A Hybrid Genetic-Simulated Annealing Algorithm for the Location-Inventory-Routing Problem Considering Returns under E-Supply Chain Environment

Pseudocode 1

Pseudocode of the proposed HGSAA.

Procedure: HGSAA for LIRP

Input: coordinates of nodes, demands and returns of DPs, MC parameters, vehicle capacity,

   HGSAA parameters

Output: the best solution (include routes, MCs locations, order times and order size)

Begin

Take pop

 for 𝑖=1 to pop_size

     Calculate individual fitness value 𝑓_𝑖

  end

    𝑓_best=max{𝑓_𝑖}

 𝑛=1

 𝑘=1

while  𝑛≤300

      select operator

         if 𝑟𝑎𝑛𝑑𝑜𝑚≤𝑝_𝑐 then

            crossover operator

         end

         if 𝑟𝑎𝑛𝑑𝑜𝑚≤𝑝_𝑚 then

          mutation operator

         end

     newpop

         for 𝑖=1  to newpop_size

             Calculate individual fitness value 𝑓_𝑖

         end

     𝑓_newbest=max{𝑓_𝑖}

     𝑓_worst=min{𝑓_𝑖}

              if 𝑓_newbest>𝑓_best then

               𝑛=1

               𝑓_best=𝑓_newbest

               pop(best,:) = newpop(newbest,:)

              elseif 𝑓_newbest==𝑓_best

                 𝑛=𝑛+1

              else

                 𝑛=1

               1Δ=𝑓_newbest−1𝑓_best

               𝑧=𝑒^(−Δ/𝑡)

                   if 𝑧>𝑟𝑎𝑛𝑑𝑜𝑚 then

                    𝑓_best=𝑓_newbest

                    pop(best,:) = newpop(newbest,:)

                   end

              𝑇=𝛼𝑇

                end

     newpop(worst,:) = pop(best,:)

     pop = newpop

     𝑘=𝑘+1

 end

 output the best solution

end