[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"project-9767":3},{"id":4,"name":5,"fullName":6,"owner":7,"repo":5,"description":8,"homepage":9,"htmlUrl":10,"language":11,"languages":10,"totalLinesOfCode":10,"stars":12,"forks":13,"watchers":14,"openIssues":15,"contributorsCount":16,"subscribersCount":16,"size":16,"stars1d":16,"stars7d":17,"stars30d":18,"stars90d":16,"forks30d":16,"starsTrendScore":19,"compositeScore":20,"rankGlobal":10,"rankLanguage":10,"license":21,"archived":22,"fork":22,"defaultBranch":23,"hasWiki":24,"hasPages":24,"topics":25,"createdAt":10,"pushedAt":10,"updatedAt":39,"readmeContent":40,"aiSummary":41,"trendingCount":16,"starSnapshotCount":16,"syncStatus":19,"lastSyncTime":42,"discoverSource":43},9767,"scikit-opt","guofei9987\u002Fscikit-opt","guofei9987","Genetic Algorithm, Particle Swarm Optimization, Simulated Annealing, Ant Colony Optimization Algorithm,Immune Algorithm, Artificial Fish Swarm Algorithm, Differential Evolution and TSP(Traveling salesman) ","https:\u002F\u002Fscikit-opt.github.io\u002Fscikit-opt\u002F#\u002Fen\u002F",null,"Python",6581,1112,52,69,0,8,42,2,40.14,"MIT License",false,"master",true,[26,27,28,29,30,31,32,33,34,35,36,37,38],"ant-colony-algorithm","artificial-intelligence","fish-swarms","genetic-algorithm","heuristic-algorithms","immune","immune-algorithm","optimization","particle-swarm-optimization","pso","simulated-annealing","travelling-salesman-problem","tsp","2026-06-12 02:02:12","\n# [scikit-opt](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt)\n\n[![PyPI](https:\u002F\u002Fimg.shields.io\u002Fpypi\u002Fv\u002Fscikit-opt)](https:\u002F\u002Fpypi.org\u002Fproject\u002Fscikit-opt\u002F)\n[![Build Status](https:\u002F\u002Ftravis-ci.com\u002Fguofei9987\u002Fscikit-opt.svg?branch=master)](https:\u002F\u002Ftravis-ci.com\u002Fguofei9987\u002Fscikit-opt)\n[![codecov](https:\u002F\u002Fcodecov.io\u002Fgh\u002Fguofei9987\u002Fscikit-opt\u002Fbranch\u002Fmaster\u002Fgraph\u002Fbadge.svg)](https:\u002F\u002Fcodecov.io\u002Fgh\u002Fguofei9987\u002Fscikit-opt)\n[![License](https:\u002F\u002Fimg.shields.io\u002Fpypi\u002Fl\u002Fscikit-opt.svg)](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002FLICENSE)\n![Python](https:\u002F\u002Fimg.shields.io\u002Fbadge\u002Fpython->=3.5-green.svg)\n![Platform](https:\u002F\u002Fimg.shields.io\u002Fbadge\u002Fplatform-windows%20|%20linux%20|%20macos-green.svg)\n[![fork](https:\u002F\u002Fimg.shields.io\u002Fgithub\u002Fforks\u002Fguofei9987\u002Fscikit-opt?style=social)](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Ffork)\n[![Downloads](https:\u002F\u002Fpepy.tech\u002Fbadge\u002Fscikit-opt)](https:\u002F\u002Fpepy.tech\u002Fproject\u002Fscikit-opt)\n[![Discussions](https:\u002F\u002Fimg.shields.io\u002Fbadge\u002Fdiscussions-green.svg)](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fdiscussions)\n\u003Ca href=\"https:\u002F\u002Fhellogithub.com\u002Frepository\u002Fguofei9987\u002Fscikit-opt\" target=\"_blank\">\u003Cimg src=\"https:\u002F\u002Fabroad.hellogithub.com\u002Fv1\u002Fwidgets\u002Frecommend.svg?rid=6763d615842e4449a02f024f3e2e345c&claim_uid=se0WHo8cbiLv2w1&theme=small\" alt=\"Featured｜HelloGitHub\" \u002F>\u003C\u002Fa>\n\n\nSwarm Intelligence in Python  \n(Genetic Algorithm, Particle Swarm Optimization, Simulated Annealing, Ant Colony Algorithm, Immune Algorithm, Artificial Fish Swarm Algorithm in