Open AccessWe consider the relatively new and rapidly developing class of methods to solve a problem of multi-objective optimization, based on the preliminary built finite-dimensional approximation of the set, and thereby, the Pareto front of this problem as well. The work investigates the efficiency of several modifications of the method of adaptive weighted sum (AWS). This method proposed in the paper of Ryu and Kim Van (JH. Ryu, S. Kim, H. Wan) is intended to build Pareto approximation of the multi-objective optimization problem.
The AWS method uses quadratic approximation of the objective functions in the current sub-domain of the search space (the area of trust) based on the gradient and Hessian matrix of the objective functions. To build the (quadratic) meta objective functions this work uses methods of the experimental design theory, which involves calculating the values of these functions in the grid nodes covering the area of trust (a sensing method of the search domain). There are two groups of the sensing methods under consideration: hypercube- and hyper-sphere-based methods. For each of these groups, a number of test multi-objective optimization tasks has been used to study the efficiency of the following grids: "Latin Hypercube"; grid, which is uniformly random for each measurement; grid, based on the LP sequences.