68 lines
2.8 KiB
Python
68 lines
2.8 KiB
Python
"""问题二近似最优参考：在保证接收盘内做稠密网格枚举。
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目标函数与生产实现一致（最坏后验包围半径 + 移动时间同分决胜），但候选点
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取自**均匀网格**而非环形采样族，因此可用来检验生产采样是否接近该目标下的
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网格最优。注意这是"同一目标下的网格参考"，不是连续问题的严格全局最优。
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"""
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from __future__ import annotations
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import math
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from mcm26b.config import ProblemConfig
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from mcm26b.planner import (_worst_posterior_radius, safe_disk_radius)
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from project.common import Method, problem_config
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from project.q2.region import first_bearing_region
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METHOD = Method(
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key="reference",
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name="保证接收盘内网格枚举",
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kind="reference",
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note="同一目标下的稠密网格参考，非连续全局最优",
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)
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GRID_SIDES = 9
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WITNESS_SPACING_M = 150.0
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def candidate(case: dict, config: ProblemConfig | None = None) -> dict:
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config = config or problem_config()
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region = first_bearing_region(case, config)
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station = (case["station"][0], case["station"][1])
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center = region.mec()[0]
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safe = safe_disk_radius(region, config)
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if safe < 0:
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return _payload(center, region, config, station, "无保证接收盘：退回 MEC 圆心")
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field, search = config.field, config.search
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half_angle = field.bearing_error_half_deg + search.bearing_rounding_margin_deg
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witnesses = region.witnesses(WITNESS_SPACING_M)
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step = 2.0 * safe / (GRID_SIDES - 1)
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best_key, best_point, best_worst = None, center, None
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for i in range(GRID_SIDES):
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for j in range(GRID_SIDES):
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point = (center[0] - safe + i * step, center[1] - safe + j * step)
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if math.dist(point, center) > safe + 1e-9:
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continue
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worst = _worst_posterior_radius(region, point, witnesses, half_angle,
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field.near_radius_m, search.polygon_sides)
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move = math.dist(station, point) / config.cost.speed_mps
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key = (round(worst, 6), round(move, 6))
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if best_key is None or key < best_key:
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best_key, best_point, best_worst = key, point, worst
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return _payload(best_point, region, config, station,
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f"安全盘网格 {GRID_SIDES}×{GRID_SIDES} 取最坏后验最小",
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worst_value=best_worst)
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def _payload(point, region, config, station, reason, worst_value=None) -> dict:
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return {
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"method": METHOD.key,
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"position": [round(point[0], 4), round(point[1], 4)],
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"worst_posterior_radius_m": worst_value,
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"move_cost_s": math.dist(station, point) / config.cost.speed_mps,
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"safe_disk_radius_m": safe_disk_radius(region, config),
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"initial_radius_m": region.mec()[1],
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"reason": reason,
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}
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