diff --git a/A4/CSC_373_EC3.ipynb b/A4/CSC_373_EC3.ipynb index 8bffdd6..4bbc399 100644 --- a/A4/CSC_373_EC3.ipynb +++ b/A4/CSC_373_EC3.ipynb @@ -8662,19 +8662,19 @@ }, { "cell_type": "code", - "execution_count": 50, + "execution_count": 148, "id": "84ab68a4-8efa-48ba-83e3-26eb8323be7f", "metadata": { "id": "84ab68a4-8efa-48ba-83e3-26eb8323be7f" }, "outputs": [], "source": [ - "cs_students, business_students = get_random_responses(4, seed=\"replace with your groups UTorIDs\")" + "cs_students, business_students = get_random_responses(30, seed=\"replace with your groups UTorIDs\")" ] }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 149, "id": "14557dcf-ec81-4618-9701-427c33268e1e", "metadata": { "colab": { @@ -8690,7 +8690,7 @@ "Response(student_id='0', availability={'Sunday_PM', 'Monday_PM', 'Saturday_AM'})" ] }, - "execution_count": 51, + "execution_count": 149, "metadata": {}, "output_type": "execute_result" } @@ -8701,7 +8701,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 150, "id": "_bFZl5lUEvg7", "metadata": { "colab": { @@ -8718,7 +8718,7 @@ "'0'" ] }, - "execution_count": 52, + "execution_count": 150, "metadata": {}, "output_type": "execute_result" } @@ -8729,7 +8729,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 142, "id": "dOa40fmkEyjh", "metadata": { "colab": { @@ -8745,7 +8745,7 @@ "{'Monday_PM', 'Saturday_AM', 'Sunday_PM'}" ] }, - "execution_count": 53, + "execution_count": 142, "metadata": {}, "output_type": "execute_result" } @@ -8774,7 +8774,7 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 151, "id": "55b2c4b2-7dae-4b9d-a298-d67fa5173826", "metadata": { "id": "55b2c4b2-7dae-4b9d-a298-d67fa5173826" @@ -8784,9 +8784,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "Students Matched: 1\n", + "Students Matched: 15\n", "Student ID Matches:\n", - "\t('2', '0')\n" + "\t('15', '8')\n", + "\t('16', '4')\n", + "\t('17', '13')\n", + "\t('18', '12')\n", + "\t('19', '3')\n", + "\t('20', '14')\n", + "\t('21', '11')\n", + "\t('22', '10')\n", + "\t('23', '5')\n", + "\t('24', '1')\n", + "\t('25', '9')\n", + "\t('26', '6')\n", + "\t('27', '2')\n", + "\t('28', '0')\n", + "\t('29', '7')\n" ] }, { @@ -8802,18 +8816,57 @@ }, "mode": "markers+text", "text": [ - "2", - "3" + "15", + "16", + "17", + "18", + "19", + "20", + "21", + "22", + "23", + "24", + "25", + "26", + "27", + "28", + "29" ], "textposition": "middle left", "type": "scatter", "x": [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, 0, 0 ], "y": [ 0, - 1 + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9, + 10, + 11, + 12, + 13, + 14 ] }, { @@ -8823,17 +8876,56 @@ "mode": "markers+text", "text": [ "0", - "1" + "1", + "2", + "3", + "4", + "5", + "6", + "7", + "8", + "9", + "10", + "11", + "12", + "13", + "14" ], "textposition": "middle right", "type": "scatter", "x": [ + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, + 1, 1, 1 ], "y": [ 0, - 1 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" - ] - }, - "metadata": {}, - "output_type": "display_data" } ], "source": [ - "# https://cs.stackexchange.com/a/12118 was used to cast to boolean\n", + "cs_students_count = len(cs_students)\n", + "business_students_count = len(business_students)\n", "\n", - "# Generating Order for Tracking Purposes (not necessarily needed) (can be replaced with simple 15*15)\n", - "possible_student_pairings = []\n", - "for cs_student in cs_students:\n", - " for business_student in business_students:\n", - " possible_student_pairings.append((cs_student.student_id, business_student.student_id))\n", - "print(f\"Possible student pairings: {len(possible_student_pairings)}\")\n", - "# Setting up objective coefficients and constraints\n", - "\n", - "c = np.concatenate((\n", - " np.ones(len(possible_student_pairings)), # flow variables (X)\n", - " np.ones(len(possible_student_pairings)) # usage boolean Y (should these be zeros?)\n", - "))\n", - "\n", - "import sys\n", - "np.set_printoptions(threshold=sys.maxsize)\n", - "print(f\"c: \\n{c}\")\n", - "\n", - "A = np.vstack((\n", - " np.hstack((np.identity(len(possible_student_pairings)), np.zeros((len(possible_student_pairings), len(possible_student_pairings))))), # flow coefficients 1, row represents one edge, non corresponding coefficients to that row are 0, thus, identity.