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Packing While Traveling Due date: 11:59 pm, 28 October 2022, Weight: 10.00 % of total assignment work 1 Overview Assignments should be done in groups consisting of five to six (56) students. Each student has to take major responsibility for one of the exercises and collaborate with the team members on the remaining exercises. Each exercise needs one student taking major responsibility. The group has to make sure that the workload is evenly distributed. For Assignment 3 the minimum requirement is that the different algorithms for the ( dynamic) PWT are implemented as described below and that they have been evaluated on the designed (dynamic) benchmarks. 2 Assignment We consider the packing while traveling (PWT) problem described in S. Polyakovskiy, F. Neumann: The Packing While Traveling Problem. CoRR abs/1512.08831 (2015), It results from the traveling thief problem (TTP) when the tour is fixed. The PWT can be formally defined as follows. Given are n + 1 cities, distances di, 1 in, from city i to city i+ 1, and a set of items M, |M| = m, distributed all over the firstncities. Eachcityi,1in,containsasetofitemsMi M,|Mi|=mi. Each item eij Mi, 1 j mi, is characterised by its positive integer profit pij and weight wij . In addition, a fixed route N = (1, 2, …, n + 1) is given that is traveled by a vehicle with velocity v [vmin,vmax]. Let xij {0,1} be a variable indicating whether or not item eij is chosen in a solution. Then a set SM of selected items can be represented by a decision vector x = (x11, x12, …, x1m1 , x21, …, xnmn ) .The weight of the items selected by x is given by n mi W(x) = wijxij i=1 j=1 and the total benefit of selecting a subset of items S is calculated as B(x) = P(x) RT( x), 1 COMP SCI 3316 7316 Combined Evol. Comp. Semester 2, 2022 where P (x) represents the total profit of selected items and T (x) is the total travel time for the vehicle carrying these items. We have Here, = vmaxvmin W n mi P(x) = pijxij i=1 j=1 di and T(x) has the following interpretation. When the vehicle is traveling from city i to city i + 1, the selected items have to be carried and the maximal speed vmax of the vehicle is reduced by a normalized amount that depends linearly on the weight of these items. Because the velocity is influenced by the weight of collected items, the total travel time increases along with their weight. Given a renting rate R (0, ),RT (x) is the total cost of carrying the items chosen by x. In the single-objective formulation of this problem, the goal is to find a solution x = arg maxx{0,1}m B(x). For our instances in the experimental investigations, we set vmin = 0.1, vmax = 1.0. We use the TTP benchmark instances for a fixed tour. Items can be collected at the first n cities of the tour and are delivered to the city where the vehicle started ( city ​​1 and city n + 1 are the same). This implies that B(x) is given by the TTP objective value for the fixed tour and the selection of items given by x. We are studying multi-objective formulations of this problem which take different con- flicting components into account. JMetal (see im- plements most of the important evolutionary multi-objective algorithms and you are able to use this framework for Assignment 3. Exercise 1 Your first multi-objective optimisation (10 marks) Download and install jMetal. Follow the case study in Section 3.3 from the jMetal user manual (available from the jMetal website). Run NSGA-II for 10.000 generations on the benchmark functions ZDT 2 and ZDT 3 with population sizes 10, 100, and 1.000. Visualise the six final populations. Exercise 2 Evolutionary multi -objective algorithms for PWT – Static Scenario (10+25+10=45 marks) We study the multi-objective version f(x) = (W(x),B(x)) of PWT, where the goal is to minimize the weight of the selected items W(x) and to maximize the total benefit B(x).Use a parent and offspring population size of 20 for all algorithms and run each algorithm 10 times for 100,000 generations. You have to test your algorithms on the nine instances provided in the file (https://cs.adelaide. 16s2-ec-adelaide/ using the fixed tour eil101.linkern.tour provided in this zip file. n T(x) = i=1vmax wkjxkj is the constant defined by the input parameters, where W is the capacity of the vehicle. i mk k=1 j=1 2 COMP SCI 3316 7316 Combined Evol. Comp. Semester 2, 2022 Design appropriate mutation and crossover operators that can be used in NSGA- II, SPEA2 and IBEA and apply the algorithms to solve the given benchmarks. Improve the operators used in the algorithms such that they perform as best as possible and visualize the results for each performing algorithm (NSGA-II, SPEA2,IBEA) after 1000, 10000, 50000, 100000 generations. Submit a document Exercise2.pdf in which you describe your best performing al- gorithm and the results on the benchmarks. You may use diagrams and examples to support your arguments. Exercise 3 Evolutionary multi -objective algorithms for PWT – Dynamic Scenario (10 + 25 + 10 =45 marks) We now consider your dynamic benchmarks created 6 benchmarks with 280 cities for the dynamic TTP that you have created for Assignment 2, Exercise 2 and the multi-objective problem given by f(x) = (W(x),B(x)). Here items may become unavailable/available over time. Note that for the PWT, items are picked at the first n cities of the tour and city n + 1 is equal to the first city of the tour. Unavailable items can not be selected and therefore should not have an impact on the fitness.Use a parent and offspring population size of 20 for all algorithms. Run your approaches for NSGA-II, SPEA2 and IBEA from Exercise 2 on your benchmarks and visualize the populations in the objective space at generations 1000, 10000, 50000, 10000. Compare the results that are achieved by these algorithms. Design new operators for the three algorithms that are performing as best as possible on these benchmarks. All algorithms for dynamic problems have to be online algorithms which can only take into account the changes made to the instance up to the generation it has already processed. They can not look into the future. Visualize the results for each best performing algorithm (NSGA-II, SPEA2, IBEA) after 1000, 10000, 50000, 100000 generations. Submit a document Exercise3.pdf in which you describe your best performing al- gorithm and the results on the benchmarks. You may use diagrams and examples to support your arguments. Exercise 4 Team work: who has done what? (zero points) We would like each team member to write one paragraph about what each member has contributed to this assignment. We will not mark this, and it will not have any effect on the marking of the other exercises. We would like to encourage self-regulation within the group and cooperative learning. Submit a document Exercise4.pdf in which each team member describe the own contribution. 3 COMP SCI 3316 7316 Combined Evol. Comp. Semester 2, 2022 3 Marking Marking of implementations will be done according to the following criteria:4 correct overall implementation – 20% design of the operators and algorithms for the problems and justification – 30% quality of the results achieved on the different problems and algorithm comparison – 50% Procedure for handing in the assignment Work should be handed in using the course website. The submission must include: all source files: if your code does not compile or if it is not sufficiently well docu- mented, we will cap the code-related marks at 50% all configuration files a README.txt file containing instructions to run the code the names, student numbers, and email addresses of the group members a pdf containing all figures which show the performance of your algorithms. Exercise1.pdf, Exercise2.pdf, Exercise3.pdf, Exercise4.pdf as required in the exer- cises.Failure to meet all requirements of the General procedure for handing in the assignment will lead to a reduction by twenty (20) marks. Note: there will be a progress presentation session for this assignment. This is a great opportunity for you to get feedback on your progress, and to make last adjust- ments for the final submission. In these progress presentations, we are expecting each group to briefly outline their achievements. 4