Python)\n\n\n- **Documentation:** [https:\u002F\u002Fscikit-opt.github.io\u002Fscikit-opt\u002F#\u002Fen\u002F](https:\u002F\u002Fscikit-opt.github.io\u002Fscikit-opt\u002F#\u002Fen\u002F)\n- **文档：** [https:\u002F\u002Fscikit-opt.github.io\u002Fscikit-opt\u002F#\u002Fzh\u002F](https:\u002F\u002Fscikit-opt.github.io\u002Fscikit-opt\u002F#\u002Fzh\u002F)  \n- **Source code:** [https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt)\n- **Help us improve scikit-opt** [https:\u002F\u002Fwww.wjx.cn\u002Fjq\u002F50964691.aspx](https:\u002F\u002Fwww.wjx.cn\u002Fjq\u002F50964691.aspx)\n\n# install\n```bash\npip install scikit-opt\n```\n\nFor the current developer version:\n```bach\ngit clone git@github.com:guofei9987\u002Fscikit-opt.git\ncd scikit-opt\npip install .\n```\n\n# Features\n## Feature1: UDF\n\n**UDF** (user defined function) is available now!\n\nFor example, you just worked out a new type of `selection` function.  \nNow, your `selection` function is like this:  \n-> Demo code: [examples\u002Fdemo_ga_udf.py#s1](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_udf.py#L1)\n```python\n# step1: define your own operator:\ndef selection_tournament(algorithm, tourn_size):\n    FitV = algorithm.FitV\n    sel_index = []\n    for i in range(algorithm.size_pop):\n        aspirants_index = np.random.choice(range(algorithm.size_pop), size=tourn_size)\n        sel_index.append(max(aspirants_index, key=lambda i: FitV[i]))\n    algorithm.Chrom = algorithm.Chrom[sel_index, :]  # next generation\n    return algorithm.Chrom\n\n\n```\n\nImport and build ga  \n-> Demo code: [examples\u002Fdemo_ga_udf.py#s2](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_udf.py#L12)\n```python\nimport numpy as np\nfrom sko.GA import GA, GA_TSP\n\ndemo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + (x[2] - 0.5) ** 2\nga = GA(func=demo_func, n_dim=3, size_pop=100, max_iter=500, prob_mut=0.001,\n        lb=[-1, -10, -5], ub=[2, 10, 2], precision=[1e-7, 1e-7, 1])\n\n```\nRegist your udf to GA  \n-> Demo code: [examples\u002Fdemo_ga_udf.py#s3](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_udf.py#L20)\n```python\nga.register(operator_name='selection', operator=selection_tournament, tourn_size=3)\n```\n\nscikit-opt also provide some operators  \n-> Demo code: [examples\u002Fdemo_ga_udf.py#s4](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_udf.py#L22)\n```python\nfrom sko.operators import ranking, selection, crossover, mutation\n\nga.register(operator_name='ranking', operator=ranking.ranking). \\\n    register(operator_name='crossover', operator=crossover.crossover_2point). \\\n    register(operator_name='mutation', operator=mutation.mutation)\n```\nNow do GA as usual  \n-> Demo code: [examples\u002Fdemo_ga_udf.py#s5](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_udf.py#L28)\n```python\nbest_x, best_y = ga.run()\nprint('best_x:', best_x, '\\n', 'best_y:', best_y)\n```\n\n> Until Now, the **udf** surport `crossover`, `mutation`, `selection`, `ranking` of GA\n> scikit-opt provide a dozen of operators, see [here](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Ftree\u002Fmaster\u002Fsko\u002Foperators)\n\nFor advanced users:\n\n-> Demo code: [examples\u002Fdemo_ga_udf.py#s6](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_udf.py#L31)\n```python\nclass MyGA(GA):\n    def selection(self, tourn_size=3):\n        FitV = self.FitV\n        sel_index = []\n        for i in range(self.size_pop):\n            aspirants_index = np.random.choice(range(self.size_pop), size=tourn_size)\n            sel_index.append(max(aspirants_index, key=lambda i: FitV[i]))\n        self.Chrom = self.Chrom[sel_index, :]  # next generation\n        return self.Chrom\n\n    ranking = ranking.ranking\n\n\ndemo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + (x[2] - 0.5) ** 2\nmy_ga = MyGA(func=demo_func, n_dim=3, size_pop=100, max_iter=500, lb=[-1, -10, -5], ub=[2, 10, 2],\n             precision=[1e-7, 1e-7, 1])\nbest_x, best_y = my_ga.run()\nprint('best_x:', best_x, '\\n', 'best_y:', best_y)\n```\n\n##  feature2: continue to run\n(New in version 0.3.6)  \nRun an algorithm for 10 iterations, and then run another 20 iterations base on the 10 iterations before:\n```python\nfrom sko.GA import GA\n\nfunc = lambda x: x[0] ** 2\nga = GA(func=func, n_dim=1)\nga.run(10)\nga.run(20)\n```\n\n## feature3: 4-ways to accelerate\n- vectorization\n- multithreading\n- multiprocessing\n- cached\n\nsee [https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fexample_function_modes.py](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fexample_function_modes.py)\n\n\n\n## feature4: GPU computation\n We are developing GPU computation, which will be stable on version 1.0.0  \nAn example is already available: [https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_gpu.py](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_gpu.py)\n\n\n# Quick start\n\n## 1. Differential Evolution\n**Step1**：define your problem  \n-> Demo code: [examples\u002Fdemo_de.py#s1](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_de.py#L1)\n```python\n'''\nmin f(x1, x2, x3) = x1^2 + x2^2 + x3^2\ns.t.\n    x1*x2 >= 1\n    x1*x2 \u003C= 5\n    x2 + x3 = 1\n    0 \u003C= x1, x2, x3 \u003C= 5\n'''\n\n\ndef obj_func(p):\n    x1, x2, x3 = p\n    return x1 ** 2 + x2 ** 2 + x3 ** 2\n\n\nconstraint_eq = [\n    lambda x: 1 - x[1] - x[2]\n]\n\nconstraint_ueq = [\n    lambda x: 1 - x[0] * x[1],\n    lambda x: x[0] * x[1] - 5\n]\n\n```\n\n**Step2**: do Differential Evolution  \n-> Demo code: [examples\u002Fdemo_de.py#s2](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_de.py#L25)\n```python\nfrom sko.DE import DE\n\nde = DE(func=obj_func, n_dim=3, size_pop=50, max_iter=800, lb=[0, 0, 0], ub=[5, 5, 5],\n        constraint_eq=constraint_eq, constraint_ueq=constraint_ueq)\n\nbest_x, best_y = de.run()\nprint('best_x:', best_x, '\\n', 'best_y:', best_y)\n\n```\n\n## 2. Genetic Algorithm\n\n**Step1**：define your problem  \n-> Demo code: [examples\u002Fdemo_ga.py#s1](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga.py#L1)\n```python\nimport numpy as np\n\n\ndef schaffer(p):\n    '''\n    This function has plenty of local minimum, with strong shocks\n    global minimum at (0,0) with value 0\n    https:\u002F\u002Fen.wikipedia.org\u002Fwiki\u002FTest_functions_for_optimization\n    '''\n    x1, x2 = p\n    part1 = np.square(x1) - np.square(x2)\n    part2 = np.square(x1) + np.square(x2)\n    return 0.5 + (np.square(np.sin(part1)) - 0.5) \u002F np.square(1 + 0.001 * part2)\n\n\n```\n\n**Step2**: do Genetic Algorithm  \n-> Demo code: [examples\u002Fdemo_ga.py#s2](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga.py#L16)\n```python\nfrom sko.GA import GA\n\nga = GA(func=schaffer, n_dim=2, size_pop=50, max_iter=800, prob_mut=0.001, lb=[-1, -1], ub=[1, 1], precision=1e-7)\nbest_x, best_y = ga.run()\nprint('best_x:', best_x, '\\n', 'best_y:', best_y)\n```\n\n-> Demo code: [examples\u002Fdemo_ga.py#s3](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga.py#L22)\n```python\nimport pandas as pd\nimport matplotlib.pyplot as plt\n\nY_history = pd.DataFrame(ga.all_history_Y)\nfig, ax = plt.subplots(2, 1)\nax[0].plot(Y_history.index, Y_history.values, '.', color='red')\nY_history.min(axis=1).cummin().plot(kind='line')\nplt.show()\n```\n\n![Figure_1-1](https:\u002F\u002Fimg1.github.io\u002Fheuristic_algorithm\u002Fga_1.png)\n\n### 2.2 Genetic Algorithm for TSP(Travelling Salesman Problem)\nJust import the `GA_TSP`, it overloads the `crossover`, `mutation` to solve the TSP\n\n**Step1**: define your problem. Prepare your points coordinate and the distance matrix.  \nHere I generate the data randomly as a demo:  \n-> Demo code: [examples\u002Fdemo_ga_tsp.py#s1](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_tsp.py#L1)\n```python\nimport numpy as np\nfrom scipy import spatial\nimport matplotlib.pyplot as plt\n\nnum_points = 50\n\npoints_coordinate = np.random.rand(num_points, 2)  # generate coordinate of points\ndistance_matrix = spatial.distance.cdist(points_coordinate, points_coordinate, metric='euclidean')\n\n\ndef cal_total_distance(routine):\n    '''The objective function. input routine, return total distance.\n    cal_total_distance(np.arange(num_points))\n    '''\n    num_points, = routine.shape\n    return sum([distance_matrix[routine[i % num_points], routine[(i + 1) % num_points]] for i in range(num_points)])\n\n\n```\n\n**Step2**: do GA  \n-> Demo code: [examples\u002Fdemo_ga_tsp.py#s2](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_tsp.py#L19)\n```python\n\nfrom sko.GA import GA_TSP\n\nga_tsp = GA_TSP(func=cal_total_distance, n_dim=num_points, size_pop=50, max_iter=500, prob_mut=1)\nbest_points, best_distance = ga_tsp.run()\n\n```\n\n**Step3**: Plot the result:  \n-> Demo code: [examples\u002Fdemo_ga_tsp.py#s3](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ga_tsp.py#L26)\n```python\nfig, ax = plt.subplots(1, 2)\nbest_points_ = np.concatenate([best_points, [best_points[0]]])\nbest_points_coordinate = points_coordinate[best_points_, :]\nax[0].plot(best_points_coordinate[:, 0], best_points_coordinate[:, 1], 'o-r')\nax[1].plot(ga_tsp.generation_best_Y)\nplt.show()\n```\n\n![GA_TPS](https:\u002F\u002Fimg1.github.io\u002Fheuristic_algorithm\u002Fga_tsp.png)\n\n\n## 3. PSO(Particle swarm optimization)\n\n### 3.1 PSO\n**Step1**: define your problem:  \n-> Demo code: [examples\u002Fdemo_pso.py#s1](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_pso.py#L1)\n```python\ndef demo_func(x):\n    x1, x2, x3 = x\n    return x1 ** 2 + (x2 - 0.05) ** 2 + x3 ** 2\n\n\n```\n\n**Step2**: do PSO  \n-> Demo code: [examples\u002Fdemo_pso.py#s2](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_pso.py#L6)\n```python\nfrom sko.PSO import PSO\n\npso = PSO(func=demo_func, n_dim=3, pop=40, max_iter=150, lb=[0, -1, 0.5], ub=[1, 1, 1], w=0.8, c1=0.5, c2=0.5)\npso.run()\nprint('best_x is ', pso.gbest_x, 'best_y is', pso.gbest_y)\n\n```\n\n**Step3**: Plot the result  \n-> Demo code: [examples\u002Fdemo_pso.py#s3](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_pso.py#L13)\n```python\nimport matplotlib.pyplot as