We introduce Local Reinforcement-Based Selection of Auxiliary Objectives (LRSAO), a novel approach that selects auxiliary objectives using reinforcement learning (RL) to support the optimization process of an evolutionary algorithm (EA) as in EA+RL framework and furthermore incorporates the ability to unlearn previously used objectives. By modifying the reward mechanism to penalize moves that do no increase the fitness value and relying on the local auxiliary objectives, LRSAO dynamically adapts its selection strategy to optimize performance according to the landscape and unlearn previous objectives when necessary.

The move-acceptance hyper-heuristic was recently shown to be able to leave local optima with astonishing efficiency (Lissovoi et al., Artificial Intelligence (2023)). In this work, we propose two modifications to this algorithm that demonstrate impressive performances on a large class of benchmarks including the classic CLIFF_d and JUMP_m function classes. (i) Instead of randomly choosing between the only-improving and any-move acceptance operator, we take this choice via a simple two-state Markov chain. This modification alone reduces the runtime on JUMP_m functions with gap parameter m from ?(n²ᵐ⁻¹) to O(nᵐ⁺¹). (ii) We then replace the all-moves acceptance operators with the operator that only accepts worsenings. Such a, counter-intuitive, operator has not been used before in the literature. However, our proofs show that our only-worsening operator can greatly help in leaving local optima, reducing, e.g., the runtime on Jump functions to O(n³ log n) independent of the gap size. In general, we prove a remarkably good runtime of O(nᵏ⁺¹ log n) for our Markov move-acceptance hyper-heuristic on all members of a new benchmark class SEQOPT_k, which contains a large number of functions having k successive local optima, and which contains the commonly studied JUMP_m and CLIFF_d functions for k=2.