It is often desirable to evolve a resource allocation network (RAN) into a simpler one for improved controllability, operability, and ease of implementation. In this paper, a methodology, based on the concept of graph theory and process integration, is proposed to evolve a preliminary RAN into a simpler one involving fewer interconnections (matches) by incurring the minimum resource penalty. The proposed methodology is essentially based on four evolution strategies: loop breaking without. violation, two-loop relaxation, loop breaking with path relaxation, and direct path elimination. The procedure is applied to various RANs such as water allocation, hydrogen allocation, and material allocation in a reuse network. The evolved networks are compared With results obtained from a new mathematical optimization formulation involving mixed integer linear programming.