Random-Key Optimizer for Mixed Integer Problems: Case Study in Portfolio Optimization

Mixed-Integer Programming (MIPs) contains NP-hard optimization problems with integer and continuous variables, applicable across various industries such as logistics, telecommunications, and finance. Commercial solvers (CPLEX, Gurobi, Xpress) primarily use the branch-and-bound method but are expensive and may become inefficient for large problems. This work proposes the Random-Key Optimizer (RKO), a flexible framework where the user develops a decoding function to handle MIP constraints. The method is applied to the Markowitz portfolio optimization problem with purchase and cardinality constraints as a proof of concept.