Resolution of a quadratic combinatorial problem by dynamic programming

Abstract

The problem of arranging heliostats on the collector field of a solar central receiver system can give rise to the following quadratic combinatorial formulation:

Maximize X^tP X subject to X^tX≤M

With X=(X₁, ...X_i, ...X_n)^t and i ɛ (1,...N); X_i=0 or 1.

We compute average intrinsic efficiencies of each location (p_ii) and average interaction rates due to shadow effects for each pair or heliostats (−p_ij). Then we want to optimally choose a maximum of M heliostat locations among N possible ones.

For finding the optimal vector, X*, we propose an original approach based on dynamic programming.