plt\n\nplt.plot(pso.gbest_y_hist)\nplt.show()\n```\n\n\n![PSO_TPS](https:\u002F\u002Fimg1.github.io\u002Fheuristic_algorithm\u002Fpso.png)\n\n### 3.2 PSO with nonlinear constraint\n\nIf you need nolinear constraint like `(x[0] - 1) ** 2 + (x[1] - 0) ** 2 - 0.5 ** 2\u003C=0`  \nCodes are like this:\n```python\nconstraint_ueq = (\n    lambda x: (x[0] - 1) ** 2 + (x[1] - 0) ** 2 - 0.5 ** 2\n    ,\n)\npso = PSO(func=demo_func, n_dim=2, pop=40, max_iter=max_iter, lb=[-2, -2], ub=[2, 2]\n          , constraint_ueq=constraint_ueq)\n```\n\nNote that, you can add more then one nonlinear constraint. Just add it to `constraint_ueq`\n\nMore over, we have an animation:  \n![pso_ani](https:\u002F\u002Fimg1.github.io\u002Fheuristic_algorithm\u002Fpso.gif)  \n↑**see [examples\u002Fdemo_pso_ani.py](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_pso_ani.py)**\n\n\n## 4. SA(Simulated Annealing)\n### 4.1 SA for multiple function\n**Step1**: define your problem  \n-> Demo code: [examples\u002Fdemo_sa.py#s1](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_sa.py#L1)\n```python\ndemo_func = lambda x: x[0] ** 2 + (x[1] - 0.05) ** 2 + x[2] ** 2\n\n```\n**Step2**: do SA  \n-> Demo code: [examples\u002Fdemo_sa.py#s2](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_sa.py#L3)\n```python\nfrom sko.SA import SA\n\nsa = SA(func=demo_func, x0=[1, 1, 1], T_max=1, T_min=1e-9, L=300, max_stay_counter=150)\nbest_x, best_y = sa.run()\nprint('best_x:', best_x, 'best_y', best_y)\n\n```\n\n**Step3**: Plot the result  \n-> Demo code: [examples\u002Fdemo_sa.py#s3](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_sa.py#L10)\n```python\nimport matplotlib.pyplot as plt\nimport pandas as pd\n\nplt.plot(pd.DataFrame(sa.best_y_history).cummin(axis=0))\nplt.show()\n\n```\n![sa](https:\u002F\u002Fimg1.github.io\u002Fheuristic_algorithm\u002Fsa.png)\n\n\nMoreover, scikit-opt provide 3 types of Simulated Annealing: Fast, Boltzmann, Cauchy. See [more sa](https:\u002F\u002Fscikit-opt.github.io\u002Fscikit-opt\u002F#\u002Fen\u002Fmore_sa)\n### 4.2 SA for TSP\n**Step1**: oh, yes, define your problems. To boring to copy this step.  \n\n**Step2**: DO SA for TSP  \n-> Demo code: [examples\u002Fdemo_sa_tsp.py#s2](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_sa_tsp.py#L21)\n```python\nfrom sko.SA import SA_TSP\n\nsa_tsp = SA_TSP(func=cal_total_distance, x0=range(num_points), T_max=100, T_min=1, L=10 * num_points)\n\nbest_points, best_distance = sa_tsp.run()\nprint(best_points, best_distance, cal_total_distance(best_points))\n```\n\n**Step3**: plot the result  \n-> Demo code: [examples\u002Fdemo_sa_tsp.py#s3](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_sa_tsp.py#L28)\n```python\nfrom matplotlib.ticker import FormatStrFormatter\n\nfig, ax = plt.subplots(1, 2)\n\nbest_points_ = np.concatenate([best_points, [best_points[0]]])\nbest_points_coordinate = points_coordinate[best_points_, :]\nax[0].plot(sa_tsp.best_y_history)\nax[0].set_xlabel(\"Iteration\")\nax[0].set_ylabel(\"Distance\")\nax[1].plot(best_points_coordinate[:, 0], best_points_coordinate[:, 1],\n           marker='o', markerfacecolor='b', color='c', linestyle='-')\nax[1].xaxis.set_major_formatter(FormatStrFormatter('%.3f'))\nax[1].yaxis.set_major_formatter(FormatStrFormatter('%.3f'))\nax[1].set_xlabel(\"Longitude\")\nax[1].set_ylabel(\"Latitude\")\nplt.show()\n\n```\n![sa](https:\u002F\u002Fimg1.github.io\u002Fheuristic_algorithm\u002Fsa_tsp.png)\n\n\nMore: