近年來演化演算法被廣泛應用於求解問題，在現實世界中有許多問題可以用單目標實數最佳化問題來表示。此類型的問題在生活中隨處可見，例如電力調度使成本最小化問題、水資源分配問題。許多事都能用以此類型的問題來思考，尤其現實世界的問題處在的環境變化大，通常我們需要在短時間內就要求得一個良好的解，因此如何設計出有效率且效能好的演化演算法一直都是被研究者關注的重要議題。
本研究基於當今主流的L-SHADE 演算法，探討它自適應控制參數的方法並提出變體—mL-SHADE 求解單目標實數最佳化問題。在mL-SHADE演算法中移除了終止符號的設置，使演算法不會過早收斂；調整了CR值的修復方法，增加高斯分佈產生隨機值的效率；加入記憶體擾動機制，避免族群與記憶體長久未更新造成惡性循環；最後線性提升柯西分佈的尺度參數，使得在演化後期產生隨機值能夠較常選到離平均值較遠的數值。另外，本研究也探討族群多樣性的偵測與維護機制，從族群目前的狀態資訊提供演算法調整演化方向。實驗結果顯示mL-SHADE演算法所採用的機制與調整能夠有效的改善演算法效能。

[1] Wikipedia—Evolutionary Computation, url : https://en.wikipedia.org/wiki/Evolutionary_computation
[2] M. A. Abido, “Environmental/economic power dispatch using multiobjective evolutionary algorithms,” 2003 IEEE Power Engineering Society General Meeting, pp. 920-925, 2003.
[3] O. B. Haddad, A. Afshar and M. A. Mariño, “Honey-Bees Mating Optimi-zation (HBMO) Algorithm: A New Heuristic Approach for Water Re-sources Optimization,” Water Resources Management, vol. 20, pp. 661–680, 2006.
[4] R. Storn and K. Price, “Differential Evolution a Simple and Efficient Heuristic for Global Optimization over Continuous Spaces,” Global Optimization, vol. 11, no. 4, pp. 341–359, 1997.
[5] R. Tanabe, and A. S. Fukunaga, “Improving the Search Performance of SHADE Using Linear Population Size Reduction,” in IEEE CEC, pp. 1658–1665, 2014.
[6] E. Mezura-Montes, J. Velázquez-Reyes and C. A. C. Coello, “A Comparative Study of Differential Evolution Variants for Global Optimization,” in GECCO, pp. 485-492, 2006.
[7] M. Leon and N. Xiong, “Investigation of Mutation Strategies in Differential Evolution for Solving Global Optimization Problems,” in International Conference on Artificial Intelligence and Soft Computing (ICAISC), pp. 372-383, 2014.
[8] K. Opara and J. Arabas, “Comparison of mutation strategies in Differential Evolution – A probabilistic perspective,” Swarm and Evolutionary Computation, vol. 39, pp. 53-69, 2018.
[9] J. Zhang and A. C. Sanderson, “JADE: Adaptive Differential Evolution with Optional External Archive,” IEEE Transactions on Evolutionary Computation, vol. 13, no. 5, pp. 945– 958, 2009.
[10] R. Tanabe and A. Fukunaga, “Success-History Based Parameter Adaptation for Differential Evolution,” in IEEE CEC, pp. 71–78, 2013.
[11] S. M. Islam, S. Das, S. Ghosh, S. Roy, and P. N. Suganthan, “An Adaptive Differential Evolution Algorithm with Novel Mutation and Crossover Strategies for Global Numerical Optimization,” IEEE Transactions on SMC. B, vol. 42, no. 2, pp. 482–500, 2012.
[12] A. W. Mohamed and A. K. Mohamed, “Adaptive Guided Differential Evolution Algorithm with Novel Mutation for Numerical Optimization,” International Journal of Machine Learning and Cybernetics, vol. 10, pp. 253-277, 2019.
[13] A. W. Mohamed and A. S. Almazyad, “Differential Evolution with Novel Mutation and Adaptive Crossover Strategies for Solving Large Scale Global Optimization Problems,” Applied Computational Intelligence and Soft Computing, vol. 2017, Article ID 7974218, 18 pages, 2017.
[14] A. E. Eiben, R. Hinterding and Z. Michalewicz, “Parameter control in evolutionary algorithms,” IEEE Transactions on Evolutionary Computation, vol. 3, no. 2, pp. 124-141, 1999.
[15] R. Tanabe and A. Fukunaga, “Reviewing and Benchmarking Parameter Control Methods in Differential Evolution,” IEEE Transactions on Cybernetics, doi: 10.1109/TCYB.2019.2892735, 2019.