\n", - " np.hstack((np.identity(len(possible_student_pairings)), -len(WORK_TIMES) * np.identity(len(possible_student_pairings)))), # cast all edge values to boolean by constraining x - u*Y <= 0 set up below\n", - " np.hstack((np.zeros((len(possible_student_pairings), len(possible_student_pairings))), np.identity(len(possible_student_pairings)))), # constrain boolean variable Y <= 1\n", - " np.hstack((-np.identity(len(possible_student_pairings)), np.identity(len(possible_student_pairings)))), # constrain boolean variable Y <= X \n", - " # np.zeros((len(cs_students), len(possible_student_pairings) + len(possible_student_pairings))) # any edge can only be used once\n", - "))\n", - "print(f\"A: \\n{A}\")\n", - "\n", - "b = np.concatenate((\n", - " np.zeros(len(possible_student_pairings)), # flow capacities for X\n", - " np.zeros(len(possible_student_pairings)), # X - UY <= 0 cast to boolean\n", - " np.ones(len(possible_student_pairings)), # Y <= 1 cast to boolean\n", - " np.zeros(len(possible_student_pairings)), # Y - X <= 0 cast to boolean\n", - " # np.ones(len(cs_students)) # Single match Y sum ensures at most one pairing per cs student\n", - "))\n", - "\n", - "## Set up xor or no match\n", - "# for cs_student_row in range(len(cs_students)): # At most one edge per student (sets up for the last set of matrices)\n", - "# row_start = len(possible_student_pairings) + len(possible_student_pairings) + len(possible_student_pairings)\n", - "# for business_index in range(len(business_students)):\n", - "# A[row_start + cs_student_row][len(possible_student_pairings) + cs_student_row * len(business_students) + business_index] = 1\n", - "\n", - "## Calculate maximum overlaps\n", + "c = np.zeros(cs_students_count * business_students_count)\n", "for cs_index, cs_student in enumerate(cs_students): # order is deterministic (list)\n", " for business_index, business_student in enumerate(business_students): # order is deterministic (list)\n", " pairing_index = cs_index * len(cs_students) + business_index\n", " for availability in cs_student.availability: # O(1) since availability must be less than or equal to constant number of time slots\n", " if availability in business_student.availability:\n", - " b[pairing_index] = b[pairing_index] + 1\n", + " c[pairing_index] = c[pairing_index] + 1\n", "\n", - "print(f\"b: {b}\")\n", - "\n", - "# Run optimization\n", - "optimization_results = linprog(-c, A_ub=A, b_ub=b, bounds=(0,None))\n", - "print(optimization_results)\n", - "print(optimization_results.x)\n", - "\n", - "# Retrieve optimized values and calculate matching\n", - "t2_matching = []\n", - "business_students_matched = [False] * len(business_students)\n", - "for cs_index, cs_student in enumerate(cs_students): # order is deterministic (list)\n", - " best_business_match_student = None\n", - " best_business_match_score = 0\n", - " best_business_match_index = None\n", - " for business_index, business_student in enumerate(business_students): # order is deterministic (list)\n", - " if business_students_matched[business_index]:\n", - " print(\"ERROR, duplicate found. Should not be possible\")\n", - " continue \n", - " pairing_index = cs_index * len(cs_students) + business_index\n", - " if optimization_results.x[pairing_index] > best_business_match_score:\n", - " best_business_match_student = business_student\n", - " best_business_match_score = optimization_results.x[pairing_index]\n", - " best_business_match_index = business_index\n", - " if best_business_match_student is None:\n", - " continue\n", - " business_students_matched[best_business_match_index] = True\n", - " t2_matching.append((best_business_match_student.student_id, cs_student.student_id))\n", - "\n", - "# Graph the matchings\n", - "plot_bipartite(t1_graph, left=business_student_ids, matching=t2_matching)" + "print(c)" ] }, { "cell_type": "code", - "execution_count": null, - "id": "b0dd6379", + "execution_count": 145, + "id": "2fe82c44", "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1. 1. 1. 1. 1. 1. 1. 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0. 0. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", + " 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1.\n", + " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", + " 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 0. 0. 0. 1.]]