This study focuses on the performance of the Swarm Intelligence (SI) metaheuristics on the Traveling Tournament Problem (TTP). An Artificial Bees Colony Algorithm for the Traveling Tournament Problem”, Proceedings of the 41st Annual Conference of the Operations Research Society of South Africa (ORSSA), pp. Due to the complexity of the TTP, this has proven difficult to resolve. through exact methods, even for very small problem cases.
Metaheuristics
Metaheuristics are classified into solution-to-solution search methods such as SA and Tabu Search (TS) and set-based search methods such as GA etc. Nevertheless, whether it is a solution-to-solution or set-based metaheuristic, the basic structure is in the search remains the same. This evaluation involves calculating or estimating the performance of the candidate solution(s) and comparing them to the performance of θk and sometimes to each other.
Swarm Intelligence
Decision Making
- Where to Forage?
- Exploration vs. Exploitation
- Where to Live?
The dance encodes information about the distance and direction of the food source and is performed by successful foragers (recruits). The number of wave phases performed by the dancer in a given jump measures the duration of the jump and the time interval between the phases of the movement measures power. Assuming that the ants that missed out are able to discover new food sources and thus help as explorers or scouts for the colony, depending on the profitability of the food source that is/are already used, this strategy allows the number of scouts to be fine-tuned .
Purpose of Study
Once the number of dancers decreases in the colony, there is an increased probability that some foragers who are not employed cannot find a dancer and therefore the colony sends out some more scouts. Even more surprising is that the same communication methods are often used to achieve a very different goal; selecting a new slot. A new house must be chosen under two conditions; either an old nest is destroyed and the whole colony has to move, or a new nest site is required by part of the colony for reasons of reproductive aggregation ie.
Scope of Study
Thesis Structure
The variables also represent the distances between the places which are in the sequence, but these variables are used strictly in the target calculation. The double values and the total distance associated with the games in the tournament must be less than zero. Rasmussen [14] used variables similar to those used in the IP model to formulate the problem as a CP model which allowed them to redefine the constraints and this is why their CP model differs from their IP model.
Related Research
Comparative Study
Tables 2.1 and 2.2 below show the solutions obtained for two different data sets by the metaheuristics discussed above. Some metaheuristics were only tested for only one of the cases and some were only tested for cases with n ≥ 8 because most metaheuristics get very good solutions for smaller cases. The highlighted entries illustrate the best solution obtained for that data instance by comparing all the metaheuristics.
From Table 2.1 and 2.2 we can observe that in most Circn and NL10 cases good solutions are obtained by Lim et al.
Other Scheduling Problems
The School Timetabling Problem
Scheduling involves "assigning a set of events to a number of rooms and time slots so that they satisfy a number of constraints" [23]. The most common versions of the problem are the University Course Time Table Problem (UCTP) and the Examination Time Table Problem (ETP). 25] also proposed a combination of PSO and local search to efficiently search the solution space in solving UCTP.
PSO is applied to schedule topics in the timetable at each iteration and when there are collisions in the timetable, the local search is applied to search for the nearest available time slot and room nearby [25]. The proposed algorithm was tested on three different data sets of different sizes and performed very well compared to other algorithms used for benchmarking. Djamaras and Ku-Mahamud [26] presented an algorithm; an ant system based algorithm for solving the UCTP.
The third factor gives high priority to courses that need more time to deliver, and finally, high priority is given to edges that represent expertise of the lectures in the selection of courses and preferable time slots by the fourth factor and this leads to high quality schedules [26]. The proposed algorithm was tested on randomly generated data and using the four heuristic factors and negative pheromone concept improved the performance of the algorithm. The curriculum-based UCTP was considered in [27] mapping between a set of periods, devices, rooms and a set of courses in such a way that the requirements of the university are satisfied.
The proposed algorithm was applied to 9 real datasets and achieved very promising results that were much better than hand-crafted results.
Job Shop Scheduling Problem
Airline Crew Scheduling
Conclusion
New Objective Function
When applying the algorithm, it is difficult to satisfy all the TTP constraints in all iterations, especially the no-repetition and at-most constraints. Exploring the infeasible regions can help find solutions that are of high quality and thus the need to change the objective function. Where d is the cost of a schedule (total distance traveled between all teams), is the penalty weight imposed by an infeasible schedule, and n(S) represents the number of violations of the at-most-no-repetition constraints.
