Sample approximations of multiobjective stochastic optimization problems

The article describes approximation technique for solving multiobjective stochastic optimization problems. As a generalized model of a stochastic system to be optimized a vector "input -- random output" system is used. Random outputs are converted into a vector of deterministic performance/risk indicators. The problem is to find those inputs that correspond to Pareto-optimal values of the output indicators. The problem is approximated by a sequence of deterministic multicriterion optimization problems, where, for example, the objective vector function is a sample average approximation of the original one and the feasible set is a discrete sample approximation of the feasible inputs. Approximate optimal solutions are defined as weakly Pareto efficient ones within some vector tolerance. Convergence analysis includes establishing convergence of the general approximation scheme and establishing conditions of convergence with probability one under proper regulation of sampling parameters. Parallel computations are used for statistical evaluation of the performance indicators, as well as to accelerate sampling in the space of the system inputs. The proposed solution technique can also be interpreted as an interactive parallel Monte Carlo method with selection of approximately Pareto-nondominated points. The proposed technique is illustrated by an example of multicriterion optimization in insurance.


Norkin B.V. Sample approximations of multiobjective stochastic optimization problems. Glushkov Institute of Cybernetics, Kyiv, November 2014



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