Genetic Programming With Mixed-Integer Linear Programming-Based Library Search

Genetic programming (GP) is one of the commonly used tools for symbolic regression. In the field of GP, the use of semantics and an external library of subexpressions for designing better search operators has recently gained significant attention. A notable example is semantic backpropagation, which has demonstrated an ability to obtain expressions with extremely small prediction errors. However, these expressions often tend to be long and difficult to interpret, which may restrict their applicability in real-life problems. In this paper, we propose a GP framework that includes two key elements, a new library construction scheme and a novel semantic operator based on mixed-integer linear programming (MILP). The proposed library construction scheme maintains diverse subexpressions and keeps the library size in check by imposing an upper limit. The proposed semantic operator constructs new expressions by effectively combining a given number of subexpressions from the library. These improvements have been integrated in a bi-objective GP framework with random desired operator (RDO), which attempts to simultaneously reduce the complexity and improve the fitness of the evolving expressions. The contributions of individual components are studied in detail using 15 benchmarks. It is observed that the use of the proposed scheme with RDO leads to shorter expressions without sacrificing accuracy of approximation. The addition of MILP further improves the results for certain types of problems.