Genetic Algorithms for Feature Weighting in Multi-criteria Recommender Systems Chein-Shung hwang Crossover probability(pe): 0.5,,, 0.8, 0.9, 1.0 Mutation probability (pm): 0.01, 0.02, 0.03, 0.04, 0.05 Population size(PS)20, 30, 50, 75, 100 Generation number (GN):10,20,30,40,50,60,70,80,90,100 5.3. Performance results To demonstrate the effectiveness of the proposed system, we compare our approaches with two other algorithms the single-criterion user-based CF (SUCF) algorithm in which the overall rating is used as the sole criterion and the equally weighted multi-criteria CF(EWMCF) that applies an equal weight to each criterion rating. We denote our two approaches by their abbreviations: GA-based filter method for multi-criteria CF(GAFMCF)and GA-based wrapper method for multi-criteria CF (GAWMCF In the subsequent part of this section, we will first explore the optimal setting of GA parameters and n assess the performance effectiveness of the different approaches 5.3. 1 GA Parameters setting Crossover and mutation operators play the major roles in GA, so defining proper crossover and operators is necessary in order to achieve a better performance of the GA. However, the optimal values of crossover and mutation probabilities are problem specific and cannot be obtained independently [14]. All combinations of crossover and mutation, within given starting ranges, must be investigated in order to allow for the interaction effect. Accordingly, we examine the impacts of various combinations of Pe and Pm on the recommendations quality of the GAWMCF approach. We fix NB to 30, Ps to 50, and produce 5 recommendations for each user. Due to space limitations, Figure 2 shows the performance results for optimal values of Pc=0.9 and Pm=0. 05 by varying the number of generations For more detailed results of various combinations of Pc and pm, please refer to Appendix I 0.7 ▲ Precision 1020304050607080901 Figure 2. Performance results of GAWMCF approach vs. generation number for optimal values of pe 0.9 and Pm=0.05 In Figure 2, the number of generations necessary for convergence is also evaluated. We can see that performance is gradually improved generation by generation. However, the improvement becomes insignificant when the number of generations is greater than 80. Since the ga process is terminated the number of generations for convergence is reached, the greater the number of generations, the r the computational cost. For better computational efficiency, we fix the number of generations to 80 for subsequent experiments The population size is a critical parameter for the performance of GA. There is no clear indication as to how high the population size should be [15]. In general, increasing the population size not only reases the accuracy of the ga but also increases the number of generations to converge. Figure 3Genetic Algorithms for Feature Weighting in Multi-criteria Recommender Systems Chein-Shung Hwang - Crossover probability (pc): 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 - Mutation probability (pm): 0.01, 0.02, 0.03, 0.04, 0.05 - Population size (PS) 20, 30, 50, 75, 100 - Generation number (GN): 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 5. 3. Performance Results To demonstrate the effectiveness of the proposed system, we compare our approaches with two other algorithms: the single-criterion user-based CF (SUCF) algorithm in which the overall rating is used as the sole criterion and the equally weighted multi-criteria CF (EWMCF) that applies an equal weight to each criterion rating. We denote our two approaches by their abbreviations: GA-based filter method for multi-criteria CF (GAFMCF) and GA-based wrapper method for multi-criteria CF (GAWMCF). In the subsequent part of this section, we will first explore the optimal setting of GA parameters and then assess the performance effectiveness of the different approaches. 5. 3. 1. GA Parameters setting Crossover and mutation operators play the major roles in GA, so defining proper crossover and operators is necessary in order to achieve a better performance of the GA. However, the optimal values of crossover and mutation probabilities are problem specific and cannot be obtained independently [14]. All combinations of crossover and mutation, within given starting ranges, must be investigated in order to allow for the interaction effect. Accordingly, we examine the impacts of various combinations of pc and pm on the recommendations quality of the GAWMCF approach. We fix NB to 30, PS to 50, and produce 5 recommendations for each user. Due to space limitations, Figure 2 shows the performance results for optimal values of pc =0.9 and pm =0.05 by varying the number of generations. For more detailed results of various combinations of pc and pm , please refer to Appendix I. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 10 20 30 40 50 60 70 80 90 100 Performance Metric GN F1 Recall Precision Figure 2. Performance results of GAWMCF approach vs. generation number for optimal values of pc = 0.9 and pm = 0.05 In Figure 2, the number of generations necessary for convergence is also evaluated. We can see that performance is gradually improved generation by generation. However, the improvement becomes insignificant when the number of generations is greater than 80. Since the GA process is terminated when the number of generations for convergence is reached, the greater the number of generations, the higher the computational cost. For better computational efficiency, we fix the number of generations to 80 for subsequent experiments. The population size is a critical parameter for the performance of GA. There is no clear indication as to how high the population size should be [15]. In general, increasing the population size not only increases the accuracy of the GA but also increases the number of generations to converge. Figure 3 132