Multi-Objective Optimization under Positivity Constraints, with a Meteorological Example

Abstract—In many practical situations, we need to optimize several objectives under the positivity constraints. For example, in meteorological and environmental studies, it is important to collect various types of data, such as temperature and wind speed and direction, from weather stations. For maintenance purposes, it is convenient to place instruments that collect different weather data on the same weather station. Thus, we need to find the “best ” location for a weather station. The “best ” means, for example, that the external influences, such as flux of cars passing on nearby road, have a minimal impact on the measurement results. There are several such criteria, so we face a multi-objective optimization problem. In this paper, we show that traditional approaches for solving such problems – such as the weighted sum approach – are not fully adequate for solving our problem. We show tha