Optimization of coefficients of lists of polynomials by evolutionary algorithms

We here discuss the optimization of coefficients of lists of polynomials using evolutionary computation. The given polynomials have 5 variables, namely t, a₁, a₂, a₃, a₄, and integer coefficients. The goal is to find integer values α_i , with i ∊ {1, 2, 3, 4}, substituting ai such that, after crossing out the gcd (greatest common divisor) of all coefficients of the polynomials, the resulting integers are minimized in absolute value. Evolution strategies, a special class of heuristic, evolutionary algorithms, are here used for solving this problem. In this paper we describe this approach in detail and analyze test results achieved for two benchmark problem instances; we also show a visual analysis of the fitness landscapes of these problem instances.