A Hybrid Fuzzy Evolutionary Algorithm for A Multi-Objective Resource Allocation Problem Lily Rachmawati Department of Electrical and Computer Engineering National University of Singapore lily@nus.edu.sg Dipti Srinivasan Department of Electrical and Computer Engineering National University of Singapore dipti@nus.edu.sg Abstract In this paper a hybrid fuzzy evolutionary algorithm for a multi-objective resource allocation problem, the student project allocation (SPA) problem, is presented. Student Project Allocation must satisfy a number of soft objectives stemming from multiple points of view. The proposed algorithm employs a fuzzy inference system to model and aggregate the objectives, assuming the role of the fitness function in the evolutionary algorithm. The fuzzy system captures preferences of the decision maker in the compromise between various objectives, thereby guiding the search to interesting regions in the objective space. The results demonstrate the effectiveness of this hybrid approach for a large data set 1. Introduction Resource allocation problems are widely encountered in industrial as well as academic practices. Owing to its combinatorial complexity, large-scale resource allocation often proves mathematically intractable. The search capability of evolutionary algorithm (EA) warrants its extensive application to such resource allocation problems. The allocation of resources often needs to satisfy multiple criteria, some of which may be soft and perception-based. Some examples of such problems are university timetabling [1], nurse scheduling [2], and network topology design [3]. For relevant variables in these problems, fuzzy representation has been suitably chosen [3-6] in the EA. However, the observed trend is that fuzzified values of perception-based objectives are treated with the conventional crisp mathematics instead of the approximate reasoning facility provided by fuzzy logic. In this paper we propose a hybrid Fuzzy EA algorithm employing fuzzy representation and reasoning for multi-objective resource allocation problem involving fuzzy objectives. In particular, the objectives are represented as fuzzy variables, which act as inputs to a fuzzy inference system evaluating the fitness of the associated candidate solution. The motivation of incorporating fuzzy logic in this manner is twofold. Firstly, fuzzy logic offers an effective representation and reasoning framework in evaluating the quality of candidate solutions. Secondly, based on the pre-specified preference of the user, the fitness function guides the search to interesting regions of the fitness space. Evolutionary Multi-objective Optimization (EMO) has been dominated recently by the concepts of Pareto-ranking based on domination criteria. This a posteriori approach essentially seeks a set of non- dominated solutions, the Pareto-optimal set, which exhibits various trade-off properties. The convergence and extensive coverage of the true Pareto-optimal front of associated multi-objective problems are the main preoccupation of the approach. Having attained the set of Pareto-optimal solutions, it is the task of the decision maker (DM) to select one solution from the set that suits his/her requirements the best. A number of efficient algorithms have been proposed based on these principles [7-14]. However, the definition of domination when many objectives are involved is inadequate to represent that of a human decision maker’s perception. Further, Pareto-ranking based approaches cannot incorporate the DM’s preferences in trade-offs between objectives. The number of Pareto-optimal solutions may well overwhelm a decision maker. These limitations have been highlighted and addressed to a certain degree in several papers [15-20]. Proceedings of the Fifth International Conference on Hybrid Intelligent Systems (HIS’05) 0-7695-2457-5/05 $20.00 © 2005 IEEE