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Existing state-of-the-art methods, including graph-based and sampling-based approaches, often produce sharp, suboptimal paths and struggle in complex search spaces, while trajectory-based algorithms suffer from high computational costs. Recently, meta-heuristic optimization algorithms have shown effective performance but often lack learning ability due to their inherent randomness. This paper introduces a unified benchmarking framework, named Reda\u2019s Path Planning Benchmark 2024 (RP2B-24), alongside two novel reinforcement learning (RL)-based path-planning algorithms: Q-Spline Multi-Operator Differential Evolution (QSMODE), utilizing Q-learning (Q-tables), and Deep Q-Spline Multi-Operator Differential Evolution (DQSMODE), based on Deep Q-networks (DQN). Both algorithms are integrated under a single framework and enhanced with cubic spline interpolation to improve path smoothness and adaptability. The proposed RP2B-24 library comprises 50 distinct benchmark problems, offering a comprehensive and generalizable testing ground for diverse path-planning algorithms. Unlike traditional approaches, RL in QSMODE\/DQSMODE is not merely a parameter adjustment method but is fully utilized to generate paths based on the accumulated search experience to enhance path quality. QSMODE\/DQSMODE introduces a unique self-training update mechanism for the Q-table and DQN based on candidate paths within the algorithm\u2019s population, complemented by a secondary update method that increases population diversity through random action selection. An adaptive RL switching probability dynamically alternates between these Q-table update modes. DQSMODE and QSMODE demonstrated superior performance, outperforming 22 state-of-the-art algorithms, including the IMODEII. The algorithms ranked first and second in the Friedman test and SNE-SR ranking test, achieving scores of 99.2877 (DQSMODE) and 93.0463 (QSMODE), with statistically significant results in the Wilcoxon test. The practical applicability of the algorithm was validated on a ROS-based system using a four-wheel differential drive robot, which successfully followed the planned paths in two driving scenarios, demonstrating the algorithm\u2019s feasibility and effectiveness for real-world scenarios. The source code for the proposed benchmark and algorithm is publicly available for further research and experimentation at: <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/github.com\/MohamedRedaMu\/RP2B24-Benchmark\" ext-link-type=\"uri\">https:\/\/github.com\/MohamedRedaMu\/RP2B24-Benchmark<\/jats:ext-link> and <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/github.com\/MohamedRedaMu\/QSMODEAlgorithm\" ext-link-type=\"uri\">https:\/\/github.com\/MohamedRedaMu\/QSMODEAlgorithm<\/jats:ext-link>.<\/jats:p>","DOI":"10.1007\/s10462-025-11129-6","type":"journal-article","created":{"date-parts":[[2025,2,24]],"date-time":"2025-02-24T02:13:59Z","timestamp":1740363239000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A novel reinforcement learning-based multi-operator differential evolution with cubic spline for the path planning problem"],"prefix":"10.1007","volume":"58","author":[{"given":"Mohamed","family":"Reda","sequence":"first","affiliation":[]},{"given":"Ahmed","family":"Onsy","sequence":"additional","affiliation":[]},{"given":"Amira Y.","family":"Haikal","sequence":"additional","affiliation":[]},{"given":"Ali","family":"Ghanbari","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,24]]},"reference":[{"key":"11129_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2024.123762","volume":"249","author":"MN Ab\u00a0Wahab","year":"2024","unstructured":"Ab\u00a0Wahab MN, Nazir A, Khalil A, Ho WJ, Akbar MF, Noor MHM, Mohamed ASA (2024) Improved genetic algorithm for mobile robot path planning in static environments. 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