Evolution of Deterministic Hill-climbers

Vincent Hénaux, Adrien Goëffon, Frédéric Saubion

Abstract: Local search algorithms consist in evolving a solution guided by a fitness function, which is usually directly derived from the objective function of the problem. Solving difficulties appear when the fitness landscape, naturally induced by the problem instance, is not perfectly exploitable, has a certain level of ruggedness and therefore has many local optima. We propose here to shift the problem from searching for a solution, to searching for a fitness function, which maximizes the efficiency of a deterministic and basic hill-climber. Considering that a LS algorithm is defined by a starting point, a neighborhood structure, a fitness function and a move strategy, we propose here to fix all components but the fitness function, so that each fitness function induces an algorithm generating a unique search trajectory. Through a simple evolution strategy applied to NK fitness functions, we propose to search for a basic hill-climbing algorithm specifically dedicated to attain the best possible solution of the original problem.