Algorithm 4. Pseudo-code of the tabu search algorithm.

Tabu_Search procedure;

/input: n—problem size,

/     p—current solution, Ξ—difference matrix

/output: p•—the best found solution (along with the corresponding difference matrix)

/parameters: τ—total number of tabu search iterations, h—tabu tenure, α—randomization coefficient,

/          Lidle_iter—idle iterations limit

begin

clear tabu list TabuList and hash table HashTable;

p•: = p; k: = 1; k′: = 1; secondary_memory_index: = 0; improved: = FALSE;

while (k ≤ τ) or (improved = TRUE) then begin / main cycle

Δ′min: = ∞; Δ″min: = ∞; u′: = 1; v′: = 1;

for i: = 1 to n − 1 do

for j: = i + 1 to n do begin / n(n − 1)/2 neighbours of p are scanned

Δ: = Ξ(i, j);

forbidden: = iif(((TabuList(i, j) ≥ k) and (HashTable((z(p) + Δ) mod HashSize) = TRUE) and

(random() ≥ α)), TRUE, FALSE);

aspired := iif(z(p) + Δ < z(p•), TRUE, FALSE);

if ((Δ < Δ′min) and (forbidden = FALSE)) or (aspired = TRUE) then begin

if Δ < Δ′min then begin Δ″min: = Δ′min; u″: = u′; v″: = v′; Δ′min: = Δ; u′: = i; v′: = j; endif

else if Δ < Δ″min then begin Δ″min: = Δ; u″: = i; v″: = j; endif

endif

endfor;

if Δ″min < ∞ then begin / archiving second solution, Ξ, u″, v″

secondary_memory_index: = secondary_memory_index + 1; Γ(secondary_memory_index) ← p, Ξ, u″, v″

endif;

if Δ′min < ∞$\mathbf{then} \mathbf{begin} / \mathrm{replacement} \mathrm{of} \mathrm{the} \mathrm{current} \mathrm{solution} \mathrm{and} \mathrm{recalculation} \mathrm{of} \mathrm{the} \mathrm{values} \mathrm{of} \mathsf{\Xi }$

$p: = \varphi (p, u^{\prime }, v^{\prime })$;

recalculate the values of the matrix Ξ;

if z(p) < z(p•) then begin p•: = p; k′: = k endif; / the best so far solution is memorized

TabuList(u′, v′): = k + h; / the elements p(u′), p(v′) become tabu

HashTable((z(p) + Δ) mod HashSize): = TRUE

endif;

improved: = iif(Δ′min < 0, TRUE, FALSE);

if (improved = FALSE) and (k − k′ > Lidle_iter) and (k < τ − Lidle_iter) then begin

/ retrieving solution from the secondary memory

random_access_index: = random(β × secondary_memory_index, secondary_memory_index);

p, Ξ, u″, v″ ← Γ(random_access_index);

$p: = \varphi (p, u^{″}, v^{″})$;

recalculate the values of the matrix Ξ;

clear tabu list TabuList;

TabuList(u″, v″): = k + h; / the elements p(u″), p(v″) become tabu

k′: = k

endif;

k: = k + 1

endwhile

end.