Using convex quadratic approximation as a local search operator in evolutionary multiobjective algorithms

Local search techniques based on Convex Quadratic Approximation (CQA) of functions are studied here, in order to speed up the convergence and the quality of solutions in evolutionary multiobjective algorithms. The hybrid methods studied here pick up points from the nondominated population and determine a CQA for each objective function. Since the CQA of the functions and the respective weighted sums are convex, fast deterministic methods can be used in order to generate approximated Pareto-optimal solutions from the approximated functions. A new scheme is proposed in this paper, using a CQA model that represents a lower bound for the function points, which can be solved via linear programming. This scheme and also another one using the methodology of linear matrix inequality (LMI) for CQA are coupled with a canonical implementation of the NSGA-II. Comparison tests are performed, using Monte Carlo simulations, considering the S-metric with an equivalent final number of evaluated objective functions and the algorithm execution time. The results indicate that the proposed scheme is promising.