Channel routing is a type of problems arising in the detailed routing phase of VLSI physical design automation as well as in the design of printed circuit boards (PCBs). It has been known that channel routing problems can be formulated as constraint programming (CP) problems and thus CP solvers can be used to find solutions. In this article, we present a mixed integer linear programming (MILP) formulation to gridded dogleg channel routing problems. As a result, parallel MILP solvers, which have the ability to exploit the computational power of multi-core processors, can be used to find solutions. Experimental results show that high degrees of scalability can be achieved. Owing to the properties of MILP problems, it is possible to further shorten the execution time if a computer containing more processor cores is available.
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