Multi-objective Optimization for Common and Special Components: First Step Toward Network Optimization of Regular and Non-Regular Flights

To optimize the problem composed of (i) the common components which should be optimized from the viewpoint of all objective functions and (ii) the special components which should be optimized from the viewpoint of one of the objective functions, this paper proposes a new multi-objective optimization method which optimizes not only the common components for all objective functions but also the special ones for each objective function. To investigate the effectiveness of the proposed method, this paper tested our method on the test-bed problem which is an extended version of the 0/1 knapsack problem. The intensive experiments have revealed the following implications: (i) Our method finds better solutions which have higher fitness than the conventional method (NSGA-II); (ii) our method can find the solutions that had a large norm (which corresponds to a high profit of an airline company in the flight scheduling problem) with the high rate of the common components; and (iii) since the crowding distance employed in our method contributes to keeping the diversity during the solution search, our method has high exploration capability of solutions.