A Nonlinear Multiobjective Bilevel Model for Minimum Cost Network Flow Problem in a Large-Scale Construction Project

Algorithm 1

Procedure The updating of the best position in the subsequent iterations

generate an initial random solution 𝑝^𝑙1,best_𝑗(𝜏₁) and add it to the archive;

update 𝑝^𝑙1,best_𝑗(𝜏₁) to produce 𝑝^𝑙1_𝑗(𝜏₁+1) and evaluate 𝑝^𝑙1_𝑗(𝜏₁+1);

 If (𝑝^𝑙1,best_𝑗(𝜏₁)dominates𝑝^𝑙1_𝑗(𝜏₁+1))  then discard 𝑝^𝑙1_𝑗(𝜏₁+1);

 else if (𝑝^𝑙1_𝑗(𝜏₁+1)dominates𝑝^𝑙1,best_𝑗(𝜏₁))  then replace 𝑝^𝑙1,best_𝑗(𝜏₁) with 𝑝^𝑙1_𝑗(𝜏₁+1), and add 𝑝^𝑙1_𝑗(𝜏₁+1)

 to the archive 𝑝^𝑙1,best_𝑗(𝜏₁+1)=𝑝^𝑙1_𝑗(𝜏₁+1);

 else if (𝑝^𝑙1_𝑗(𝜏₁+1)isdominatedbyanymemberofthearchive) then discard 𝑝^𝑙_𝑗(𝜏₁+1);

 else apply test (𝑝^𝑙1,best_𝑗(𝜏₁),𝑝^𝑙1_𝑗(𝜏₁+1),archive) to determine which becomes the new current

solution and whether to add 𝑝^𝑙1_𝑗(𝜏₁+1) to the archive;

until a termination criterion has been reached, return to line 2.