Open AccessWe consider the task to assess the quality of Pareto set (front) numerical approximation in a multi-criteria optimization (MOC) problem. We mean that Pareto-approximation is obtained by means of this or that population e.g. genetic algorithm.
Eventually, the purpose of work is a comparative assessment of the efficiency of population algorithms of Pareto-approximation. The great number of characteristics (indicators) of the Pareto-approximation quality is developed. Therefore an assessment problem of the Paretoapproximation quality is also considered as multi-criteria (multi-indicator). There are a number of well-known software systems to solve an assessment problem of the Pareto-approximation quality in different degree. Common drawback of these systems is a lack of both the WEB INTERFACE and the support of a multi-indicator assessment of Pareto-approximation quality (though there is a support to calculate the values of a large number of these indicators). The PARETO RATING software system is urged to eliminate the specified shortcomings of known systems. As population algorithms of Pareto-approximation are, as a rule, stochastic, we consider statistical methods to assess the quality of two and more Pareto-approximations (and thereby the estimates of algorithms used to obtain these approximations as well) as follows: methods based on the ranging of the specified approximations; methods based on the quality indicators; methods based on the so-called empirical functions of approachability. We give formal statement of the MOC-problem and general scheme of the population algorithms of its solution, present reviews of known indicators of Pareto-approximation quality and statistical methods for assessment of Pareto-approximation quality. We describe the system architecture and main features of its software implementation and illustrate efficiency of made algorithmic and software solutions.