A performance guarantee heuristic for electronic components placements problems including thermal effects

In this work, Benders decomposition algorithm is used to deal with a computer motherboard design problem. Amongst all the possible formulations for the component placement problem, the chosen one creates an instance of the extensively studied Quadratic Assignment Problem (QAP). This problem arises as a great challenge for engineers and computer scientists. The QAP inherent combinatorial structure makes the most efficient optimization algorithms to exhibit low performance for real size instances. It is also considered here the important addition of linear costs. This approach is directly responsible for the performance gain presented by our decomposition method. Coupled with the placement problem, it is under investigation the maximum temperature rising on the board surface. In order to solve the Energy Conduction Equation the Finite Volume Method is implemented, becoming possible to derive a secondary quality solution criterion. A set of test instances is then solved and the corresponding results are reported.