Operational Research in Education

Operational Research (OR) techniques have been applied, from the early stages of the discipline, to a wide variety of issues in education. At the government level, these include questions of what resources should be allocated to education as a whole and how these should be divided amongst the individual sectors of education and the institutions within the sectors. Another pertinent issue concerns the efficient operation of institutions, how to measure it, and whether resource allocation can be used to incentivise efficiency savings. Local governments, as well as being concerned with issues of resource allocation, may also need to make decisions regarding, for example, the creation and location of new institutions or closure of existing ones, as well as the day-to-day logistics of getting pupils to schools. Issues of concern for managers within schools and colleges include allocating the budgets, scheduling lessons and the assignment of students to courses. This survey provides an overview of the diverse problems faced by government, managers and consumers of education, and the OR techniques which have typically been applied in an effort to improve operations and provide solutions

Multi-objective vehicle routing and loading with time window constraints:a real-life application

Motivated by a real-life application, this research considers the multi-objective vehicle routing and loading problem with time window constraints which is a variant of the Capacitated Vehicle Routing Problem with Time Windows with one/two-dimensional loading constraints. The problem consists of routing a number of vehicles to serve a set of customers and determining the best way of loading the goods ordered by the customers onto the vehicles used for transportation. The three objectives pertaining to minimisation of total travel distance, number of routes to use and total number of mixed orders in the same pallet are, more often than not, conflicting. To achieve a solution with no preferential information known in advance from the decision maker, the problem is formulated as a Mixed Integer Linear Programming (MILP) model with one objective—minimising the total cost, where the three original objectives are incorporated as parts of the total cost function. A Generalised Variable Neighbourhood Search (GVNS) algorithm is designed as the search engine to relieve the computational burden inherent to the application of the MILP model. To evaluate the effectiveness of the GVNS algorithm, a real instance case study is generated and solved by both the GVNS algorithm and the software provided by our industrial partner. The results show that the suggested approach provides solutions with better overall values than those found by the software provided by our industrial partner

Meta-raps: Parameter Setting And New Applications

Recently meta-heuristics have become a popular solution methodology, in terms of both research and application, for solving combinatorial optimization problems. Meta-heuristic methods guide simple heuristics or priority rules designed to solve a particular problem. Meta-heuristics enhance these simple heuristics by using a higher level strategy. The advantage of using meta-heuristics over conventional optimization methods is meta-heuristics are able to find good (near optimal) solutions within a reasonable computation time. Investigating this line of research is justified because in most practical cases with medium to large scale problems, the use of meta-heuristics is necessary to be able to find a solution in a reasonable time. The specific meta-heuristic studied in this research is, Meta-RaPS; Meta-heuristic for Randomized Priority Search which is developed by DePuy and Whitehouse in 2001. Meta-RaPS is a generic, high level strategy used to modify greedy algorithms based on the insertion of a random element (Moraga, 2002). To date, Meta-RaPS had been applied to different types of combinatorial optimization problems and achieved comparable solution performance to other meta-heuristic techniques. The specific problem studied in this dissertation is parameter setting of Meta-RaPS. The topic of parameter setting for meta-heuristics has not been extensively studied in the literature. Although the parameter setting method devised in this dissertation is used primarily on Meta-RaPS, it is applicable to any meta-heuristic\u27s parameter setting problem. This dissertation not only enhances the power of Meta-RaPS by parameter tuning but also it introduces a robust parameter selection technique with wide-spread utility for many meta-heuristics. Because the distribution of solution values generated by meta-heuristics for combinatorial optimization problems is not normal, the current parameter setting techniques which employ a parametric approach based on the assumption of normality may not be appropriate. The proposed method is Non-parametric Based Genetic Algorithms. Based on statistical tests, the Non-parametric Based Genetic Algorithms (NPGA) is able to enhance the solution quality of Meta-RaPS more than any other parameter setting procedures benchmarked in this research. NPGA sets the best parameter settings, of all the methods studied, for 38 of the 41 Early/Tardy Single Machine Scheduling with Common Due Date and Sequence-Dependent Setup Time (ETP) problems and 50 of the 54 0-1 Multidimensional Knapsack Problems (0-1 MKP). In addition to the parameter setting procedure discussed, this dissertation provides two Meta-RaPS combinatorial optimization problem applications, the 0-1 MKP, and the ETP. For the ETP problem, the Meta-RaPS application in this dissertation currently gives the best meta-heuristic solution performance so far in the literature for common ETP test sets. For the large ETP test set, Meta-RaPS provided better solution performance than Simulated Annealing (SA) for 55 of the 60 problems. For the small test set, in all four different small problem sets, the Meta-RaPS solution performance outperformed exiting algorithms in terms of average percent deviation from the optimal solution value. For the 0-1 MKP, the present Meta-RaPS application performs better than the earlier Meta-RaPS applications by other researchers on this problem. The Meta-RaPS 0-1 MKP application presented here has better solution quality than the existing Meta-RaPS application (Moraga, 2005) found in the literature. Meta-RaPS gives 0.75% average percent deviation, from the best known solutions, for the 270 0-1 MKP test problems

Nature-inspired Methods for Stochastic, Robust and Dynamic Optimization

Nature-inspired algorithms have a great popularity in the current scientific community, being the focused scope of many research contributions in the literature year by year. The rationale behind the acquired momentum by this broad family of methods lies on their outstanding performance evinced in hundreds of research fields and problem instances. This book gravitates on the development of nature-inspired methods and their application to stochastic, dynamic and robust optimization. Topics covered by this book include the design and development of evolutionary algorithms, bio-inspired metaheuristics, or memetic methods, with empirical, innovative findings when used in different subfields of mathematical optimization, such as stochastic, dynamic, multimodal and robust optimization, as well as noisy optimization and dynamic and constraint satisfaction problems

Routing Unmanned Aerial Vehicles While Considering General Restricted Operating Zones

U.S. military forces employ unmanned aerial vehicles (UAVs) to conduct intelligence-gathering missions worldwide. For a typical mission, commanders may task UAV operators to gather imagery on 100 or more sites or targets. UAV operators must quickly prepare mission plans that meet the needs of their commanders while dealing with real-world constraints such as time windows, site priorities, imagery requirements, UAVs with different capabilities (i.e. imagery equipment, speed, and range), and UAVs departing from different bases. Previous AFIT research provided the UAV Battlelab with a tool, AFIT Router, for generating high-quality routes to aid mission planning. This research enhances the AFIT Router by providing the ability to define general restricted operating zones and to build routes that consider these zones. This research also examines and compares a probabilistic tabu search heuristic and two reactive tabu search heuristics for solving vehicle routing problems