Dynamic landscape analysis for open-ended stacking

Fitness landscape analysis (FLA) is a useful tool in the domain of (meta-)heuristic optimization but depends on explicitly knowing what fitness value is assigned to each solution. Dynamic optimization problems often do not provide their fitness landscape in such an explicit form, but by employing problem-specific knowledge, information about the problem itself and its current state can still be obtained. In this paper, a type of gray-box analysis of states of the open-ended stacking problem in two variations is presented. The current states obtained by monitoring the problem and algorithm during optimization are described via statistical measures similar to FLA measures. From this the distribution of possible states (the state landscape) and the transitions between problem states are analyzed. Visualization of the empirically obtained results reveals insights into algorithm-problem dynamics.