数据集

json 形式（c.json）的中国各省市经纬度数据集，一共 2241 个市的数据，为后来的 TSP 问题中主要采用的数据集

[{"name": "北京市","log": "116.46","lat": "39.92","children": [{ "name": "北京", "log": "116.46", "lat": "39.92" },{ "name": "平谷", "log": "117.1", "lat": "40.13" },{ "name": "密云", "log": "116.85", "lat": "40.37" },{ "name": "顺义", "log": "116.65", "lat": "40.13" },{ "name": "通县", "log": "116.67", "lat": "39.92" },{ "name": "怀柔", "log": "116.62", "lat": "40.32" },{ "name": "大兴", "log": "116.33", "lat": "39.73" },{ "name": "房山", "log": "115.98", "lat": "39.72" },{ "name": "延庆", "log": "115.97", "lat": "40.47" },{ "name": "昌平", "log": "116.2", "lat": "40.22" }]},{"name": "上海市","log": "121.48","lat": "31.22","children": [{ "name": "上海", "log": "121.48", "lat": "31.22" },{ "name": "嘉定", "log": "121.24", "lat": "31.4" },{ "name": "宝山", "log": "121.48", "lat": "31.41" },{ "name": "川沙", "log": "121.7", "lat": "31.19" },{ "name": "南汇", "log": "121.76", "lat": "31.05" },{ "name": "奉贤", "log": "121.46", "lat": "30.92" },{ "name": "松江", "log": "121.24", "lat": "31" },{ "name": "金山", "log": "121.16", "lat": "30.89" },{ "name": "青浦", "log": "121.1", "lat": "31.15" },{ "name": "崇明", "log": "121.4", "lat": "31.73" }]},{"name": "天津市","log": "117.2","lat": "39.13","children": [{ "name": "天津", "log": "117.2", "lat": "39.13" },{ "name": "宁河", "log": "117.83", "lat": "39.33" },{ "name": "静海", "log": "116.92", "lat": "38.93" },{ "name": "蓟县", "log": "117.4", "lat": "40.05" },{ "name": "宝坻", "log": "117.3", "lat": "39.75" },{ "name": "武清", "log": "117.05", "lat": "39.4" }]},{"name": "重庆市","log": "106.54","lat": "29.59","children": [{ "name": "重庆", "log": "106.54", "lat": "29.59" },{ "name": "綦江", "log": "106.56", "lat": "29.41" },{ "name": "长寿", "log": "106.64", "lat": "29.01" },{ "name": "南桐", "log": "107.04", "lat": "29.86" },{ "name": "合川", "log": "106.28", "lat": "29.26" },{ "name": "潼南", "log": "106.22", "lat": "30.03" },{ "name": "铜梁", "log": "105.8", "lat": "30.16" },{ "name": "壁山", "log": "106.03", "lat": "29.86" },{ "name": "荣昌", "log": "106.21", "lat": "29.62" },{ "name": "大足", "log": "105.59", "lat": "29.4" },{ "name": "永川", "log": "105.71", "lat": "29.75" },{ "name": "万盛", "log": "105.91", "lat": "29.38" }]},{"name": "河北省","log": "114.48","lat": "38.03","children": [{ "name": "石家庄", "log": "114.48", "lat": "38.03" },{ "name": "唐山", "log": "118.02", "lat": "39.63" },{ "name": "行唐", "log": "114.54", "lat": "38.42" },{ "name": "灵寿", "log": "114.38", "lat": "38.31" },{ "name": "束鹿", "log": "115.18", "lat": "37.94" },{ "name": "晋县", "log": "115.03", "lat": "38.03" },{ "name": "藁城", "log": "114.84", "lat": "38.03" },{ "name": "高邑", "log": "114.58", "lat": "37.62" },{ "name": "赵县", "log": "114.78", "lat": "37.76" },{ "name": "井陉", "log": "114.13", "lat": "38.03" },{ "name": "获鹿", "log": "114.03", "lat": "38.08" },{ "name": "新乐", "log": "114.67", "lat": "38.33" },{ "name": "正定", "log": "114.56", "lat": "38.13" },{ "name": "深泽", "log": "115.2", "lat": "38.2" },{ "name": "无极", "log": "114.96", "lat": "38.16" },{ "name": "赞皇", "log": "114.35", "lat": "37.65" },{ "name": "元氏", "log": "114.5", "lat": "37.74" },{ "name": "栾城", "log": "114.64", "lat": "38.87" },{ "name": "平山", "log": "114.24", "lat": "38.2" },{ "name": "邯郸", "log": "114.47", "lat": "36.6" },{ "name": "永年", "log": "114.5", "lat": "36.77" },{ "name": "曲周", "log": "114.92", "lat": "36.78" },{ "name": "馆陶", "log": "115.4", "lat": "36.47" },{ "name": "魏县", "log": "114.94", "lat": "36.37" },{ "name": "成安", "log": "114.68", "lat": "36.43" },{ "name": "大名", "log": "115.14", "lat": "36.28" },{ "name": "涉县", "log": "113.67", "lat": "36.57" },{ "name": "鸡泽", "log": "113.85", "lat": "36.95" },{ "name": "丘县", "log": "115.18", "lat": "36.84" },{ "name": "广平", "log": "114.94", "lat": "36.49" },{ "name": "肥乡", "log": "114.8", "lat": "36.56" },{ "name": "临漳", "log": "114.62", "lat": "36.35" },{ "name": "磁县", "log": "114.37", "lat": "36.37" },{ "name": "武安", "log": "114.2", "lat": "36.7" },{ "name": "邢台", "log": "114.48", "lat": "37.05" },{ "name": "柏乡", "log": "114.68", "lat": "37.49" },{ "name": "宁普", "log": "114.9", "lat": "37.62" },{ "name": "隆尧", "log": "114.75", "lat": "37.35" },{ "name": "临西", "log": "115.5", "lat": "36.87" },{ "name": "南官", "log": "115.37", "lat": "37.37" },{ "name": "巨鹿", "log": "115.03", "lat": "37.22" },{ "name": "任县", "log": "114.68", "lat": "37.11" },{ "name": "沙河", "log": "114.52", "lat": "36.94" },{ "name": "临城", "log": "114.5", "lat": "37.43" },{ "name": "内丘", "log": "114.5", "lat": "37.28" },{ "name": "新河", "log": "115.22", "lat": "37.53" },{ "name": "清河", "log": "115.67", "lat": "37.07" },{ "name": "威县", "log": "115.08", "lat": "36.97" },{ "name": "广宗", "log": "115.14", "lat": "37.06" },{ "name": "平乡", "log": "115.02", "lat": "37.06" },{ "name": "南和", "log": "114.71", "lat": "37" },{ "name": "保定", "log": "115.48", "lat": "38.85" },{ "name": "涞水", "log": "115.71", "lat": "39.39" },{ "name": "涿县", "log": "115.98", "lat": "39.48" },{ "name": "定兴", "log": "115.78", "lat": "39.28" },{ "name": "容城", "log": "115.86", "lat": "39.06" },{ "name": "安新", "log": "115.92", "lat": "38.92" },{ "name": "蠡县", "log": "115.58", "lat": "38.49" },{ "name": "博野", "log": "115.46", "lat": "38.46" },{ "name": "定县", "log": "114.02", "lat": "38.52" },{ "name": "阜平", "log": "114.18", "lat": "38.85" },{ "name": "唐县", "log": "114.97", "lat": "38.75" },{ "name": "涞源", "log": "114.67", "lat": "39.37" },{ "name": "易县", "log": "115.49", "lat": "39.35" },{ "name": "新城", "log": "115.84", "lat": "39.34" },{ "name": "雄县", "log": "116.1", "lat": "38.98" },{ "name": "徐水", "log": "115.65", "lat": "39.02" },{ "name": "高阳", "log": "115.78", "lat": "38.68" },{ "name": "安国", "log": "115.3", "lat": "38.41" },{ "name": "清苑", "log": "115.47", "lat": "38.76" },{ "name": "望都", "log": "115.14", "lat": "38.71" },{ "name": "曲阳", "log": "114.68", "lat": "38.62" },{ "name": "完县", "log": "115.12", "lat": "38.84" },{ "name": "满城", "log": "115.45", "lat": "38.95" },{ "name": "张家口", "log": "114.87", "lat": "40.82" },{ "name": "康保", "log": "114.6", "lat": "41.87" },{ "name": "赤城", "log": "115.82", "lat": "40.92" },{ "name": "怀来", "log": "115.54", "lat": "40.4" },{ "name": "蔚县", "log": "114.53", "lat": "39.83" },{ "name": "宣化", "log": "115.03", "lat": "40.63" },{ "name": "张北", "log": "114.7", "lat": "41.15" },{ "name": "沽源", "log": "115.68", "lat": "41.68" },{ "name": "崇礼", "log": "115.25", "lat": "40.98" },{ "name": "涿鹿", "log": "115.2", "lat": "40.37" },{ "name": "阳原", "log": "114.15", "lat": "40.12" },{ "name": "怀安", "log": "114.38", "lat": "40.67" },{ "name": "尚义", "log": "113.95", "lat": "41.05" },{ "name": "万全", "log": "114.73", "lat": "40.84" },{ "name": "承德", "log": "117.93", "lat": "40.97" },{ "name": "围场", "log": "117.72", "lat": "41.95" },{ "name": "平泉", "log": "118.68", "lat": "41.02" },{ "name": "宽城", "log": "118.47", "lat": "40.62" },{ "name": "兴隆", "log": "117.48", "lat": "40.42" },{ "name": "滦平", "log": "117.53", "lat": "40.95" },{ "name": "隆化", "log": "117.7", "lat": "41.32" },{ "name": "青龙", "log": "118.93", "lat": "40.43" },{ "name": "丰宁", "log": "116.63", "lat": "41.2" },{ "name": "秦皇岛", "log": "119.57", "lat": "39.95" },{ "name": "迁西", "log": "118.3", "lat": "40.15" },{ "name": "迁安", "log": "118.69", "lat": "40.02" },{ "name": "昌黎", "log": "119.15", "lat": "39.72" },{ "name": "卢龙", "log": "118.85", "lat": "39.89" },{ "name": "滦南", "log": "118.67", "lat": "39.49" },{ "name": "玉田", "log": "117.9", "lat": "39.9" },{ "name": "唐海", "log": "118.54", "lat": "39.31" },{ "name": "遵化", "log": "117.97", "lat": "40.2" },{ "name": "抚宁", "log": "119.22", "lat": "39.88" },{ "name": "乐亭", "log": "118.9", "lat": "39.43" },{ "name": "滦县", "log": "118.73", "lat": "39.74" },{ "name": "丰南", "log": "118.1", "lat": "39.58" },{ "name": "丰润", "log": "118.13", "lat": "39.82" },{ "name": "廊坊", "log": "116.7", "lat": "39.53" },{ "name": "安次", "log": "116.69", "lat": "39.52" },{ "name": "三河", "log": "117.06", "lat": "39.97" },{ "name": "香河", "log": "117", "lat": "39.76" },{ "name": "霸县", "log": "116.38", "lat": "39.12" },{ "name": "固安", "log": "116.29", "lat": "39.44" },{ "name": "大城", "log": "116.63", "lat": "38.7" },{ "name": "文安", "log": "116.45", "lat": "38.87" },{ "name": "永清", "log": "116.48", "lat": "39.32" },{ "name": "大厂", "log": "116.98", "lat": "39.98" },{ "name": "沧州", "log": "116.83", "lat": "38.33" },{ "name": "黄骅", "log": "117.33", "lat": "38.4" },{ "name": "盐山", "log": "117.22", "lat": "38.07" },{ "name": "吴桥", "log": "116.37", "lat": "37.65" },{ "name": "东光", "log": "116.52", "lat": "37.89" },{ "name": "肃宁", "log": "115.82", "lat": "38.43" },{ "name": "河间", "log": "116.07", "lat": "38.45" },{ "name": "泊头", "log": "116.56", "lat": "38.08" },{ "name": "交河", "log": "116.27", "lat": "38.02" },{ "name": "青县", "log": "116.8", "lat": "38.58" },{ "name": "海兴", "log": "117.85", "lat": "38.17" },{ "name": "南皮", "log": "116.7", "lat": "38.05" },{ "name": "任丘", "log": "116.08", "lat": "38.72" },{ "name": "献县", "log": "116.12", "lat": "38.2" },{ "name": "孟村", "log": "117.1", "lat": "38.06" },{ "name": "衡水", "log": "115.72", "lat": "37.72" },{ "name": "饶阳", "log": "115.74", "lat": "38.24" },{ "name": "阜城", "log": "116.14", "lat": "37.87" },{ "name": "景县", "log": "116.26", "lat": "37.69" },{ "name": "枣强", "log": "115.72", "lat": "37.52" },{ "name": "深县", "log": "115.56", "lat": "38.02" },{ "name": "安平", "log": "115.5", "lat": "38.22" },{ "name": "武强", "log": "115.96", "lat": "38.03" },{ "name": "武邑", "log": "115.9", "lat": "37.81" },{ "name": "故城", "log": "115.96", "lat": "37.36" },{ "name": "冀县", "log": "115.56", "lat": "37.59" }]},{"name": "山西省","log": "112.53","lat": "37.87","children": [{ "name": "太原", "log": "112.53", "lat": "37.87" },{ "name": "阳曲", "log": "112.65", "lat": "38.05" },{ "name": "娄烦", "log": "111.78", "lat": "38.05" },{ "name": "清徐", "log": "112.33", "lat": "37.62" },{ "name": "大同", "log": "113.3", "lat": "40.12" },{ "name": "阳泉", "log": "113.57", "lat": "37.85" },{ "name": "长治", "log": "113.08", "lat": "36.18" },{ "name": "天镇", "log": "114.08", "lat": "40.42" },{ "name": "灵丘", "log": "114.2", "lat": "39.47" },{ "name": "怀仁", "log": "113.1", "lat": "39.82" },{ "name": "山阴", "log": "112.82", "lat": "39.52" },{ "name": "平鲁", "log": "112.12", "lat": "39.53" },{ "name": "右玉", "log": "112.33", "lat": "40.18" },{ "name": "阳高", "log": "113.72", "lat": "40.38" },{ "name": "广灵", "log": "113.27", "lat": "39.75" },{ "name": "浑源", "log": "113.68", "lat": "39.7" },{ "name": "应县", "log": "113.18", "lat": "39.58" },{ "name": "朔县", "log": "112.42", "lat": "39.32" },{ "name": "左云", "log": "112.67", "lat": "40.02" },{ "name": "忻县", "log": "112.7", "lat": "38.38" },{ "name": "代县", "log": "112.97", "lat": "39.07" },{ "name": "五台", "log": "113.32", "lat": "38.72" },{ "name": "静乐", "log": "111.9", "lat": "38.37" },{ "name": "保德", "log": "111.09", "lat": "38.01" },{ "name": "河曲", "log": "111.17", "lat": "39.38" },{ "name": "神池", "log": "112.17", "lat": "39.1" },{ "name": "原平", "log": "112.7", "lat": "38.73" },{ "name": "繁峙", "log": "113.28", "lat": "39.2" },{ "name": "定襄", "log": "112.95", "lat": "38.5" },{ "name": "岢岚", "log": "111.58", "lat": "38.7" },{ "name": "五寨", "log": "111.82", "lat": "38.93" },{ "name": "偏关", "log": "111.47", "lat": "39.45" },{ "name": "宁武", "log": "112.28", "lat": "39" },{ "name": "榆次", "log": "112.72", "lat": "37.68" },{ "name": "孟县", "log": "113.37", "lat": "38.01" },{ "name": "昔阳", "log": "113.68", "lat": "37.62" },{ "name": "左权", "log": "113.35", "lat": "37.07" },{ "name": "太谷", "log": "112.53", "lat": "37.42" },{ "name": "平遥", "log": "112.18", "lat": "37.2" },{ "name": "灵石", "log": "111.77", "lat": "36.83" },{ "name": "寿阳", "log": "113.17", "lat": "37.88" },{ "name": "平定", "log": "113.62", "lat": "37.79" },{ "name": "和顺", "log": "113.55", "lat": "37.33" },{ "name": "榆社", "log": "112.97", "lat": "37.08" },{ "name": "祁县", "log": "112.33", "lat": "37.36" },{ "name": "介休", "log": "111.88", "lat": "37.03" },{ "name": "离石", "log": "111.13", "lat": "37.53" },{ "name": "兴县", "log": "111.22", "lat": "38.47" },{ "name": "方由", "log": "111.24", "lat": "37.86" },{ "name": "岚县", "log": "111.62", "lat": "38.28" },{ "name": "交城", "log": "112.14", "lat": "37.55" },{ "name": "文水", "log": "112.02", "lat": "37.42" },{ "name": "汾阳", "log": "111.75", "lat": "37.27" },{ "name": "孝义", "log": "111.8", "lat": "37.12" },{ "name": "交口", "log": "111.2", "lat": "36.97" },{ "name": "石楼", "log": "110.83", "lat": "37" },{ "name": "中阳", "log": "111.17", "lat": "37.37" },{ "name": "临县", "log": "110.95", "lat": "37.95" },{ "name": "柳林", "log": "110.85", "lat": "37.45" },{ "name": "襄垣", "log": "113.02", "lat": "36.55" },{ "name": "黎城", "log": "113.4", "lat": "36.56" },{ "name": "壶关", "log": "113.23", "lat": "35.11" },{ "name": "高平", "log": "112.88", "lat": "35.48" },{ "name": "阳城", "log": "112.38", "lat": "35.84" },{ "name": "长子", "log": "112.87", "lat": "36.13" },{ "name": "沁源", "log": "112.32", "lat": "36.5" },{ "name": "潞城", "log": "113.22", "lat": "36.33" },{ "name": "武乡", "log": "112.83", "lat": "36.83" },{ "name": "平顺", "log": "113.43", "lat": "36.19" },{ "name": "陵川", "log": "113.27", "lat": "35.78" },{ "name": "晋城", "log": "112.83", "lat": "35.52" },{ "name": "沁水", "log": "112.15", "lat": "35.67" },{ "name": "屯留", "log": "112.87", "lat": "36.32" },{ "name": "沁县", "log": "112.68", "lat": "36.75" },{ "name": "临汾", "log": "111.5", "lat": "36.08" },{ "name": "汾西", "log": "111.53", "lat": "36.63" },{ "name": "安泽", "log": "112.2", "lat": "36.15" },{ "name": "古县", "log": "111.9", "lat": "36.29" },{ "name": "翼城", "log": "111.68", "lat": "35.73" },{ "name": "曲沃", "log": "111.33", "lat": "35.63" },{ "name": "吉县", "log": "110.65", "lat": "36.12" },{ "name": "大宁", "log": "110.72", "lat": "36.47" },{ "name": "侯马", "log": "111.45", "lat": "35.03" },{ "name": "永和", "log": "110.64", "lat": "36.62" },{ "name": "洪洞", "log": "111.68", "lat": "36.25" },{ "name": "霍县", "log": "111.72", "lat": "36.57" },{ "name": "浮山", "log": "111.83", "lat": "35.97" },{ "name": "襄汾", "log": "111.43", "lat": "35.86" },{ "name": "乡宁", "log": "110.8", "lat": "35.97" },{ "name": "蒲县", "log": "111.07", "lat": "36.42" },{ "name": "运城", "log": "110.97", "lat": "35.03" },{ "name": "闻喜", "log": "111.2", "lat": "35.37" },{ "name": "垣曲", "log": "111.63", "lat": "35.3" },{ "name": "芮城", "log": "110.68", "lat": "34.71" },{ "name": "临猗", "log": "110.78", "lat": "35.15" },{ "name": "新绛", "log": "111.22", "lat": "35.62" },{ "name": "河津", "log": "110.7", "lat": "35.58" },{ "name": "夏县", "log": "111.22", "lat": "35.12" },{ "name": "绛县", "log": "111.58", "lat": "35.48" },{ "name": "平陆", "log": "111.2", "lat": "34.12" },{ "name": "永济", "log": "110.42", "lat": "34.88" },{ "name": "万荣", "log": "110.83", "lat": "110.83" },{ "name": "稷山", "log": "110.97", "lat": "35.6" }]},{"name": "辽宁省","log": "123.38","lat": "41.8","children": [{ "name": "沈阳", "log": "123.38", "lat": "41.8" },{ "name": "新民", "log": "122.83", "lat": "42" },{ "name": "辽中", "log": "122.7", "lat": "41.52" },{ "name": "大连", "log": "121.62", "lat": "38.92" },{ "name": "金县", "log": 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"name": "察雅", "log": "97.56", "lat": "30.69" },{ "name": "芒康", "log": "98.68", "lat": "29.64" },{ "name": "八宿", "log": "96.95", "lat": "30.04" },{ "name": "边坝", "log": "94.69", "lat": "30.94" },{ "name": "类乌齐", "log": "96.57", "lat": "31.2" },{ "name": "乃东", "log": "91.76", "lat": "29.18" },{ "name": "加查", "log": "92.6", "lat": "29.09" },{ "name": "曲松", "log": "92.11", "lat": "29.08" },{ "name": "错那", "log": "91.91", "lat": "27.98" },{ "name": "穷结", "log": "91.65", "lat": "29.04" },{ "name": "贡嘎", "log": "90.96", "lat": "29.25" },{ "name": "浪卡子", "log": "90.33", "lat": "29.96" },{ "name": "桑日", "log": "92", "lat": "29.26" },{ "name": "朗县", "log": "93.11", "lat": "29.06" },{ "name": "隆子", "log": "92.42", "lat": "28.46" },{ "name": "措美", "log": "91.4", "lat": "28.49" },{ "name": "洛扎", "log": "90.83", "lat": "28.42" },{ "name": "扎囊", "log": "91.26", "lat": "29.22" },{ "name": "日喀则", "log": "88.82", "lat": "29.28" },{ "name": "定结", "log": "87.77", "lat": "28.38" },{ "name": "拉孜", "log": "87.62", "lat": "29.1" },{ "name": "聂拉木", "log": "85.94", "lat": "28.19" },{ "name": "谢通门", "log": "88.25", "lat": "29.43" },{ "name": "仲巴", "log": "84.15", "lat": "29.66" },{ "name": "康马", "log": "89.67", "lat": "28.57" },{ "name": "亚东", "log": "88.93", "lat": "27.55" },{ "name": "岗巴", "log": "88.5", "lat": "28.29" },{ "name": "南木林", "log": "89.02", "lat": "29.71" },{ "name": "萨迦", "log": "88", "lat": "28.87" },{ "name": "定日", "log": "87.11", "lat": "28.57" },{ "name": "吉隆", "log": "85.29", "lat": "28.94" },{ "name": "昂仁", "log": "87.22", "lat": "29.3" },{ "name": "江孜", "log": "89.63", "lat": "28.94" },{ "name": "仁布", "log": "89.77", "lat": "29.21" },{ "name": "白朗", "log": "89.16", "lat": "29.11" },{ "name": "萨嘎", "log": "85.3", "lat": "29.38" },{ "name": "噶尔", "log": "80", "lat": "32.08" },{ "name": "革吉", "log": "81.13", "lat": "32.45" },{ "name": "扎达", "log": "79.76", "lat": "31.47" },{ "name": "措勤", "log": "85.16", "lat": "31.06" },{ "name": "日上", "log": "79.61", "lat": "33.44" },{ "name": "改则", "log": "84.1", "lat": "32.33" },{ "name": "普兰", "log": "81.18", "lat": "30.37" }]},{"name": "宁夏回族自治区","log": "106.27","lat": "38.47","children": [{ "name": "银川", "log": "106.27", "lat": "38.47" },{ "name": "永宁", "log": "106.24", "lat": "38.28" },{ "name": "贺兰", "log": "106.35", "lat": "38.55" },{ "name": "石嘴山", "log": "106.39", "lat": "39.04" },{ "name": "平罗", "log": "106.54", "lat": "38.91" },{ "name": "陶乐", "log": "106.69", "lat": "38.82" },{ "name": "吴忠", "log": "106.21", "lat": "37.99" },{ "name": "同心", "log": "105.94", "lat": "36.97" },{ "name": "灵武", "log": "106.34", "lat": "38.1" },{ "name": "中宁", "log": "105.66", "lat": "37.48" },{ "name": "盐池", "log": "107.41", "lat": "37.78" },{ "name": "中卫", "log": "105.18", "lat": "37.51" },{ "name": "青铜峡", "log": "106.07", "lat": "38.02" },{ "name": "固原", "log": "106.28", "lat": "36.01" },{ "name": "西吉", "log": "105.7", "lat": "35.97" },{ "name": "泾源", "log": "106.33", "lat": "35.5" },{ "name": "海原", "log": "105.64", "lat": "36.56" },{ "name": "隆德", "log": "106.11", "lat": "35.63" }]},{"name": "中国台湾","log": "121.5","lat": "25.14","children": [{ "name": "台湾", "log": "121.5", "lat": "25.14" }]},{"name": "中国香港","log": "114.1","lat": "22.2","children": [{ "name": "香港", "log": "114.1", "lat": "22.2" }]},{"name": "中国澳门","log": "113.33","lat": "22.13","children": [{ "name": "澳门", "log": "113.33", "lat": "22.13" }]},{"name": "安徽省","log": "117.27","lat": "31.86","children": [{ "name": "合肥", "log": "117.27", "lat": "31.86" },{ "name": "长丰", "log": "117.16", "lat": "32.47" },{ "name": "淮南", "log": "116.98", "lat": "32.62" },{ "name": "凤台", "log": "116.71", "lat": "32.68" },{ "name": "淮北", "log": "116.77", "lat": "33.97" },{ "name": "濉溪", "log": "116.76", "lat": "33.92" },{ "name": "芜湖", "log": "118.38", "lat": "31.33" },{ "name": "铜陵", "log": "117.82", "lat": "30.93" },{ "name": "蚌埠", "log": "117.34", "lat": "32.93" },{ "name": "马鞍山", "log": "118.48", "lat": "31.56" },{ "name": "安庆", "log": "117.03", "lat": "30.52" },{ "name": "宿州", "log": "116.97", "lat": "33.63" },{ "name": "砀山", "log": "116.34", "lat": "34.42" },{ "name": "萧县", "log": "116.93", "lat": "34.19" },{ "name": "吴壁", "log": "117.55", "lat": "33.55" },{ "name": "泗县", "log": "117.89", "lat": "33.49" },{ "name": "五河", "log": "117.87", "lat": "33.14" },{ "name": "固镇", "log": "117.32", "lat": "33.33" },{ "name": "怀远", "log": "117.19", "lat": "32.95" },{ "name": "滁州", "log": "118.31", "lat": "32.33" },{ "name": "嘉山", "log": "117.98", "lat": "32.78" },{ "name": "天长", "log": "119", "lat": "32.68" },{ "name": "来安", "log": "118.44", "lat": "32.44" },{ "name": "全椒", "log": "118.27", "lat": "32.1" },{ "name": "定远", "log": "117.68", "lat": "32.52" },{ "name": "凤阳", "log": "117.4", "lat": "32.86" },{ "name": "巢湖", "log": "117.87", "lat": "31.62" },{ "name": "肥东", "log": "117.47", "lat": "31.89" },{ "name": "含山", "log": "118.11", "lat": "31.7" },{ "name": "和县", "log": "118.37", "lat": "31.7" },{ "name": "无为", "log": "117.75", "lat": "31.3" },{ "name": "卢江", "log": "117.29", "lat": "31.23" },{ "name": "宣城", "log": "118.73", "lat": "31.95" },{ "name": "当涂", "log": "118.49", "lat": "31.55" },{ "name": "郎溪", "log": "119.17", "lat": "31.14" },{ "name": "广德", "log": "119.41", "lat": "30.89" },{ "name": "泾县", "log": "118.41", "lat": "30.68" },{ "name": "南陵", "log": "118.32", "lat": "30.91" },{ "name": "繁昌", "log": "118.21", "lat": "31.07" },{ "name": "宁国", "log": "118.95", "lat": "30.62" },{ "name": "青阳", "log": "117.84", "lat": "30.64" },{ "name": "屯溪", "log": "118.31", "lat": "29.72" },{ "name": "休宁", "log": "118.19", "lat": "29.81" },{ "name": "旌得", "log": "118.53", "lat": "30.28" },{ "name": "绩溪", "log": "118.57", "lat": "30.07" },{ "name": "歙县", "log": "118.44", "lat": "29.88" },{ "name": "祁门", "log": "117.7", "lat": "29.86" },{ "name": "黟县", "log": "117.92", "lat": "29.93" },{ "name": "太平", "log": "118.13", "lat": "30.28" },{ "name": "石台", "log": "117.48", "lat": "30.19" },{ "name": "桐城", "log": "116.94", "lat": "31.04" },{ "name": "纵阳", "log": "117.21", "lat": "30.69" },{ "name": "怀宁", "log": "116.63", "lat": "30.41" },{ "name": "望江", "log": "116.69", "lat": "30.12" },{ "name": "宿松", "log": "116.13", "lat": "30.15" },{ "name": "太湖", "log": "116.27", "lat": "30.42" },{ "name": "岳西", "log": "116.36", "lat": "30.84" },{ "name": "潜山", "log": "116.53", "lat": "30.62" },{ "name": "东至", "log": "116.99", "lat": "30.08" },{ "name": "贵池", "log": "117.48", "lat": "30.66" },{ "name": "六安", "log": "116.49", "lat": "31.73" },{ "name": "霍丘", "log": "116.27", "lat": "32.32" },{ "name": "寿县", "log": "116.78", "lat": "32.57" },{ "name": "肥西", "log": "117.15", "lat": "31.7" },{ "name": "舒城", "log": "116.94", "lat": "31.45" },{ "name": "霍山", "log": "116.32", "lat": "31.38" },{ "name": "金寨", "log": "115.87", "lat": "31.67" },{ "name": "阜阳", "log": "115.81", "lat": "32.89" },{ "name": "毫县", "log": "116.76", "lat": "33.86" },{ "name": "涡阳", "log": "116.21", "lat": "33.49" },{ "name": "蒙城", "log": "116.55", "lat": "33.25" },{ "name": "利辛", "log": "116.19", "lat": "33.12" },{ "name": "颖上", "log": "116.26", "lat": "32.62" },{ "name": "阜南", "log": "115.6", "lat": "32.63" },{ "name": "临泉", "log": "115.24", "lat": "33.06" },{ "name": "界首", "log": "115.34", "lat": "33.24" },{ "name": "太和", "log": "115.61", "lat": "33.16" }]},{"name": "江苏省","log": "118.78","lat": "32.04","children": [{ "name": "南京", "log": "118.78", "lat": "32.04" },{ "name": "江宁", "log": "118.83", "lat": "31.95" },{ "name": "六合", "log": "118.83", "lat": "32.36" },{ "name": "江浦", "log": "118.62", "lat": "32.07" },{ "name": "徐州", "log": "117.2", "lat": "34.26" },{ "name": "连云港", "log": "119.16", "lat": "34.59" },{ "name": "南通", "log": "120.86", "lat": "32.01" },{ "name": "苏州", "log": "120.62", "lat": "31.32" },{ "name": "无锡", "log": "120.29", "lat": "31.59" },{ "name": "常州", "log": "119.95", "lat": "31.79" },{ "name": "丰县", "log": "116.57", "lat": "34.79" },{ "name": "沛县", "log": "116.93", "lat": "34.73" },{ "name": "赣榆", "log": "119.11", "lat": "34.83" },{ "name": "东海", "log": "118.75", "lat": "34.54" },{ "name": "新沂", "log": "118.33", "lat": "34.38" },{ "name": "邳县", "log": "117.97", "lat": "34.3" },{ "name": "睢宁", "log": "117.94", "lat": "33.89" },{ "name": "清江", "log": "119.02", "lat": "33.59" },{ "name": "灌云", "log": "119.23", "lat": "34.3" },{ "name": "灌南", "log": "119.36", "lat": "34.09" },{ "name": "沭阳", "log": "118.79", "lat": "34.12" },{ "name": "宿迁", "log": "118.3", "lat": "33.96" },{ "name": "泗阳", "log": "118.68", "lat": "33.73" },{ "name": "盱眙", "log": "118.05", "lat": "33" },{ "name": "涟水", "log": "119.26", "lat": "33.77" },{ "name": "淮阴", "log": "119.02", "lat": "33.62" },{ "name": "淮安", "log": "119.15", "lat": "33.5" },{ "name": "洪泽", "log": "118.85", "lat": "33.28" },{ "name": "泗洪", "log": "118.23", "lat": "33.46" },{ "name": "金湖", "log": "119.02", "lat": "33.01" },{ "name": "盐城", "log": "120.13", "lat": "33.38" },{ "name": "滨海", "log": "119.84", "lat": "34.01" },{ "name": "阜宁", "log": "119.79", "lat": "33.78" },{ "name": "射阳", "log": "120.26", "lat": "33.77" },{ "name": "建湖", "log": "119.77", "lat": "33.46" },{ "name": "响水", "log": "119.56", "lat": "34.2" },{ "name": "大丰", "log": "120.45", "lat": "33.19" },{ "name": "东台", "log": "120.31", "lat": "32.84" },{ "name": "海安", "log": "120.45", "lat": "32.57" },{ "name": "如皋", "log": "120.56", "lat": "32.39" },{ "name": "如东", "log": "121.18", "lat": "32.33" },{ "name": "启东", "log": "121.66", "lat": "31.8" },{ "name": "海门", "log": "121.15", "lat": "31.89" },{ "name": "南通", "log": "121.05", "lat": "32.08" },{ "name": "扬州", "log": "119.42", "lat": "32.39" },{ "name": "宝应", "log": "119.32", "lat": "33.23" },{ "name": "兴化", "log": "119.82", "lat": "32.93" },{ "name": "高邮", "log": "119.45", "lat": "32.78" },{ "name": "泰兴", "log": "120.02", "lat": "32.16" },{ "name": "泰县", "log": "120.15", "lat": "32.51" },{ "name": "泰州", "log": "119.9", "lat": "32.49" },{ "name": "靖江", "log": "120.26", "lat": "32.03" },{ "name": "江都", "log": "119.55", "lat": "32.43" },{ "name": "仪征", "log": "119.16", "lat": "32.27" },{ "name": "镇江", "log": "119.44", "lat": "32.2" },{ "name": "扬中", "log": "119.81", "lat": "32.24" },{ "name": "丹阳", "log": "119.55", "lat": "32" },{ "name": "武进", "log": "119.95", "lat": "31.78" },{ "name": "宜兴", "log": "119.82", "lat": "31.36" },{ "name": "金坛", "log": "119.56", "lat": "31.74" },{ "name": "溧阳", "log": "119.48", "lat": "31.43" },{ "name": "句容", "log": "119.16", "lat": "31.95" },{ "name": "溧水", "log": "119.02", "lat": "31.65" },{ "name": "高淳", "log": "118.87", "lat": "31.32" },{ "name": "江阴", "log": "120.26", "lat": "31.91" },{ "name": "沙洲", "log": "120.55", "lat": "31.86" },{ "name": "常熟", "log": "120.74", "lat": "31.64" },{ "name": "太仓", "log": "121.1", "lat": "31.45" },{ "name": "昆山", "log": "120.95", "lat": "31.39" },{ "name": "吴江", "log": "120.63", "lat": "31.16" }]}
]

