Solving Differential Equations with Evolutionary Algorithms

Supervisor: Dr.E. Carmona

Many fundamental laws of physics and chemistry can be formulated as differential equations and they are useful to model different problems in fields as biology, economics or engineering. Some differential equations admit solutions given by explicit formulae. However, in the general case only approximated solutions can be found. In the present work several algorithms to solve differential equations using Evolutionary Computation techniques are presented, such as Grammatical Evolution and Evolutionary Strategies. For that, the original problem is transformed into a new optimization problem using several collocation points. The proposed methods have several advantages respect to the traditional ones: the methods are mesh-free (no connectivity is needed), the solutions are expressed symbolically, and they can cope with a wide variety of equations (linear and no linear, systems of equations and partial differential equations). In order to facilitate the optimization process, a basis
function could be used to express the candidate solutions, such as trigonometric functions or Gaussian kernels. To show the performance of the proposed algorithms, they are applied on several differential equations extracted from the literature a comparison with other methods are briefly commented.

Jose María Chaquet