CUG智能优化课设 Python实现NSGA-Ⅱ算法，解决CEC-2021竞赛中的问题 .zip
在这个CUG智能优化课设中，学生通过Python编程语言实现了著名的多目标优化算法NSGA-Ⅱ（非支配排序遗传算法第二代），以此来解决CEC-2021（国际计算智能挑战赛）中的复杂优化问题。NSGA-Ⅱ是一种在遗传算法基础上发展起来的高效优化工具，尤其适用于解决多目标优化问题，这些问题通常涉及到多个相互冲突的目标函数，需要找到一组最优解，而非单一的全局最优解。
**NSGA-Ⅱ算法详解**
NSGA-Ⅱ的核心思想是基于非支配排序和拥挤距离的概念来寻找帕累托前沿，这是多目标优化问题中的理想解集。算法通过随机生成初始种群，然后进行以下步骤：
1. **选择操作**：NSGA-Ⅱ采用“锦标赛选择”策略，通过比较个体间的适应度值来决定保留哪些个体。适应度值是根据个体在所有目标函数上的表现计算得出的。
2. **交叉操作**：通过“均匀交叉”或“部分匹配交叉”等策略，将两个父代个体的部分基因片段交换，生成新的子代。
3. **变异操作**：应用“位翻转变异”或“区间变异”等方法，对个体的某些基因进行随机改变，增加种群多样性。
4. **非支配排序**：对所有个体进行两两比较，根据是否被其他个体支配，分为不同层级的 fronts。第一层front的个体是最优的，后面的front依次次优。
5. **拥挤距离计算**：在相同层级的front中，为了保持种群多样性，引入拥挤距离指标，衡量个体在目标空间中的分布情况。
6. **精英保留策略**：确保最优解能够传递到下一代，避免优良解的丢失。
7. **新一代种群构建**：结合非支配排序结果和拥挤距离，采用快速解拥挤策略选择最优子代进入下一代种群。
8. **迭代与终止条件**：重复上述步骤，直到达到预设的迭代次数或满足其他停止条件。
**CEC-2021竞赛介绍**
CEC（Competition on Evolutionary Computation）是由国际计算智能学会（IEEE Computational Intelligence Society）组织的年度挑战赛，旨在推动计算智能领域的研究和应用。CEC-2021可能包含多个复杂优化问题，如多目标优化、单目标优化、动态优化等，这些问题通常具有高维度、非线性、多模态和不连续的特性。参赛者需要设计和实现优化算法，对这些问题进行求解，评估算法的性能和效率。
通过这个课设，学生不仅能够深入理解NSGA-Ⅱ算法的原理和实现细节，还能通过实际问题的解决，提高解决复杂优化问题的能力。同时，这也为他们提供了参与高水平竞赛的机会，进一步提升其在计算智能领域的研究水平。
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