實戰：最佳化求解 API

Vibe Prompt

「幫我用 FastAPI 建立一個通用最佳化 API：使用者輸入目標函數與範圍，後端用模擬退火求解。」

from fastapi import FastAPI, HTTPException
from pydantic import BaseModel
import random, math

app = FastAPI(title="最佳化求解 API")

class OptimizeRequest(BaseModel):
    objective: str  # 數學表達式，如 "x**2 + y**2"
    bounds: list[list[float]]  # [[x_min,x_max], [y_min,y_max]]
    algorithm: str = "simulated_annealing"

class OptimizeResponse(BaseModel):
    best_solution: list[float]
    best_value: float
    algorithm: str
    iterations: int

@app.post("/optimize", response_model=OptimizeResponse)
def optimize(req: OptimizeRequest):
    dim = len(req.bounds)
    
    def objective(x):
        # 安全 eval
        env = {"x": x} if dim == 1 else {f"x{i}": x[i] for i in range(dim)}
        env.update({"sin": math.sin, "cos": math.cos, "sqrt": math.sqrt,
                     "abs": abs, "sum": sum, "pow": pow})
        return eval(req.objective, {"__builtins__": {}}, env)
    
    best = None
    best_val = float('inf')
    
    if req.algorithm == "simulated_annealing":
        current = [random.uniform(b[0], b[1]) for b in req.bounds]
        current_val = objective(current)
        temp = 1000
        iterations = 0
        
        while temp > 0.01:
            neighbor = [current[i] + random.uniform(-1, 1) for i in range(dim)]
            neighbor = [max(req.bounds[i][0], min(req.bounds[i][1], neighbor[i])) 
                       for i in range(dim)]
            neighbor_val = objective(neighbor)
            delta = neighbor_val - current_val
            
            if delta < 0 or random.random() < math.exp(-delta/temp):
                current = neighbor
                current_val = neighbor_val
                if current_val < best_val:
                    best = current[:]
                    best_val = current_val
            
            temp *= 0.995
            iterations += 1
    
    return OptimizeResponse(
        best_solution=best, best_value=round(best_val, 6),
        algorithm=req.algorithm, iterations=iterations
    )

if __name__ == "__main__":
    import uvicorn
    uvicorn.run(app, host="0.0.0.0", port=8000)

本日總結

• ✅ 模擬退火
• ✅ 遺傳演算法
• ✅ PSO
• ✅ 超參數調優
• ✅ 最佳化 API