Multi-objective Evolutionary Algorithms for Resource Allocation Problems

A resource allocation problem (RAP) is encountered in a variety of areas in operations research and management science. It is generally treated as a combinatorial optimization problem, where a limited amount of resources are to be allocated to certain number of competitive events in order to achieve the most effective allotment of the resources. An RAP usually contains a huge number of integer and/or real variables and constraints, a discrete search space, and multiple objectives. Moreover, the general RAP is NP-complete (Ibaraki and Katoh [1988], Zhang [2002], Kameshwaran [2004]). It is said that the properties of an NP-complete RAP can be used in characterizing another NP-complete RAP. Hence, it is very important to explore the similarities among different types of RAPs. However, though a number of RAPs are being studied independently, the study of similarities among them are still undeveloped. In this thesis work, two NP-complete RAPs of quite different natures, namely university class timetabling and land-use management, are considered for such studies. Based on their similarities, two similar versions of NSGA-II (Deb [2001], Deb et al. [2002]), a very popular multi-objective evolutionary algorithm, are developed for handling these two RAPs. The preparation of a class timetable is required in every academic institute once or twice a year. The problem involves the scheduling of classes (lectures), students, teachers and rooms at a fixed number of time-slots, subject to a certain number of constraints. Traditionally, the problem is solved manually by a trial and hit method, which either does not guarantee a valid solution or likely to miss far better solutions.