This paper presents basic concepts of inverse and optimization problems. Deterministic and stochastic minimization techniques in finite and infinite dimensional spaces are revised; advantages and disadvantages of each of them are discussed and a hybrid technique is introduced. Applications of the techniques discussed for inverse and optimization problems in heat transfer are presented

This article presents fully three-dimensional conjugate heat transfer analysis and a multi-objective, constrained optimization to find sizes of pin-fins, inlet water pressure, and average speed for arrays of micro pin-fins used in the forced convection cooling of an integrated circuit with a uniformly heated 4 × 3 mm footprint and a centrally located 0.5 × 0.5 mm hot spot. Sizes of micro pin-fins having cross sections shaped as circles, symmetric airfoils, and symmetric convex lenses are optimized to completely remove heat due to a steady, uniform heat flux of 500 W cm⁻² imposed over the entire footprint (background heat flux) and a steady, uniform heat flux of 2000 W cm⁻² imposed on the hot spot area only (hot spot heat flux). The two simultaneous objectives are to minimize maximum substrate temperature and minimize pumping power, while keeping the maximum temperature constrained below 85°C and removing all of input thermal energy by convection. The design variables are the inlet average velocity and size of the pin-fins. A response surface is generated for each of the objectives and coupled with a genetic algorithm to arrive at a Pareto frontier of the best trade-off solutions. Numerical results show that, for a specified maximum temperature, optimized arrays with pin-fins having symmetric convex lens shapes create the lowest pressure drop, followed by the symmetric airfoil and circular cross-section pin-fins. An a posteriori three-dimensional stress–deformation analysis incorporating hydrodynamic and thermal loads shows that Von-Mises stress for each pin-fin array is significantly below the yield strength of silicon, thus, confirming structural integrity of such arrays of micro pin-fins.

In this article, we describe a hybrid optimizer based on a highly accurate response surface method, which uses several radial basis functions and polynomials as interpolants. The response surface is capable to interpolate linear as well as highly non-linear functions in multi-dimensional spaces having up to 500 dimensions. The accuracy, robustness, efficiency, transparency and conceptual simplicity are discussed. Based on the extensive testing performed on 296 test functions, the radial basis functions (RBFs) approach seems computationally easy to implement and results are superior, requiring small computing time. The performance of the RBF approximation is compared with wavelets neural networks for several selected test cases and the optimizer is compared with other hybrid optimizers, as well as with the IOSO commercial code.