// Numbas version: finer_feedback_settings
{"name": "Musa's SIT316 MH-Population based - Week 9 - V2021", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Musa's SIT316 MH-Population based - Week 9 - V2021", "tags": [], "metadata": {"description": "<p>This question tests the student's ability to solve Integer Programming problems applying Population-based Metaheuristics.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"k": {"name": "k", "group": "part a", "definition": "random(1..5)", "description": "", "templateType": "anything", "can_override": false}, "kx": {"name": "kx", "group": "part a", "definition": "k*random(6..18)", "description": "", "templateType": "anything", "can_override": false}, "ky": {"name": "ky", "group": "part a", "definition": "k*10", "description": "", "templateType": "anything", "can_override": false}, "k5": {"name": "k5", "group": "part a", "definition": "random(1..7)", "description": "", "templateType": "anything", "can_override": false}, "k6": {"name": "k6", "group": "part a", "definition": "random(-10..-5)", "description": "", "templateType": "anything", "can_override": false}, "k1": {"name": "k1", "group": "part a", "definition": "random(0.1,0.2,0.3)", "description": "", "templateType": "anything", "can_override": false}, "k22": {"name": "k22", "group": "part a", "definition": "random(0.1,0.2,0.3)", "description": "", "templateType": "anything", "can_override": false}, "k2": {"name": "k2", "group": "part a", "definition": "random(0.6,0.7,0.8,0.9)", "description": "", "templateType": "anything", "can_override": false}, "k11": {"name": "k11", "group": "part a", "definition": "random(0.6,0.7,0.8,0.9)", "description": "", "templateType": "anything", "can_override": false}, "s": {"name": "s", "group": "part a", "definition": "k2*a+k1*b+k1*k2", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "part a", "definition": "random(40..60)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "part a", "definition": "random(15..25)", "description": "", "templateType": "anything", "can_override": false}, "ss": {"name": "ss", "group": "part a", "definition": "k22*a+k11*b+k11*k22", "description": "", "templateType": "anything", "can_override": false}, "k7": {"name": "k7", "group": "part a", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}, "k8": {"name": "k8", "group": "part a", "definition": "random(2..6)", "description": "", "templateType": "anything", "can_override": false}, "sss": {"name": "sss", "group": "part a", "definition": "-k7*a+k8*b-k7*k8", "description": "", "templateType": "anything", "can_override": false}, "rand": {"name": "rand", "group": "Ungrouped variables", "definition": "repeat(random(20..40),2)", "description": "", "templateType": "anything", "can_override": false}, "aup": {"name": "aup", "group": "Ungrouped variables", "definition": "a+rand[0]", "description": "", "templateType": "anything", "can_override": false}, "bup": {"name": "bup", "group": "Ungrouped variables", "definition": "b+rand[1]", "description": "", "templateType": "anything", "can_override": false}, "tol": {"name": "tol", "group": "Ungrouped variables", "definition": "int(kx*(a-1) + ky*(b-1)*0.95)", "description": "", "templateType": "anything", "can_override": false}, "fv": {"name": "fv", "group": "Ungrouped variables", "definition": "kx*(a) + ky*b", "description": "", "templateType": "anything", "can_override": false}, "s4": {"name": "s4", "group": "part a", "definition": "a*a+b*b+random(1..5)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["rand", "aup", "bup", "tol", "fv"], "variable_groups": [{"name": "part a", "variables": ["k", "kx", "ky", "k5", "k6", "k1", "k22", "k2", "k11", "s", "a", "b", "ss", "k7", "k8", "sss", "s4"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p><strong>P-{k}{kx}{k5}{k7}{k8}{a}{b}</strong></p>\n<p>Solve the following Integer Programming problem:</p>\n<p>Maximize: $f(x,y) = \\simplify{{kx} x + {ky} y}$</p>\n<p>Subject to</p>\n<p>$ \\simplify{{k5} x - y} \\ge&nbsp; \\var{k6}$</p>\n<p>$ \\simplify{100*{k2} x&nbsp; + 100*{k1} y} \\le&nbsp; \\var{100*s}$</p>\n<p>$ \\simplify{x^2&nbsp; + y^2} \\le&nbsp; \\var{s4}$</p>\n<p>$ \\simplify{100*{k11}/{a} x^2+(100*{k22}-100*{k11}*2) x + 100*{k11}y} \\le \\simplify{100*{ss} - 100*{k11*a}}$</p>\n<p>$x \\in [0,\\var{aup}],~~y \\in [0,\\var{bup}]$</p>\n<p><strong></strong></p>\n<p><strong>Submitting your results:</strong></p>\n<ol>\n<li>Click on<strong> \"End Exam\" </strong>and then<strong> \"Print this results summary\" </strong>(your problem will be extracted as pdf with all the necessary information/data). <strong>Do not worry</strong> about the \"<strong>Total 0/0 (0%)</strong>\" score, this pdf is only for generating a LP problem).</li>\n<li>Create your own implementation of a <strong>Population-based algorithm</strong>, in the language of your choice, and solve your problem and print the output.</li>\n<li>For the OnTrack task - submit the pdf from NAMBAS (i.e. your problem), your code and your best solution obtained; that is:</li>\n</ol>\n<p style=\"padding-left: 40px;\"><strong>(i)</strong> Best soultion found is $(x, y) = (\\cdots, \\cdots)$</p>\n<p style=\"padding-left: 40px;\"><strong>(ii)</strong> Objevtive function value $f(x,y) = \\cdots $ (expected to be $\\ge \\var{tol}$)</p>\n<p style=\"padding-left: 40px;\"><strong>(iii)</strong> Checking all the constraints:</p>\n<p style=\"padding-left: 80px;\">$ \\simplify{{k5} x - y} = \\cdots $ (expected to be $\\ge&nbsp; \\var{k6}$)</p>\n<p style=\"padding-left: 80px;\">$ \\simplify{100*{k2} x&nbsp; + 100*{k1} y} = \\cdots $ (expected to be $\\le&nbsp; \\var{100*s}$)</p>\n<p style=\"padding-left: 80px;\">$ \\simplify{x^2&nbsp; + y^2} = \\cdots $ (expected to be $\\le&nbsp; \\var{s4}$)</p>\n<p style=\"padding-left: 80px;\">$ \\simplify{100*{k11}/{a} x^2+(100*{k22}-100*{k11}*2) x + 100*{k11}y} = \\cdots$&nbsp; (expected to be $\\le \\simplify{100*{ss} - 100*{k11*a}}$)</p>\n<p></p>", "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}, {"name": "Musa Mammadov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4417/"}]}