Plot the animation:  \n\n![sa](https:\u002F\u002Fimg1.github.io\u002Fheuristic_algorithm\u002Fsa_tsp1.gif)  \n↑**see [examples\u002Fdemo_sa_tsp.py](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_sa_tsp.py)**\n\n\n\n\n## 5. ACA (Ant Colony Algorithm) for tsp\n-> Demo code: [examples\u002Fdemo_aca_tsp.py#s2](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_aca_tsp.py#L17)\n```python\nfrom sko.ACA import ACA_TSP\n\naca = ACA_TSP(func=cal_total_distance, n_dim=num_points,\n              size_pop=50, max_iter=200,\n              distance_matrix=distance_matrix)\n\nbest_x, best_y = aca.run()\n\n```\n\n![ACA](https:\u002F\u002Fimg1.github.io\u002Fheuristic_algorithm\u002Faca_tsp.png)\n\n\n## 6. immune algorithm (IA)\n-> Demo code: [examples\u002Fdemo_ia.py#s2](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_ia.py#L6)\n```python\n\nfrom sko.IA import IA_TSP\n\nia_tsp = IA_TSP(func=cal_total_distance, n_dim=num_points, size_pop=500, max_iter=800, prob_mut=0.2,\n                T=0.7, alpha=0.95)\nbest_points, best_distance = ia_tsp.run()\nprint('best routine:', best_points, 'best_distance:', best_distance)\n\n```\n\n![IA](https:\u002F\u002Fimg1.github.io\u002Fheuristic_algorithm\u002Fia2.png)\n\n## 7. Artificial Fish Swarm Algorithm (AFSA)\n-> Demo code: [examples\u002Fdemo_afsa.py#s1](https:\u002F\u002Fgithub.com\u002Fguofei9987\u002Fscikit-opt\u002Fblob\u002Fmaster\u002Fexamples\u002Fdemo_afsa.py#L1)\n```python\ndef func(x):\n    x1, x2 = x\n    return 1 \u002F x1 ** 2 + x1 ** 2 + 1 \u002F x2 ** 2 + x2 ** 2\n\n\nfrom sko.AFSA import AFSA\n\nafsa = AFSA(func, n_dim=2, size_pop=50, max_iter=300,\n            max_try_num=100, step=0.5, visual=0.3,\n            q=0.98, delta=0.5)\nbest_x, best_y = afsa.run()\nprint(best_x, best_y)\n```\n\n\n\n# Projects using scikit-opt\n\n- [Yu, J., He, Y., Yan, Q., & Kang, X. (2021). SpecView: Malware Spectrum Visualization Framework With Singular Spectrum Transformation. IEEE Transactions on Information Forensics and Security, 16, 5093-5107.](https:\u002F\u002Fieeexplore.ieee.org\u002Fabstract\u002Fdocument\u002F9607026\u002F)\n- [Zhen, H., Zhai, H., Ma, W., Zhao, L., Weng, Y., Xu, Y., ... & He, X. (2021). Design and tests of reinforcement-learning-based optimal power flow solution generator. Energy Reports.](https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS2352484721012737)\n- [Heinrich, K., Zschech, P., Janiesch, C., & Bonin, M. (2021). Process data properties matter: Introducing gated convolutional neural networks (GCNN) and key-value-predict attention networks (KVP) for next event prediction with deep learning. Decision Support Systems, 143, 113494.](https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS016792362100004X)\n- [Tang, H. K., & Goh, S. K. (2021). A Novel Non-population-based Meta-heuristic Optimizer Inspired by the Philosophy of Yi Jing. arXiv preprint arXiv:2104.08564.](https:\u002F\u002Farxiv.org\u002Fabs\u002F2104.08564)\n- [Wu, G., Li, L., Li, X., Chen, Y., Chen, Z., Qiao, B., ... & Xia, L. (2021). Graph embedding based real-time social event matching for EBSNs recommendation. World Wide Web, 1-22.](https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11280-021-00934-y)\n- [Pan, X., Zhang, Z., Zhang, H., Wen, Z., Ye, W., Yang, Y., ... & Zhao, X. (2021). A fast and robust mixture gases