Injection-molding part designers are frequently faced with multiple quality and cost issues. These issues are usually in conflict with each other; thus, a trade-off needs to be made to reach a final compromised solution. Because evaluation of part quality and cost via injection-molding simulation is very time-consuming, implementation of a conventional multicriteria optimization procedure for injection-molding problems is economically unfavorable. However, many injection-molding problems dealing with multiple quality and cost issues can be modeled as constrained problems, with the total cost as the objective function and quality quantities as the constraints. By introducing a concept of penalized total cost, such constrained problems are further simplified into bounded single-criterion problems. The bounded single-criterion problems are then optimized using a direct search-based optimization procedure. Strategies of modeling, transformation, and optimization for these problems are discussed in this article. A case study is provided.