-code of the genetic-hierarchical algorithm.

Genetic_Hierarchical_Algorithm Procedure;

/ input: n—problem size, A, B—data matrices,

/     PS—population size, Ngen—total number of generations,

/    InitPopVar—initial population variant, SelectVar—parents selection variant, CrossVar—crossover variant,

/     MutVar—mutation variant, RepVar—population replacement variant,

/    σ—selection factor, DT—distance threshold, Lidle_gen—idle generations limit

/ output: p✸—the best found solution (final solution)

begin

/ create a starting population P of size PS, depending on the initial population variant

InitPopVar

switch (InitPopVar)

1: create the initial population P by applying the algorithm

k-Level_Hierarchical_Iterated_Tabu_Search;

2: create the initial population P by applying a copy of

Genetic_Hierarchical_Algorithm using InitPopVar = 1

endswitch;

p✸ = GetBestMember(P); / initialization of the best so far solution

for i := 1 to Ngen do begin / main loop

sort the members of the population P in the ascending order of the values of the

objective function;

select parents p′, p″ ∈ P for reproduction (crossover), depending on the selection

variant SelectVar and the selection factor σ;

perform the crossover operator on the solution-parents p′, p″

and get the offspring p″′, taking into account the crossover variant CrossVar;

apply improvement procedure k-Level_Hierarchical_Iterated_Tabu_Search

to the offspring p″′, get the (improved) offspring p✩;

get new population P from the union of the existing parents’

population and the offspring P ∪ {p✩} (such that |P| = PS)

(the minimum distance criterion and population replacement variant RepVar

are taken into account);

if z(p✩) < z(p✸) then p✸ = p✩; / the best found solution is memorized

if number of idle generations exceeds the predefined limit Lidle_gen then begin

perform the population restart process;

if z(GetBestMember(P)) < z(p✸) then p✸ = GetBestMember(P)

endif

endfor;

return p✸

end.