Creating Initial Schedules
After each round, each abstract team is immediately moved clockwise to the next node until all n−1 assignments are completed. The next stage of initial planning is to assign real teams to the abstract teams. Each entry (i,j) is equal to the number of times the two teams are consecutive opponents of other teams.
Real teams with smaller distances between their home cities are likely to be assigned to abstract teams that are played back-to-back more often, to reduce the total travel distance. The final stage is assigning locations to each game. Locations are randomly assigned and feasibility constraints must be met. If the schedule is not feasible, the assignments are repeated until a feasible schedule is obtained. Home and away games are shown with different signs: -ti is an away game and ti is a home game.
The schedule is then duplicated and the locations are reversed to create the second half of the tournament, thus producing a DRRT.
Neighbourhoods
Team Swap: This move randomly selects two teams Ti and Tj and swaps the schedule of the two teams except when they are playing each other. Round Swap: This move selects two rounds at random KlandKm and then simply swaps all games between the two rounds. After applying the move, be aware that it is also necessary to switch to team T8 to obtain a DRRT.
Algorithms
- Artificial Bee Colony (ABC) Algorithm
- Cuckoo Search (CS) Algorithm
- Bacterial Foraging Optimization (BFO) Algorithm
- Bat Algorithm
- Bacterial Foraging, Bat and Cuckoo Search (BBC)
ABC [35, 36] is an optimization algorithm based on the bee swarm's foraging behavior. If the fitness of the new solution is better than the previous solution, the busy bee forgets the previous solution and remembers the new one. The employed bees share information about the solutions with the observer bees, who then choose a solution based on the suitability of the solutions.
Parasitic cuckoos mostly choose a nest where the host bird has just laid eggs. Use the moves discussed in 4.2 to get a new solution. Calculate the fitness of the new solution (fi). The main parameters of the algorithm are loudness and pulseRate.
The loudness parameter works like the cooling scheme in the Simulated Annealing (SA) algorithm [39] and the pulse frequency is responsible for controlling the frequency of the pulse. Once a bat has found its solution, the loudness decreases and the accuracy of the attack is increased by increasing pulse emission. Generate a new solution by randomly exploring the neighborhood f tns← Evaluate the suitability of the new solution.
The name of the instance is denoted by NLn, where n is the number of teams playing in the league and 8 ≤ n ≤ 16.
Results
- Cuckoo Search (CS)
- Artificial Bee Colony (ABC)
- Bat
- Bacterial Foraging (BFO)
- Bacterial Foraging, Bat and Cuckoo Search (BBC)
The colony size (colony size) was set to 100, the maximum number of cycles (maxCycle) for foraging was also set to 100 and the algorithm was run 50 times to see or test its robustness. The population size (populatonSize) is set to 100, the hardness to 0.95 and the pulse rate (pulseRate) to 1, the maximum number of iterations is set to 100 and the number of runs to 50.
Discussion
Select dataset: To select a dataset, click the upload button, the open dialog shown in Figure A.2 will pop up, navigate to the folder where the dataset is located, and then click open when you have selected the desired file. Algorithm selection: Select the algorithm you want to run from the list as shown in Figure A.3, then click ok. The output will be displayed in the text area on the right side of the panel as shown in Figure A.4. a) Parameters (b) Output Figure A.4: Algorithm parameters and output.
To save the result, click the save results button and a save dialog will appear as seen in Figure A.5, select the directory you want to save the results to, and then click save. Opening an existing file: To open an existing file, go to the file as shown in Figure A.6, select the file with the first option, and then select the file you want to open. Behavior and Genetics of Social Insects Laboratory, School of Biological Sciences, University of Sydney, Sydney, Australia.
Department of IEEM, Hong Kong University of Science and Technology, Clearwater Bay, Kowloon, Hong Kong. Faculty of Information Technology and Faculty of Mathematics, University of Science Ho Chi Minh City, Vietnam, 2010. School of Mechanical and Production Engineering, School of Computer Engineering and School of Electrical and Electronic Engineering, Nanyang Technological University, 2006.
Bioinformatics Laboratory, Paran Federal University of Technology (UTFPR), Curitiba (PR), Brazil and Applied Cognitive Computing Group, Santa Catarina State University (UDESC), Brazil.
