Optimization of current carrying multicables

High currents in cable bundles contribute to hotspot generation and overheating of essential car elements, especially in connecting structures. An important aspect in this context is the influence of the positioning of wires in cable harnesses. In order to find an appropriate multicable layout with minimized maximum temperatures, we formulate a corresponding optimization problem. Depending on the packing density of the cable bundle, it is solved via different optimization strategies: in case of loosely packed cable bundles solely by a gradient-based strategy (shape optimization), densely packed ones by arrangement heuristics combined with a standard genetic algorithm, others by mixed strategies.
In the simulation model, temperature dependence of the electric conductor resistances and different parameter values for the multitude of subdomains are respected in the governing semilinear and piecewise defined equation. Convective and radiative effects are summarized by a heat transfer coefficient in a nonlinear boundary condition at the exterior multicable surface. Finite elements in combination with an interior-point method and a genetic algorithm allow the solution of the optimization problem for a large number of cable bundle types. Furthermore, we present an adjoint method for the solution of the shape optimization problem. The jumps at the interfaces of different materials are essential for the Hadamard representation of the shape gradient. Numerical experiments are carried out to demonstrate the feasibility and scope of the present approach.