A polyomino is a generalization of the domino and is created by connecting a fixed number of unit squares along edges. Tiling a region with a given set of polyominoes is a hard combinatorial optimization problem. This paper is motivated by a recent application of irregular polyomino tilings in the design of phased array antennas. Specifically, we formulate the irregular polyomino tiling problem as a nonlinear exact set covering model, where irregularity is incorporated into the objective function using the information‐theoretic entropy concept. An exact solution method based on a branch‐and‐price framework along with novel branching and lower‐bounding schemes is proposed. The developed method is shown to be effective for small‐ and medium‐size instances of the problem. For large‐size instances, efficient heuristics and approximation algorithms are provided. Encouraging computational results including phased array antenna simulations are reported.
