Local search with quadratic approximations into memetic algorithms for optimization with multiple criteria.

Area of Science:

• Optimization
• Evolutionary Computation
• Numerical Analysis

Background:

• Multiobjective optimization problems (MOPs) often involve computationally expensive objective functions.
• Evolutionary algorithms (EAs) are widely used for MOPs but can require numerous function evaluations.
• Estimating the Pareto-optimal surface accurately is crucial for decision-making in MOPs.

Purpose of the Study:

• To propose a local search optimizer that improves the precision of Pareto-optimal surface estimation in multiobjective evolutionary techniques.
• To reduce the computational cost associated with function evaluations in evolutionary optimization.
• To develop a method suitable for costly black-box optimization scenarios.

Main Methods:

• The proposed local search operator utilizes quadratic approximations of objective functions and constraints.
• These approximations are constructed using existing function samples from the evolutionary algorithm.
• The local search phase involves solving a scalarized multiobjective quadratic optimization problem using an LMI solver.

Main Results:

• The local search optimizer enhances the precision of Pareto-optimal surface estimates.
• It achieves this with a reduced cost of function evaluations compared to traditional methods.
• The methodology is effective for expensive black-box optimization problems.

Conclusions:

• The integration of the proposed local search optimizer offers a cost-effective approach to improve multiobjective evolutionary algorithms.
• Quadratic approximations and LMI solvers enable efficient refinement of solutions without additional function evaluations.
• This technique is particularly beneficial for real-world problems where function evaluations are resource-intensive.