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(1) 针对约束与混合整数规划问题的改进策略
在处理非线性约束优化问题时，如何处理不可行解是关键。本文提出了基于改进Deb准则的FIPSO算法。传统的Deb准则往往直接丢弃不可行解，而FIPSO算法认为接近可行域边界的不可行解蕴含着重要的梯度信息。因此，算法允许粒子依概率保留“优秀”的不可行解作为个体历史最优，引导种群从不可行域快速穿越至可行域边界，有效跳出了局部极值陷阱。针对更为复杂的非线性混合整数规划问题，提出了EMPSO和CC-PSO/GA算法。EMPSO引入了专门针对离散变量的进化策略DS，解决了PSO天然不适合处理离散空间的短板；而CC-PSO/GA则采用协同进化框架，利用PSO处理连续变量，利用遗传算法（GA）处理离散变量，通过小种群协同交叉的方式实现了两种算法优势互补，在求解混合整数规划问题上展现了极高的求解效率和精度。
(2) 多目标与超多目标优化算法的构建
针对多目标优化问题，本文提出了MOIPSO算法。该算法根据解的支配关系，分别设计了针对支配解和非支配解的差异化学习策略，使得粒子能够更有针对性地向帕累托前沿飞行。同时，引入高斯变异增加稀疏区域的粒子密度，并提出了一种新的分布广度度量指标DM，有效评价了解集的覆盖范围。针对目标数超过3个的超多目标优化问题（MaOPs），提出了基于Tchebycheff分解的NMOPSO算法。该算法摒弃了传统的拥挤距离机制，转而采用以权重向量为中心的更新策略，将超多目标分解为多个单目标子问题协同求解。通过动态更新权重向量，保证了非劣解集在高维目标空间中的均匀分布，显著提升了算法在DTLZ和WFG等测试集上的性能。
(3) 金融预测与车间调度领域的应用实战
为了检验算法的实际效能，本文将其应用于两个截然不同的领域。在金融领域，提出了混合自适应PSO的BP神经网络算法（APSO-BP）用于股票价格预测。该算法利用PSO强大的全局搜索能力优化BP神经网络的初始权值和阈值，克服了BP算法易陷入局部最优、训练不稳定的缺点。实证分析表明，APSO-BP能更准确地捕捉股价波动趋势，为投资者提供有效的风险预警。在制造领域，针对多目标柔性作业车间调度问题（FJSP），提出了AMOPSO算法。
import numpy as np import random class ConstrainedPSO: def __init__(self, obj_func, constraints, dim, pop_size=30, max_iter=100): self.obj_func = obj_func self.constraints = constraints # List of func(x) <= 0 self.dim = dim self.pop_size = pop_size self.max_iter = max_iter self.positions = np.random.uniform(-10, 10, (pop_size, dim)) self.velocities = np.zeros((pop_size, dim)) self.pbest = self.positions.copy() self.gbest = self.positions[0] self.update_bests() def check_feasibility(self, x): violation = 0 for c in self.constraints: v = c(x) if v > 0: violation += v return violation def deb_comparison(self, idx, trial_pos): # Improved Deb's rules: # 1. Feasible > Infeasible # 2. Both feasible: better objective wins # 3. Both infeasible: lower violation wins (or keep close infeasible with prob) curr_viol = self.check_feasibility(self.pbest[idx]) trial_viol = self.check_feasibility(trial_pos) curr_obj = self.obj_func(self.pbest[idx]) trial_obj = self.obj_func(trial_pos) update = False if curr_viol == 0 and trial_viol == 0: if trial_obj < curr_obj: update = True elif trial_viol == 0 and curr_viol > 0: update = True elif trial_viol > 0 and curr_viol > 0: if trial_viol < curr_viol: update = True else: # Stochastic acceptance of infeasible solutions (Improved Deb) if np.random.rand() < 0.05: update = True if update: self.pbest[idx] = trial_pos def update_bests(self): # Update global best based on feasibility first best_viol = self.check_feasibility(self.gbest) best_obj = self.obj_func(self.gbest) for i in range(self.pop_size): viol = self.check_feasibility(self.pbest[i]) obj = self.obj_func(self.pbest[i]) if viol < best_viol: self.gbest = self.pbest[i].copy() best_viol = viol best_obj = obj elif viol == best_viol and obj < best_obj: self.gbest = self.pbest[i].copy() best_obj = obj def optimize(self): w = 0.7 c1, c2 = 1.5, 1.5 for t in range(self.max_iter): for i in range(self.pop_size): r1, r2 = np.random.rand(), np.random.rand() self.velocities[i] = (w * self.velocities[i] + c1 * r1 * (self.pbest[i] - self.positions[i]) + c2 * r2 * (self.gbest - self.positions[i])) trial_pos = self.positions[i] + self.velocities[i] # Hybrid Integer Handling (EMPSO concept simulated) # If dimensions > 5 are discrete integers: if self.dim > 5: trial_pos[5:] = np.round(trial_pos[5:]) self.deb_comparison(i, trial_pos) self.positions[i] = trial_pos self.update_bests() # Differential Evolution Strategy for gbest (FIPSO) if np.random.rand() < 0.2: idxs = list(range(self.pop_size)) a, b, c = self.pbest[np.random.choice(idxs, 3)] mutant = a + 0.5 * (b - c) if self.check_feasibility(mutant) <= self.check_feasibility(self.gbest): if self.obj_func(mutant) < self.obj_func(self.gbest): self.gbest = mutant return self.gbest, self.obj_func(self.gbest) def objective(x): return x[0]**2 + x[1]**2 def constraint(x): return x[0] + x[1] - 1.0 # x+y <= 1 if __name__ == "__main__": cpso = ConstrainedPSO(objective, [constraint], 2) sol, val = cpso.optimize() print(sol, val)成品代码50-200，定制代码300起，可以直接沟通
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