SINOPSIS

An optimization algorithm called ant colony optimization combined with numerical methods is applied to determine the unknown position of a point heat source in a two-dimensional steady-state heat conduction problem with the Dirichlet and Robin boundary conditions. The determination is based on the temperature measurements at some points on the boundaries of the solving domain. Instead of the actual experiments, the temperature measurements at the measurement points are obtained from numerical simulations with the exact position of the point heat source. The inverse problem is solved as an optimization problem in which bi-objective functions are maximized by the ant colony optimization algorithm. The bi-objective functions include both the root-mean-square deviation and the correlation coefficients between the computed and measured temperatures at the measurement points. Each of the bi-objective functions is associated with one of the coordinates of the heat source position. They reflect the features of heat conduction problems and therefore can increase the rate of convergence of the inverse problem. Several numerical experiments are performed to test the proposed mathematical model under different circumstances. The results show that it can find the position of the point heat source accurately and efficiently with the average calculation times of the direct problems being less than 0.8% of all the possible positions.