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Interactive evolutionary multi-objective optimization and decision-making using reference direction method

In this paper, we borrow the concept of reference direction approach from the multi-criterion decision-making literature and combine it with an EMOprocedure to develop an algorithm for finding a single preferred solution in a multi-objective optimization scenario efficiently. EMO methodologies are adequately used to find a set of representative efficient solutions over the past decade. This study is timely in addressing the issue of optimizing and choosing a single solution using certain preference information. In this approach, the user supplies one or more reference directions in the objective space. The population approach of EMO methodologies is exploited to find a set of efficient solutions corresponding to a number of representative points along the reference direction. By using a utility function, a single solution is chosen for further analysis. This procedure is continued till no further improvement is possible. The working of the procedure is demonstrated on a set of test problems having two to ten objectives and on an engineering design problem. Results are verified with theoretically exact solutions on two-objective test problems.