Tools.py

Tools 文件为工具函数文件，其中包含一个 get_city()函数，作用是根据输入的城 市数量，获得所需的城市信息

import json# 返回等于限制数的城市数量
def get_city(limit):city_dic = []provinces = json.loads(open("../data/c.json", encoding="utf-8").read())count = 0province_limit = limit // 30+1000if province_limit == 0:province_limit = 1for province in provinces:if count >= limit:print(count)breakcitys = province["children"]# 受限制少的省if province["name"] in ["湖南省"] and limit > 34:province_count = -1else:province_count = 0for city in citys:if province_count >= province_limit or count >= limit:breakt={}t["log"]=eval(city["log"])t["lat"] = eval(city["lat"])t["name"] = city["name"]city_dic.append(t)count += 1province_count += 1return city_dic

Ant.py

Ant 文件为蚂蚁类，实现了一只蚂蚁环绕各个城市进行一次旅行的过程 其中关键部分说明如下

初始化方法。蚂蚁自带一个记录已走过的路径长度的参数Path_length，方便之后对各条路径更新信息素，自带记录已访问过的城市序号与未访问城市序号的两个表。
初始化将所有的城市全部放在未访问城市表中，利用random库中的choice函数随机选择一个作为初始城市，并将其移出未访问城市表。

next_city函数返回蚂蚁要走的下一个城市的序号。首先利用概率公式

算出未访问城市表中各个城市的访问概率，存入select_prob数组中

接着根据计算出的概率，用轮盘赌方式选择下一个城市。这里的select_prob存放的并非真正意义上的概率，它并没有归一化。轮盘赌是产生0到各城市未归一化的概率之和之间的一个数，然后再与各城市未归一化的概率相减，减到小于0，则落入某一城市概率区间，方便了计算。
move函数是模拟蚂蚁走一步的过程，更新路径长度、已访问与未访问城市表。而find_a_way函数则是不断重复这一过程直到走完所有城市。最后蚂蚁的已访问城市表的城市序号就是该TSP一个解。

import random as rdclass Ant:def __init__(self,city_num):self.Path_length=0  #已走路径长度self.visited_city=[]self.city_to_visit=[i for i in range(city_num)]#将蚂蚁随机放在一个城市self.visited_city.append(rd.choice(self.city_to_visit))self.city_to_visit.remove(self.visited_city[-1])def next_city(self,alpha,beta,pheromone,expectation):select_prob=[]#计算选择各没有走过的城市的概率for city in self.city_to_visit:#当前所在城市为visited表最后一项temp=pow(pheromone[self.visited_city[-1]][city],alpha)*pow(expectation[self.visited_city[-1]][city],beta)select_prob.append(temp)#轮盘赌选择下一个城市gamble=rd.uniform(0,sum(select_prob))for i in range(len(self.city_to_visit)):gamble-=select_prob[i]if gamble<=0:return self.city_to_visit[i]raise Exception("轮盘赌选择错误", i,len(select_prob))def move(self,alpha,beta,pheromone,expectation):temp_city=self.next_city(alpha,beta,pheromone,expectation)self.Path_length += 1 / expectation[self.visited_city[-1]][temp_city]self.visited_city.append(temp_city)self.city_to_visit.remove(temp_city)def find_a_way(self,alpha,beta,pheromone,expectation):while self.city_to_visit!=[]:self.move(alpha,beta,pheromone,expectation)self.Path_length += 1 / expectation[self.visited_city[-1]][self.visited_city[0]]

ACO_G.py

ACO_G实现蚁群算法并将数据可视化

构造函数定义了所需的数据

从28行到126行都是调用tkinker库的数据可视化的函数定义

caculate_distance函数计算各城市之间距离的倒数，并将其存入Expectation二维数组中以方便后来调用

Update函数以及Pheromone_volatilize函数对信息素进行更新

其中Pheromone_volatilize函数对各条路径信息素进行第一步的更新，Update函数对每一只蚂蚁进行第二步的更新

iteration函数进行一次迭代。每次首先派出一支蚂蚁队伍，每只蚂蚁找一条路，然后根据每只蚂蚁情况更新信息素浓度。最后输出这一次的最佳路径与最佳路径长度。最后在图形化界面中不停地迭代，直到按下停止键。