identification and concentration detection algorithm based on attention mechanism equipped recurrent neural network with double loss function. Sensors and Actuators B: Chemical, 342, 129982.](https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fabs\u002Fpii\u002FS0925400521005517)\n- [Castella Balcell, M. (2021). Optimization of the station keeping system for the WindCrete floating offshore wind turbine.](https:\u002F\u002Fupcommons.upc.edu\u002Fhandle\u002F2117\u002F350262)\n- [Zhai, B., Wang, Y., Wang, W., & Wu, B. (2021). Optimal Variable Speed Limit Control Strategy on Freeway Segments under Fog Conditions. arXiv preprint arXiv:2107.14406.](https:\u002F\u002Farxiv.org\u002Fabs\u002F2107.14406)\n- [Yap, X. H. (2021). Multi-label classification on locally-linear data: Application to chemical toxicity prediction.](https:\u002F\u002Fetd.ohiolink.edu\u002Fapexprod\u002Frws_olink\u002Fr\u002F1501\u002F10?clear=10&p10_accession_num=wright162901936395651)\n- [Gebhard, L. (2021). Expansion Planning of Low-Voltage Grids Using Ant Colony Optimization Ausbauplanung von Niederspannungsnetzen mithilfe eines Ameisenalgorithmus.](https:\u002F\u002Fad-publications.cs.uni-freiburg.de\u002Ftheses\u002FMaster_Lukas_Gebhard_2021.pdf)\n- [Ma, X., Zhou, H., & Li, Z. (2021). Optimal Design for Interdependencies between Hydrogen and Power Systems. IEEE Transactions on Industry Applications.](https:\u002F\u002Fieeexplore.ieee.org\u002Fabstract\u002Fdocument\u002F9585654)\n- [de Curso, T. D. C. (2021). Estudo do modelo Johansen-Ledoit-Sornette de bolhas financeiras.](https:\u002F\u002Fd1wqtxts1xzle7.cloudfront.net\u002F67649721\u002FTCC_Thibor_Final-with-cover-page-v2.pdf?Expires=1639140872&Signature=LDZoVsAGO0mLMlVsQjnzpLlRhLyt5wdIDmBjm1yWog5bsx6apyRE9aHuwfnFnc96uvam573wiHMeV08QlK2vhRcQS1d0buenBT5fwoRuq6PTDoMsXmpBb-lGtu9ETiMb4sBYvcQb-X3C7Hh0Ec1FoJZ040gXJPWdAli3e1TdOcGrnOaBZMgNiYX6aKFIZaaXmiQeV3418~870bH4IOQXOapIE6-23lcOL-32T~FSjsOrENoLUkcosv6UHPourKgsRufAY-C2HBUWP36iJ7CoH0jSTo1e45dVgvqNDvsHz7tmeI~0UPGH-A8MWzQ9h2ElCbCN~UNQ8ycxOa4TUKfpCw__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA)\n- [Wu, T., Liu, J., Liu, J., Huang, Z., Wu, H., Zhang, C., ... & Zhang, G. (2021). A Novel AI-based Framework for AoI-optimal Trajectory Planning in UAV-assisted Wireless Sensor Networks. IEEE Transactions on Wireless Communications.](https:\u002F\u002Fieeexplore.ieee.org\u002Fabstract\u002Fdocument\u002F9543607)\n- [Liu, H., Wen, Z., & Cai, W. (2021, August). FastPSO: Towards Efficient Swarm Intelligence Algorithm on GPUs. In 50th International Conference on Parallel Processing (pp. 1-10).](https:\u002F\u002Fdl.acm.org\u002Fdoi\u002Fabs\u002F10.1145\u002F3472456.3472474)\n- [Mahbub, R. (2020). Algorithms and Optimization Techniques for Solving TSP.](https:\u002F\u002Fraiyanmahbub.com\u002Fimages\u002FResearch_Paper.pdf)\n- [Li, J., Chen, T., Lim, K., Chen, L., Khan, S. A., Xie, J., & Wang, X. (2019). Deep learning accelerated gold nanocluster synthesis. Advanced Intelligent Systems, 1(3), 1900029.](https:\u002F\u002Fonlinelibrary.wiley.com\u002Fdoi\u002Ffull\u002F10.1002\u002Faisy.201900029)\n","scikit-opt 是一个用 Python 实现的群智能优化算法库，包括遗传算法、粒子群优化、模拟退火、蚁群算法、免疫算法、人工鱼群算法等多种启发式算法。其核心功能支持用户自定义函数（UDF），允许开发者根据需求定制算法组件，如选择、交叉和变异等操作。该库适用于需要解决复杂优化问题的场景，比如旅行商问题（TSP）以及其他组合优化或连续优化任务。简洁的接口设计与丰富的文档使得 scikit-opt 成为研究者和工程师在人工智能领域探索高效解决方案的理想工具。","2026-06-11 03:24:37","top_topic"]