Predicted Rating 0.8 0.7 Non-Dominated 0.6 Dominated 0.5 0.4 0.3 0.2 0.1 0 0.10 0.15 0.20 0.25 0.30 0.35 0.40 Accuracy (a) (b) Coverage Coverage 0.8 0.6 0.4 0.2 0 1.5 2.0 2.5 3.0 3.5 4.0 2.6 Hypervolume 1.0 2.5 2.4 2.3 2.2 2.1 0 500 1000 1500 2000 2500 3000 Generation (c) Figure 4 Results of MOEA-ProbS on Movielens 2. (a) Plots of final non-dominated solutions with the highest hypervolume. (b) Plots of final solutions in the accuracy-coverage space (c) The error-bar of hypervolume metric of population among 30 independent runs with different generations. 0.4 0.2 0 0.90 1.15 1.40 1.65 1.90 2.15 2.40 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.10 1.40 Non-dominated Dominated 0.15 0.20 0.25 0.30 Hypervolume 0.6 Coverage Coverage 0.8 0.35 1.33 1.23 1.13 0 500 1000 1500 2000 2500 3000 Predicted Rating Accuracy Generation (a) (b) (c) Figure 5 Results of MOEA-ProbS on Movielens 3. (a) Plots of final non-dominated solutions with the highest hypervolume. (b) Plots of final solutions in the accuracy-coverage space (c) The error-bar of hypervolume metric of population among 30 independent runs with different generations. Coverage Coverage 0.8 0.6 0.4 0.2 0 2.0 2.5 3.0 3.5 4.0 Predicted Rating 4.5 (a) 5.0 0.8 0.7 Non-dominated 0.6 Dominated 0.5 0.4 0.3 0.2 0.1 0 0.20 0.25 0.30 0.35 0.40 0.45 0.50 Accuracy Hypervolume 1.0 (b) 3.3 3.2 3.1 3.0 2.9 2.8 2.7 2.6 0 500 1000 1500 2000 2500 3000 Generation (c) Figure 6 Results of MOEA-ProbS on Movielens 4. (a) Plots of final non-dominated solutions with the highest hypervolume. (b) Plots of final solutions in the accuracy-coverage space (c) The error-bar of hypervolume metric of population among 30 independent runs with different generations. the recommended items, we use selfinformation. Given an item a, the probability to collect it by a randomselected user is k a /M, where M is the total number of users, and k a is the degree of item a (i.e., the popularity of item a ) [19]. The self-information of item a is thus: N a = log 2 ` M j . (11) ka A user-relative novelty is obtained by calculating the average self-information of items in the target user's recommendation list. Then the mean novelty N (L) over all users can be obtained according to: M N (L) = 1 / / N a ML i = 1 a ! Oi L (12) where O iL is the recommendation list of user i and L is the length of the recommendation list. C. Experimental Results 1) Effectiveness of MOEA-ProbS: In this subsection, we present the experimental results of MOEA-ProbS on the four data sets. To show the effectiveness of the proposed algorithm, the final non-dominated february 2015 | Ieee ComputatIonal IntellIgenCe magazIne 57