\n" + ] + } + ], + "source": [ + "A = np.vstack((\n", + " np.zeros((cs_students_count, (cs_students_count * business_students_count))),\n", + " np.zeros((business_students_count, (cs_students_count * business_students_count)))\n", + "))\n", + "for cs_student_index in range(cs_students_count): # At most one edge per student (sets up for the last set of matrices)\n", + " for business_index in range(business_students_count):\n", + " A[cs_student_index][cs_student_index * business_students_count + business_index] = 1\n", + "for cs_student_index in range(cs_students_count): # At most one edge per student (sets up for the last set of matrices)\n", + " for business_index in range(business_students_count):\n", + " A[cs_students_count + cs_student_index][business_index * business_students_count + cs_student_index] = 1\n", + "print(A)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "id": "44be23f4", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n", + " 1. 1. 1. 1. 1. 1.]\n" + ] + } + ], + "source": [ + "\n", + "b = np.ones(cs_students_count + business_students_count)\n", + "print(b)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 159, + "id": "55063d21", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " message: Optimization terminated successfully. (HiGHS Status 7: Optimal)\n", + " success: True\n", + " status: 0\n", + " fun: -20.0\n", + " x: [ 0.000e+00 0.000e+00 ... 0.000e+00 0.000e+00]\n", + " nit: 28\n", + " lower: residual: [ 0.000e+00 0.000e+00 ... 0.000e+00\n", + " 0.000e+00]\n", + " marginals: [ 2.000e+00 1.000e+00 ... 1.000e+00\n", + " 2.000e+00]\n", + " upper: residual: [ inf inf ... inf\n", + " inf]\n", + " marginals: [ 0.000e+00 0.000e+00 ... 0.000e+00\n", + " 0.000e+00]\n", + " eqlin: residual: []\n", + " marginals: []\n", + " ineqlin: residual: [ 0.000e+00 0.000e+00 ... 0.000e+00\n", + " 0.000e+00]\n", + " marginals: [-1.000e+00 -0.000e+00 ... -1.000e+00\n", + " -1.000e+00]\n", + " mip_node_count: 0\n", + " mip_dual_bound: 0.0\n", + " mip_gap: 0.0\n", + "[ 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. -0. 1. 0. 0. 0. 0.\n", + " 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", + " 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", + " 1. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. -0. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. -0. 0. 0. 0. 0. 0.\n", + " 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. -0. 0. 0. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0.\n", + " 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. -0. 0. 0. 0. 0.\n", + " 0. 0. 0. 1. 0. 0. 1. 0. 0. 0. 0. 0. 0. -0. 0. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 0. 0. 0. 0. -0. 0. 0. 0. 1. 0. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", + " 0. 0. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n", + " 0. 0. 0. 0. -0. 1. 0. 0. 0.]\n", + "[('28', '0'), ('20', '1'), ('22', '2'), ('24', '3'), ('17', '4'), ('19', '5'), ('18', '6'), ('29', '7'), ('21', '8'), ('27', '9'), ('15', '10'), ('25', '11'), ('23', '13'), ('26', '14')]\n", + "20.0\n" + ] + } + ], + "source": [ + "# Optimize\n", + "opt_results = linprog(c=-c, A_ub=A, b_ub=b, bounds=(0,None))\n", + "print(opt_results)\n", + "print(opt_results.x)\n", + "\n", + "# Extract matching\n", + "t2_matching = []\n", + "for cs_student_index, cs_student in enumerate(cs_students): # At most one edge per student (sets up for the last set of matrices)\n", + " for business_index, business_student in enumerate(business_students):\n", + " index = cs_student_index * business_students_count + business_index\n", + " if opt_results.x[index] == 1:\n", + " t2_matching.append((business_student.student_id, cs_student.student_id))\n", + "print(t2_matching)\n", + "\n", + "# Visualize\n", + "plot_bipartite(t1_graph, left=business_student_ids, matching=t2_matching, weights=True)\n", + "\n", + "# Calculate weight\n", + "t2_total_weight = np.sum(c * opt_results.x)\n", + "print(t2_total_weight)\n", + "\n", + "# Calculate max-flow weight\n", + "t1_total_weight = 0\n", + "t1_matching_dict = {}\n", + "for business_student_id, cs_student_id in t1_matching:\n", + " t1_matching_dict[business_student_id] = cs_student_id\n", + "for cs_index, cs_student in enumerate(cs_students): # order is deterministic (list)\n", + " for business_index, business_student in enumerate(business_students): # order is deterministic (list)\n", + " pairing_index = cs_index * len(cs_students) + business_index\n", + " if business_student.student_id in t1_matching_dict and cs_student_id == t1_matching_dict[business_student.student_id]:\n", + " t1_total_weight = c[pairing_index] + t1_total_weight\n", + "print(t1_total_weight)" + ] } ], "metadata": {