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143 lines
5.3 KiB
Python
143 lines
5.3 KiB
Python
"""
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E1: GenSolver vs 通用 MIP (SCIP/CBC) — MIP 侧
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目的：与 gpu.cu 对比，展示 MIP 在复杂问题上的求解时间和质量
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实例：TSP (N=51,100,150), VRP (A-n32-k5)
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时间预算：1s, 10s, 60s
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用法：python mip.py
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"""
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import sys
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import os
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import time
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from ortools.linear_solver import pywraplp
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sys.path.insert(0, os.path.join(os.path.dirname(__file__), "..", "..", "common"))
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from instances import load_tsp, load_vrp, euc2d_dist_matrix, TSP_INSTANCES, VRP_INSTANCES
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TIME_BUDGETS = [1, 10, 60]
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def solve_tsp_mtz(dist, n, time_limit_sec, solver_id="SCIP"):
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"""TSP MTZ 公式"""
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solver = pywraplp.Solver.CreateSolver(solver_id)
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if not solver:
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return float("inf"), 0.0, "error"
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x = [[solver.IntVar(0, 1, f"x_{i}_{j}") for j in range(n)] for i in range(n)]
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u = [solver.IntVar(0, n - 1, f"u_{i}") for i in range(n)]
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for i in range(n):
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solver.Add(x[i][i] == 0)
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for i in range(n):
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solver.Add(sum(x[i][j] for j in range(n)) == 1)
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for j in range(n):
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solver.Add(sum(x[i][j] for i in range(n)) == 1)
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for i in range(1, n):
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for j in range(1, n):
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if i != j:
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solver.Add(u[i] - u[j] + n * x[i][j] <= n - 1)
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solver.Minimize(sum(dist[i][j] * x[i][j] for i in range(n) for j in range(n)))
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solver.SetTimeLimit(int(time_limit_sec * 1000))
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t0 = time.perf_counter()
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status = solver.Solve()
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elapsed_ms = (time.perf_counter() - t0) * 1000.0
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if status in (pywraplp.Solver.OPTIMAL, pywraplp.Solver.FEASIBLE):
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reason = "optimal" if status == pywraplp.Solver.OPTIMAL else "time"
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return solver.Objective().Value(), elapsed_ms, reason
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return float("inf"), elapsed_ms, "infeasible"
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def solve_vrp_mtz(dist, demands, n_nodes, n_vehicles, capacity, time_limit_sec, solver_id="SCIP"):
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"""VRP MTZ 公式（容量约束 + 子回路消除）"""
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solver = pywraplp.Solver.CreateSolver(solver_id)
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if not solver:
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return float("inf"), 0.0, "error"
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n = n_nodes
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x = [[[solver.IntVar(0, 1, f"x_{k}_{i}_{j}")
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for j in range(n)] for i in range(n)] for k in range(n_vehicles)]
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u = [[solver.IntVar(0, n - 1, f"u_{k}_{i}")
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for i in range(n)] for k in range(n_vehicles)]
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# each customer visited exactly once
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for j in range(1, n):
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solver.Add(sum(x[k][i][j] for k in range(n_vehicles) for i in range(n) if i != j) == 1)
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for k in range(n_vehicles):
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# flow conservation
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for j in range(n):
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solver.Add(sum(x[k][i][j] for i in range(n) if i != j) ==
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sum(x[k][j][i] for i in range(n) if i != j))
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# start/end at depot
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solver.Add(sum(x[k][0][j] for j in range(1, n)) <= 1)
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solver.Add(sum(x[k][j][0] for j in range(1, n)) <= 1)
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# capacity
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solver.Add(sum(demands[j] * sum(x[k][i][j] for i in range(n) if i != j)
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for j in range(1, n)) <= capacity)
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# no self-loops
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for i in range(n):
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solver.Add(x[k][i][i] == 0)
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# MTZ subtour elimination
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for i in range(1, n):
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for j in range(1, n):
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if i != j:
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solver.Add(u[k][i] - u[k][j] + n * x[k][i][j] <= n - 1)
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solver.Minimize(sum(dist[i][j] * x[k][i][j]
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for k in range(n_vehicles) for i in range(n) for j in range(n)))
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solver.SetTimeLimit(int(time_limit_sec * 1000))
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t0 = time.perf_counter()
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status = solver.Solve()
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elapsed_ms = (time.perf_counter() - t0) * 1000.0
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if status in (pywraplp.Solver.OPTIMAL, pywraplp.Solver.FEASIBLE):
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reason = "optimal" if status == pywraplp.Solver.OPTIMAL else "time"
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return solver.Objective().Value(), elapsed_ms, reason
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return float("inf"), elapsed_ms, "infeasible"
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def print_row(instance, config, obj, elapsed_ms, optimal, reason):
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if obj == float("inf"):
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print(f"{instance},{config},0,inf,0.00,{elapsed_ms:.1f},inf,0,{reason}")
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else:
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gap = (obj - optimal) / optimal * 100.0 if optimal > 0 else 0.0
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print(f"{instance},{config},0,{obj:.2f},0.00,{elapsed_ms:.1f},{gap:.2f},0,{reason}")
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sys.stdout.flush()
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def main():
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print("instance,config,seed,obj,penalty,time_ms,gap_pct,generations,stop_reason")
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tsp_targets = [e for e in TSP_INSTANCES if e["optimal"] <= 6528] # eil51, kroA100, ch150
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for entry in tsp_targets:
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inst = load_tsp(entry)
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print(f" [e1-mip] TSP {inst['name']} (n={inst['n']})", file=sys.stderr)
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dist = euc2d_dist_matrix(inst["coords"])
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for solver_id in ["SCIP", "CBC"]:
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for t in TIME_BUDGETS:
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config = f"mip_{solver_id}_{t}s"
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obj, ms, reason = solve_tsp_mtz(dist, inst["n"], t, solver_id)
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print_row(inst["name"], config, obj, ms, inst["optimal"], reason)
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for entry in VRP_INSTANCES:
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inst = load_vrp(entry)
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print(f" [e1-mip] VRP {inst['name']} (n={inst['n']})", file=sys.stderr)
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dist = euc2d_dist_matrix(inst["coords"])
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for solver_id in ["SCIP"]:
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for t in TIME_BUDGETS:
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config = f"mip_{solver_id}_{t}s"
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obj, ms, reason = solve_vrp_mtz(
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dist, inst["demands"], inst["n"],
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inst["n_vehicles"], inst["capacity"], t, solver_id)
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print_row(inst["name"], config, obj, ms, inst["optimal"], reason)
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if __name__ == "__main__":
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main()
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