import math
import Tools
from Ant import Ant
import tkinter
import timeclass ACO:def __init__(self,Alpha,Beta,Volatilize_rate,city_num,ant_num,Max_iteration,root, width=800, height=600):#信息素、距离对蚂蚁选择路径的影响程度、信息素挥发速率self.Alpha=Alphaself.Beta=Betaself.Volatilize_rate=Volatilize_rate# 城市数、城市与最大迭代次数self.city_num=city_numself.citys = Tools.get_city(city_num)print(len(self.citys))self.Max_iteration = Max_iteration#期望值(即距离的倒数)数组、信息素强度数组,信息素强度初始都为1self.Expectation=[[0.0 for col in range(city_num)] for raw in range(city_num)]self.caculate_distance()self.pheromone_intensity=[[1.0 for col in range(city_num)] for raw in range(city_num)]#蚁群数量self.ant_num=ant_num#最佳路径长度与最佳路径self.best_way=[]self.best_len=10000# 以下都是数据可视化的操作self.root = rootself.width = widthself.height = heightself.canvas = tkinter.Canvas(root,width=self.width,height=self.height,bg="#EBEBEB",  # 背景白色xscrollincrement=1,yscrollincrement=1)self.canvas.pack(expand=tkinter.YES, fill=tkinter.BOTH)self.title("TSP蚁群算法(n:初始化 g:开始搜索 s:停止搜索)")self.bindEvents()self.initCitys()self.delay=0def initCitys(self):# 坐标变换minX, minY = self.citys[0]["log"], self.citys[0]["lat"]maxX, maxY = minX, minYfor city in self.citys[1:]:if minX > city["log"]:minX = city["log"]if minY > city["lat"]:minY = city["lat"]if maxX < city["log"]:maxX = city["log"]if maxY < city["lat"]:maxY = city["lat"]w = maxX - minXh = maxY - minYxoffset = 30yoffset = 30ww = self.width - 2 * xoffsethh = self.height - 2 * yoffsetxx = ww / float(w)yy = hh / float(h)r = 5self.nodes = []self.nodes2 = []for city in self.citys:x = (city["log"] - minX) * xx + xoffsety = hh - (city["lat"] - minY) * yy + yoffsetself.nodes.append((x, y))node = self.canvas.create_oval(x - r, y - r, x + r, y + r,fill="black",outline="#000000",tags="node", )self.canvas.create_text(x, y, text=city["name"][0], fill='cyan')self.nodes2.append(node)def title(self, text):self.root.title(text)def line(self, order):self.canvas.delete("line")#先把最后一个城市和第一个连接起来for i in range(-1, len(order) - 1):p1 = self.nodes[order[i]]p2 = self.nodes[order[i + 1]]self.canvas.create_line(p1, p2, fill="red", tags="line")def line2(self, order):#先把最后一个城市和第一个连接起来for i in range(-1, len(order) - 1):p1 = self.nodes[order[i]]p2 = self.nodes[order[i + 1]]self.canvas.create_line(p1, p2, fill="grey", tags="line",dash=(4,4))def bindEvents(self):self.root.bind("n", self.new)self.root.bind("g", self.start)self.root.bind("s", self.stop)def new(self, evt=None):self.isRunning = Falseorder = range(len(self.citys))self.line(order)def start(self, evt=None):self.isRunning = Truecount=0while self.isRunning:self.line(self.iteration())self.title("TSP——蚁群:{0}次 最短路径长度{1:.2f} 最佳路径{2}".format(count,self.best_len,self.best_way))self.canvas.update()count+=1def stop(self, evt=None):self.isRunning = Falsedef mainloop(self):self.root.mainloop()#数据可视化的操作定义到此为止#计算各城市之间距离的倒数def caculate_distance(self):for raw in range(self.city_num):for col in range(raw+1,self.city_num):self.Expectation[raw][col]=1/math.sqrt(pow(self.citys[raw]["log"]-self.citys[col]["log"],2)+pow(self.citys[raw]["lat"]-self.citys[col]["lat"],2))self.Expectation[col][raw]=self.Expectation[raw][col]#print(self.Expectation)# 针对一只蚂蚁找到的路径，更新信息素def update(self,ant):for i in range(1,self.city_num):self.pheromone_intensity[ant.visited_city[i-1]][ant.visited_city[i]]+=1/ant.Path_length#信息素挥发def Pheromone_volatilize(self):for i in range(self.city_num):for j in range(i,self.city_num):self.pheromone_intensity[i][j]*=1-self.Volatilize_rateself.pheromone_intensity[j][i]=self.pheromone_intensity[i][j]#迭代def iteration(self):best_len = 10000best_way = []#重新派出一支蚂蚁队伍ant_colony=[Ant(self.city_num) for i in range(self.ant_num)]for ant in ant_colony:ant.find_a_way(self.Alpha,self.Beta,self.pheromone_intensity,self.Expectation)#获得本次最佳路径if ant.Path_length<best_len:best_len=ant.Path_lengthbest_way=ant.visited_cityif self.best_len>best_len:self.best_way=[]self.best_len=best_lenfor city in best_way:self.best_way.append(self.citys[city]["name"])print("最优解：{0},最佳路径：{1}".format(best_len, self.best_way))#更新信息素浓度self.Pheromone_volatilize()for ant in ant_colony:#根据每只蚂蚁情况更新信息素浓度self.update(ant)#画信息素线self.line2(ant.visited_city)self.canvas.update()#time.sleep(self.delay)return best_wayx=ACO(Alpha=1,Beta=2,Volatilize_rate=0.5,city_num=10,ant_num=8,Max_iteration=100,root=tkinter.Tk())
x.mainloop()#region 测试参数
test=[0,4,5,3,9,1,8,7,6,2]
l=0
for i in range(-1,len(test)-1):l+=1/x.Expectation[test[i]][test[i+1]]
print(l)
#endregion

运行效果

在α=1、β=2，ρ=0.5，城市数为10个北京城市，蚂蚁8只的情况下，运行结果如下：

灰色的虚线表示一条路径上留下的信息素，红色表示本次的最佳路径
在迭代600多次后，算法收敛

得出的最短路径为[‘北京’, ‘通县’, ‘顺义’, ‘怀柔’, ‘密云’, ‘平谷’, ‘延庆’, ‘昌平’, ‘房山’, ‘大兴’]，路径长度为3.84。

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