A new multi-objective mathematical model for the high-level synthesis of integrated circuits

An integrated circuit contains millions of components, all of which have to fit in the reserved silicon area and fulfill a defined functionality within a specified amount of execution time. Therefore, the design of an effective integrated circuit is a nontrivial task. Actually, it can be considered as a multi-objective optimization problem with two conflicting objectives: minimizing the total execution time called latency and the total silicon area of the integrated circuit. The overall problem is composed of tightly-coupled subproblems, i.e., determining the allocation of operators that execute the operations, the assignment of operations to operators, and scheduling of the operations. We formulate a multi-objective mixed-integer linear programming model (MOMILP) to solve this complex problem. It is novel since it incorporates decisions about the so-called multiplexers, which are essential components of an integrated circuit. The proposed MOMILP model is solved exactly using an augmented ε-constrained method. This enables us to find all the Pareto optimal solutions and hence the Pareto frontier for a given problem instance within a reasonable amount of computation time. The minimum latency and minimum area solutions of our model are 13.20 and 7.24% better on the average than the model that ignores multiplexers.