| (1) | 1: Initialization. |
| (2) | Iteration = 0; |
| (3) | Initialize P0, the positions of root tip group; |
| (4) | Evaluate the fitness of the group; |
| (5) | Evaluate the global general (GG) of each solution by equations (4)–(6) |
| (6) | 2: Do while (unsatisfactory conditions) |
| (7) | 3: Auxin concentration calculation |
| (8) | Compute the auxin concentration values of the root tip group by equation (9); |
| (9) | Sort the root tip group in order of descending accumulated auxin concentration; |
| (10) | Divide the root tip group into two subgroups, i.e. the main root group and the lateral root group of equation (10). |
| (11) | 4: Root branching |
| (12) | Determine the branch number of each branching root tip by equation (11); |
| (13) | 5: Main roots growing |
| (14) | Sort the main root subgroup in order of increasing cumulative auxin concentration; |
| (15) | The first half main roots are hydrotropic according to equation (12); |
| (16) | 6: Lateral roots growing |
| (17) | All the lateral root tips perform random walk operation according to equation (13); |
| (18) | 7: Dead roots eliminating |
| (19) | Remove the dead root tips (auxin concentration 0) from the root tip group; |
| (20) | 8: Generate offspring group |
| (21) | Gather the new generated solution as offspring group Ot; |
| (22) | 9: Determine the solutions of the next iteration |
| (23) | Combine parent group and offspring group |
| (24) | Non-dominated sort on Pareto dominance {F1, F2, …} |
| (25) | Add nondominated front Fi into the next group one by one until |
| (26) | Add the solutions of last nondominated front Fi with the largest p-optimality criterion one by one until . |
| (27) | 8: Memorize the best solution to date |
| (28) | Iteration = iteration + 1; |
| (29) | End while |
| (30) | 9: Output the best solution achieved. |
