M353 – Modern Heuristic Methods Coursework

| January 25, 2016

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M 353 Modern Computational Methods for Operational”Research”and”Logistics M353 – Modern Heuristic Methods Coursework Dr Banafsheh Khosravi Due Date: Wednesday 27th January 2016 by 4pm This coursework is worth 40% of the total unit mark. This is an individual assignment. Group work and/or copying of work or reports are not permitted and will be dealt with under the University rules on plagiarism. What you need to submit Please submit the following files via the coursework submission link on unit MOODLE page and CAM office: 1. Soft copy of your report on Moodle and hard copy to CAM office. Your report should be no longer than the specified word limits for each part. The font size used must be 10 or greater. 2. Your Excel files only on Moodle. Problem A publication company is interested to optimise the publication process and minimise general lead time of publication of books and journals. There are currently 10 different tasks which need to be scheduled for 20 types of publications which have certain due dates agreed with the customers. So company is interested in minimizing the total tardiness of these tasks. Each publication type is processed through a specific task with a certain time. All publications are processed with the same sequence of tasks. Each publication can be processed only under one specific task at a time, and each specific task is assigned to only one publication at a time. Processing a task is not preemptable and the processing times of the tasks are given both in Table 1 and in the file “Coursework data 2015-16.xls” on MOODLE. Company’s objective is to determine a schedule of 10 required tasks for 20 types of publications so that the total tardiness is minimised. 1. Formulate and describe in detail the fitness function and decision variables of the scheduling problem. Provide any reference you have used. [Maximum 500 words excluding references] [10 marks] 2. Consider the data given in both Table 1 and in the file “Coursework data 2015- 16.xls” on MOODLE. The data shows the processing times of 20 publications with 10 specific tasks. Set up a model of the problem using Excel spreadsheets and describe it in detail. A screenshot of your Excel model should accompany your description. Marks will be given for the layout, clarity and presentation of the model as well as its content and accuracy. [Maximum 1000 words] [10 marks] M 353 Modern Computational Methods for Operational”Research”and”Logistics 3. Set up the optimisation model on Evolver and explain clearly the implementation of the fitness function, decision variables and constraints. Describe in detail the initial feasible solution and its fitness value. Choose Genetic Algorithm (GA) as the optimisation technique. Indicate which solving method you have used to solve the problem. Solve the problem by using the population size of 60 and experimenting with the following crossover and mutation rates. Find the combination with the best minimum total tardiness: i. Crossover rate = 0.9, mutation rate = 0.01. ii. Crossover rate = 0.8, mutation rate = 0.03. iii. Crossover rate = 0.6, mutation rate = 0.25. iv. Crossover rate = 0.4, mutation rate = 0.005. v. Any other combinations that you think will produce a good solution. The stopping criterion for all the experiments should be set to 30000 generations. Describe the optimisation model and the experiments conducted. For each combination, provide a detailed description of the best solution including: sequence of jobs, total tardiness, and the computation time required to generate the best solution. [Maximum 1500 words] [15 marks] 4. Analyse your results in question 3 and discuss the effect of different crossover and mutation rates on the quality of the best solutions for each combination. Provide a graphical illustration to compare the best solutions found for different crossover and mutation rate combinations in question 3. [Maximum 300 words] [15 marks] 5. Solve the problem by choosing OptQuest as the optimisation method. Calculate the % deviation of the best minimum total tardiness value found for each combination in question 3 from the OptQuest solution. Discuss how your best solution compares to the OptQuest solution and how you could possibly improve your GA best solution. [Maximum 300 words] [20 marks] 6. Implement Simulated Annealing (SA) to solve this problem and explain in detail the SA pseudo-code. Provide an example of the initial feasible solution, neighbourhood structure, initial temperature, and cooling schedule strategy. Run manually SA for 4 iterations to solve the problem. For each iteration, describe in detail the search steps and the values of the parameters used. Provide the best total tardiness found after 4 iterations. [Maximum 1500 words excluding references] [30 marks] M 353 Modern Computational Methods for Operational”Research”and”Logistics Table 1. Processing times of 20 publications with 10 specific tasks Pub 1 Pub 2 Pub 3 Pub 4 Pub 5 Pub 6 Pub 7 Pub 8 Pub 9 Pub 10 Pub 11 Pub 12 Pub 13 Pub 14 Pub 15 Pub 16 Pub 17 Pub 18 Pub 19 Pub 20 Task1 80 13 64 77 17 78 82 4 72 93 68 25 67 80 43 93 21 33 14 30 Task2 59 83 85 85 70 35 2 76 46 72 69 46 3 57 71 77 33 49 59 82 Task3 59 70 76 10 65 19 77 86 21 75 96 3 50 57 66 84 98 55 70 32 Task4 31 64 11 9 32 58 98 95 25 4 45 60 87 31 1 96 22 95 73 77 Task5 30 88 14 22 93 48 10 7 14 91 5 43 30 79 39 34 77 81 11 10 Task6 53 19 99 62 88 93 34 72 42 65 39 79 9 26 72 29 36 48 57 95 Task7 93 79 88 77 94 39 74 46 17 30 62 77 43 98 48 14 45 25 98 30 Task8 90 92 35 13 75 55 80 67 3 93 54 67 25 77 38 98 96 20 15 36 Task9 65 97 27 25 61 24 97 61 75 92 73 21 29 3 96 51 26 44 56 31 Task10 64 38 44 46 66 31 48 27 82 51 90 63 85 36 69 67 81 18 81 72 Due$ Date 870 1520 980 750 630 1210 1870 1270 1410 830 1360 1740 1250 1650 2040 950 520 1020 1550 730

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