[16] S. Das, A. Konar, and U. K. Chakraborty, “Two Improved Differential Evolution Schemes for Faster Global Search,” in GECCO, pp. 991– 998, 2005.
[17] Y. Wang, Z. Cai, and Q. Zhang, “Differential Evolution with Composite Trial Vector Generation Strategies and Control Parameters,” IEEE Transactions on Evolutionary Computation, vol. 15, no. 1, pp. 55–66, 2011.
[18] S. Das, A. Ghosh, and S. S. Mullick, “A Switched Parameter Differential Evolution for Large Scale Global Optimization – Simpler May Be Better,” in MENDEL, pp. 103–125, 2015.
[19] J. Liu and J. Lampinen, “A Fuzzy Adaptive Differential Evolution Algorithm,” Soft Computing., vol. 9, no. 6, pp. 448–462, 2005.
[20] J. Brest, S. Greiner, B. Bošković, M. Mernik, and V. Žumer, “Self-Adapting Control Parameters in Differential Evolution: A Comparative Study on Numerical Benchmark Problems,” IEEE Transactions on Evolutionary Computation, vol. 10, no. 6, pp. 646–657, 2006.
[21] A. K. Qin and P. N. Suganthan, “Self-adaptive Differential Evolution Algorithm for Numerical Optimization,” in IEEE CEC, pp. 1785-1791, 2005.
[22] J. Tvrdık, “Competitive Differential Evolution,” in MENDEL, pp. 7–12, 2006
[23] J. Brest, M. S. Maučec, and B. Bošković, “Single Objective Real-Parameter Optimization: Algorithm jSO,” in IEEE CEC, pp. 1311–1318, 2017.
[24] N. H. Awad, M. Z. Ali, P. N. Suganthan and R. G. Reynolds, “An ensemble sinusoidal parameter adaptation incorporated with L-SHADE for solving CEC2014 benchmark problems,” in IEEE CEC, pp. 2958-2965, 2016.
[25] N. H. Awad, M. Z. Ali, P. N. Suganthan, and R.G. Reynolds, “Ensemble Sinusoidal Differential Covariance Matrix Adaptation with Euclidean Neighborhood for Solving CEC2017 Benchmark Problems,” in IEEE CEC, pp. 372-379, 2017.
[26] M. G. H. Omran, A. A. Salman, and A. P. Engelbrecht, “Self-adaptive Differential Evolution,” in CIS, pp. 192–199, 2005.
[27] G. Corriveau, R. Guilbault, A. Tahan and R. Sabourin, “Review and Study of Genotypic Diversity Measures for Real-Coded Representations,” IEEE Transactions on Evolutionary Computation, vol. 16, no. 5, pp. 695-710, 2012.
[28] IEEE Congress on Evolutionary Computation 2019 website, url : http://cec2019.org/
[29] CEC 100-Digit Challenge website, url : http://www.ntu.edu.sg/home/epnsugan/index_files/CEC2019/CEC2019.htm
[30] K. V. Price, N. H. Awad, M. Z. Ali, P. N. Suganthan, “Problem Definitions and Evaluation Criteria for the 100-Digit Challenge Special Session and Competition on Single Objective Numerical Optimization,” Technical Re-port, Nanyang Technological University, Singapore, November 2018.
[31] The SIAM 100-Digit Challenge, url : http://www-m3.ma.tum.de/m3old/bornemann/challengebook/
[32] V. Stanovov, S. Akhmedova, and E. Semenkin, “LSHADE Algorithm with Rank-Based Selective Pressure Strategy for Solving CEC 2017 Benchmark Problems,” in IEEE CEC, pp. 1-8, 2018.
[33] A. Kumar, R. K. Misra, and D. Singh, “Improving the Local Search Capability of Effective Butterfly Optimizer using Covariance Matrix Adapted Retreat Phase,” in IEEE CEC, pp. 1835-1842, 2017.
[34] G. Zhang and Y. Shi, “Hybrid Sampling Evolution Strategy for Solving Single Objective Bound Constrained Problems,” in IEEE CEC, pp. 1-7, 2018.
[35] Jia-Fong Yeh, Ting-Yu Chen, and Tsung-Che Chiang, “Modified L-SHADE for Single Objective Real-parameter Optimization,” in IEEE CEC, pp. 373-378, 2019.
[36] K. V. Price, N. H. Awad, M. Z. Ali and P. N. Suganthan, “The 2019 100-Digit Challenge on Real-Parameter, Single Objective Optimization: Final Report,” Technical Report, in IEEE CEC, 2019.