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randomly) [66].
(a) Best student: The best student is to be considered as the student who scored the overall highest marks/grade in the examination. It is an obvious fact that the best student will always try to secure his/her position in the class. For securing his/her position, the best student should have to provide more effort towards each subject than the same given by the rest of the students in the class. Therefore, it can be concluded that the best student will always provide more effort than the same given by other students in the class. Mathematically, the student of this category can be visualized with the help of (Equation 1.1) [66]
where, Xbest indicates the marks/grades obtained by the best student, Xj indicates the marks of the student, randomly selected, in the same subject, and rand generates a random number between 0 and 1. In (Equation 1.1), the D parameter randomly takes the value either 1 or 2. Marks obtained in the subjects by the best student may be increased or maybe decreased depending upon the student and the subjects. However, the primary objective of the best student in the class is to secure his/her position by continuously scoring the highest overall marks in the examination.
(b) Good student: If a student is interested in a subject, then he or she may strive to make more effort to enhance his or her performance in that subject. As a result, their overall performance in the examination will be improved. The students of this kind can be classified as subject wise good student. The effort given by all the students in this category may not be the same because the psychologies of the students are different. Some students try to give a similar or even better effort than the best student, where as; some students try to improve their performance by giving more effort after considering the effort given by the best student as well as the average effort given by the students of the class. This group of students may be further divided into two categories. The first category of this group of students is those who try to give similar or even better effort as given by the best student. This category of students gives effort to the subjects in which they are interested. So, their performance in that subject, as well as their overall performance, gets improved. Improvement of these kinds of students in a subject can be explained using (Equation 1. 2a) [66]. The other category of good students is those students who give effort considering the effort given by the best student as well as try to give more effort than the average effort of the class so that their performance in that subject, as well as overall performance, gets improved. Mathematically, the student of this category can be represented as (Equation 1. 2b) [66].
Here, Xnewi is the improved performance of the ith student in that subject; Xbest and Xi are the marks/grade obtained in that subject by the best student and the ith student, respectively; mean represents the average marks obtained in the class in that particular subject and rand variable produces a random number between 0 and 1.
(c) Average student: In order to increase their overall success in the test, students with less interest in a subject aim to offer an average effort. The students of this category can be named as subject-wise average student. While giving average effort in a particular subject, students will try to improve their overall performance by paying more effort to the other subjects which are offered to them. The performance of this category of students may be explained with the help of (Equation 1. 3) [66]
where, Xi indicates the marks/grade of the ith student of the class in a subject, mean indicates the average marks obtained in that particular subject, and rand generates a random number between 0 and 1.
(d) Students who try to improve randomly: Except the three categories of students discussed above, there are certain students who strive to enhance their results without recognising the effort offered by rest of the students in the class. The students of these kinds always try to improve their performance randomly to some extent up to their limitations, depending upon their interest in the subject. Improvement of the students’ performance based on this concept may be represented by (Equation 1. 4) [66]
where min and max are the two variables that indicate the minimum and the maximum marks of the subject, respectively, and rand generates a random number between 0 and 1.
The process of getting interested in a subject for different students is not deterministic. It depends on the students’ psychology. So, it may be said that the selection of different categories of students is a random process.
Incorporating the psychology of the aforementioned four categories of students, the SPBO algorithm can be visualized easily using the flowchart given in Figure 1.1. Each (student) population consists of various variables analogous to the subjects offered to the students. The students try to give the subjects effort so that their overall performance in the exam is improved. The fitness function is selected as the overall marks/grades obtained by the students. The effort given by the student is appreciated if her/his performance gets improved. Similarly, if the fitness function improves, a variable change is accepted. And, finally, the performance of the best student will be considered as the best solution or optimum solution. The performance of different optimization algorithms depends upon their own parameters. But SPBO has no such tuneable parameter.
1.2.2 Performance of SPBO for Solving Benchmark Functions
In order to evaluate the performance of SPBO for optimizing the benchmark functions, ten of the CEC-2005 benchmark functions are considered. The ten different CEC-2005 benchmark functions among twenty-five are presented in Table 1.1. To compare the performance of SPBO with other optimization methods, the results obtained by using SPBO are compared to those obtained by using the different optimization methods namely PSO, TLBO, CS, and SOS. Twenty-five individual runs are performed for each of the functions and for each of the algorithms.
The performance of the algorithms selected is evaluated on the basis of the optimal result obtained and on the basis of convergence mobility. For the purposes of analysis, the algorithms are found to converge when the gap between the optimal function result and the result obtained crosses below 1×10-5. The results obtained below 1×10-5 are considered as equal to zero. The parameters of PSO, TLBO, CS and SOS are considered according to the dimension of the benchmark function. But SPBO does not have any parameter and the size of the population needs