Solving Challenging Real-World Scheduling Problems

This work contains a series of studies on the optimization of three real-world scheduling problems, school timetabling, sports scheduling and staff scheduling. These challenging problems are solved to customer satisfaction using the proposed PEAST algorithm. The customer satisfaction refers to the fact that implementations of the algorithm are in industry use. The PEAST algorithm is a product of long-term research and development. The first version of it was introduced in 1998. This thesis is a result of a five-year development of the algorithm. One of the most valuable characteristics of the algorithm has proven to be the ability to solve a wide range of scheduling problems. It is likely that it can be tuned to tackle also a range of other combinatorial problems. The algorithm uses features from numerous different metaheuristics which is the main reason for its success. In addition, the implementation of the algorithm is fast enough for real-world use.Siirretty Doriast

The Traveling Tournament Problem

In this thesis we study the Traveling Tournament problem (TTP) which asks to generate a feasible schedule for a sports league such that the total travel distance incurred by all teams throughout the season is minimized. Throughout our three technical chapters a wide range of topics connected to the TTP are explored. We begin by considering the computational complexity of the problem. Despite existing results on the NP-hardness of TTP, the question of whether or not TTP is also APX-hard was an unexplored area in the literature. We prove the affirmative by constructing an L-reduction from (1,2)-TSP to TTP. To reach the desired result, we show that given an instance of TSP with a solution of cost K, we can construct an instance of TTP with a solution of cost at most 20m(m+1)cK where m = c(n-1)+1, n is the number of teams, and c > 5, c ∈ ℤ is fixed. On the other hand, we show that given a feasible schedule to the constructed TTP instance, we can recover a tour on the original TSP instance. The next chapter delves into a popular variation of the problem, the mirrored TTP, which has the added stipulation that the first and second half of the schedule have the same order of match-ups. Building upon previous techniques, we present an approximation algorithm for constructing a mirrored double round-robin schedule under the constraint that the number of consecutive home or away games is at most two. We achieve an approximation ratio on the order of 3/2 + O(1)/n. Lastly, we present a survey of local search methods for solving TTP and discuss the performance of these techniques on benchmark instances

Time Relaxed Round Robin Tournament and the NBA Scheduling Problem

This dissertation study was inspired by the National Basketball Association regular reason scheduling problem. NBA uses the time-relaxed round robin tournament format, which has drawn less research attention compared to the other scheduling formats. Besides NBA, the National Hockey League and many amateur leagues use the time-relaxed round robin tournament as well. This dissertation study is the first ever to examine the properties of general time-relaxed round robin tournaments. Single round, double round and multiple round time-relaxed round robin tournaments are defined. The integer programming and constraint programming models for those tournaments scheduling are developed and presented. Because of the complexity of this problem, several decomposition methods are presented as well. Traveling distance is an important factor in the tournament scheduling. Traveling tournament problem defined in the time constrained conditions has been well studied. This dissertation defines the novel problem of time-relaxed traveling tournament problem. Three algorithms has been developed and compared to address this problem. In addition, this dissertation study presents all major constraints for the NBA regular season scheduling. These constraints are grouped into three categories: structural, external and fairness. Both integer programming and constraint programming are used to model these constraints and the computation studies are presente

On the application of graph colouring techniques in round-robin sports scheduling

The purpose of this paper is twofold. First, it explores the issue of producing valid, compact round-robin sports schedules by considering the problem as one of graph colouring. Using this model, which can also be extended to incorporate additional constraints, the difficulty of such problems is then gauged by considering the performance of a number of different graph colouring algorithms. Second, neighbourhood operators are then proposed that can be derived from the underlying graph colouring model and, in an example application, we show how these operators can be used in conjunction with multi-objective optimisation techniques to produce high-quality solutions to a real-world sports league scheduling problem encountered at the Welsh Rugby Union in Cardiff, Wales

Ant algorithm hyperheuristic approaches for scheduling problems

For decades, optimisation research has investigated methods to find optimal solutions to many problems in the fields of scheduling, timetabling and rostering. A family of abstract methods known as metaheuristics have been developed and applied to many of these problems, but their application to specific problems requires problem-specific coding and parameter adjusting to produce the best results for that problem. Such specialisation makes code difficult to adapt to new problem instances or new problems. One methodology that intended to increase the generality of state of the art algorithms is known as hyperheuristics. Hyperheuristics are algorithms which construct algorithms: using "building block" heuristics, the higher-level algorithm chooses between heuristics to move around the solution space, learning how to use the heuristics to find better solutions. We introduce a new hyperheuristic based upon the well-known ant algorithm metaheuristic, and apply it towards several real-world problems without parameter tuning, producing results that are competitive with other hyperheuristic methods and established bespoke metaheuristic techniques

Ant algorithm hyperheuristic approaches for scheduling problems

For decades, optimisation research has investigated methods to find optimal solutions to many problems in the fields of scheduling, timetabling and rostering. A family of abstract methods known as metaheuristics have been developed and applied to many of these problems, but their application to specific problems requires problem-specific coding and parameter adjusting to produce the best results for that problem. Such specialisation makes code difficult to adapt to new problem instances or new problems. One methodology that intended to increase the generality of state of the art algorithms is known as hyperheuristics. Hyperheuristics are algorithms which construct algorithms: using "building block" heuristics, the higher-level algorithm chooses between heuristics to move around the solution space, learning how to use the heuristics to find better solutions. We introduce a new hyperheuristic based upon the well-known ant algorithm metaheuristic, and apply it towards several real-world problems without parameter tuning, producing results that are competitive with other hyperheuristic methods and established bespoke metaheuristic techniques

Fútbol strategies applied to optimize combinatortial problems to create efficent results – the soccer heuristic

Master of ScienceDepartment of Industrial & Manufacturing Systems EngineeringTodd EastonHeuristics are often implemented to find better solutions to computationally challenging problems. Heuristics use varying techniques to search for quality solutions. Several optimization heuristics have drawn inspiration from real world practices. Ant colony optimization mimics ants in search of food. Genetic algorithms emulate traits being passed from a parent to a child. Simulated annealing imitates annealing metal. This thesis presents a new variable neighborhood search optimization heuristic, fútbol Strategies applied to Optimize Combinatorial problems to Create Efficient Results, which is called the SOCCER heuristic. This heuristic mimics fútbol and the closest player to the ball performs his neighborhood search and players are assigned different neighborhoods. The SOCCER heuristic is the first application of variable neighborhood search heuristic that uses a complex structure to select neighborhoods. The SOCCER heuristic can be applied to a variety of optimization problems. This research implemented the SOCCER heuristic for job shop scheduling problems. This implementation focused on creating a quality schedule for a local limestone company. A small computational study shows that the SOCCER heuristic can quickly solve complex job shop scheduling problems with most instances finishing in under an half an hour. The optimized schedules reduced the average production time by 7.27%. This is roughly a 2 day decrease in the number of days required to produce a month’s worth of orders. Thus, the SOCCER heuristic is a new optimization tool that can aid companies and researchers find better solutions to complex problems