NUMERICAL FUNCTION
OPTIMIZATION: MODEL,
PROCEDURE AND USES
Neeraj Dahiya
Department of Computer Science and Engineering, SRM University, Delhi-NCR Campus, Sonipat, Haryana
neerajdahiya.cse@gmail.com,
Surjeet Dalal
Department of Computer Science and Engineering, SRM University, Delhi-NCR Campus, Sonipat, Haryana
profsurjeetdalal@gmail.com
Savita Khatri
Department of Computer Science and Engineering, BMIET, Sonipat, Haryana
dhynrj@gmail.com
Abstract:
A new revised teaching leaning based optimization (R-TLBO) that kind of geographies overall exploration competences along with fast merging is presented in this work. The revised teaching leaning based optimization allows the learners and teachers of the teaching, learning based optimization (TLBO) technique to guide and learn in these directions that circumvent the difficulties of early local optima & convergence. In this paper, RTLBO is given to perform such kind of operations. Various optimization techniques are used and the concluded outcomes are matched with others from related studies. An experimental outcome shows that the planned technique is better than present techniques in the way of performance and accuracy. Additionally, investigations are performed on many experiments are done on typical benchmark difficulties to prove the efficiency of the planned technique. The compassion investigation is accomplished on dissimilar constraints of RTLBO to validate their effect on overall problems and benchmark.
Keywords: Teaching, learning-based (TLBO) optimization, Meta-heuristics, Numerical Function, Algorithm, Revised Teaching, Learning based optimization (R-TLBO), Clustering.
1. Introduction
In the earlier centuries, different metaheuristic procedures have been planned to resolve difficult real-life optimization difficulties. All of these procedures are naturally inspired procedures & therefore simulator regular descriptions such as, GA [1-2], DE [3], SA [4], ACO [5], PSO [6] or ABC [7] etc. These procedures provide a variety of problem explanations. These explanations given by metheuristics may not be best explanation, but they are extremely used because of their straight forwardness & elasticity. Even there are n numbers of metaherustics algorithms are available both new and hybridization of metaphysics algorithms is a very dynamic research area [8], recently so many algorithms are proposed for the same.
1.1 Key impact of the work
Numerous research is proving in the last decades and those techniques cannot outflow a local point at the initial stage as possible; it becomes much more difficult for the algorithm to escape from that point in the latter iterations. In this study, a modified Teaching, learning based optimization algorithm (RTLBO) is proposed to overcome above mentioned drawback of the existing TLBO algorithm.
1. This algorithm gives a general idea of Artificial Intelligence. 2. This algorithm also gives basic knowledge of Soft Computing.
3. It demonstrates numerous problem areas Artificial Intelligence techniques can be used.
2. Teaching, Learning based optimization
Rao et al. [14] proposed recently an optimization technique that is teacher learning based optimization. This technique involves two approaches that are teachers approach and learner approach. To enhance the performance at earlier stage efforts is done by the teacher itself and then to enhance their performance students interact with each other for various subjects offered to them.
For example, there are x numbers of students are available in a class and S numbers of subject are offered to them. The performance of nth student, n = 1, 2, 3…………., X, in Mth subject, m=1, 2, 3…………., S is Ynm .
In teacher approach, teacher efforts to enhance the student performance (i.e. Best class student): that is New Ynm = updated performance (Ynm) + any random number, i.e. at (0, 1) (Y best, m – teacher factor, i.e. Tf) in the last of teacher approach, is modernized if it is an improved result otherwise old result is taken. , nmnew Y
The results in the termination of teacher turn out to be input to the learner approach. In learner approach, each learner interact with each other until it is finalized. This finalizes a single iteration of teaching, learning based optimization method. This procedure remains in process until or unless the preferred benchmark achieved. 2.1 Teacher approach
In the teacher approach it is deliberate as a teacher to exchange his/her awareness and capability with the other students and learners [15-18].
2.2 Learner approach
2.3 Planned Revised TLBO Procedure
Fig. 1. Proposed TLBO Algorithm.
3. Phases of Revised TLBO (R-TLBO) Procedure
Step 1: - describe and modify the optimization algorithm problem parameters. Step 2: - Compute the mean column wise for the population.
Step 3: - Compute the Alteration Mean according to step 1 by using the teaching approach factor
Step 4: - Transform the answers in the teacher approach based on step 3 and take the new result if it is improved than the current one.
Step 5: - Modernize the result in the learner approach as per to the step 4,5 and use the best output result of the given population.
Step 6: - Re-compute the steps 2 to5 until the goal state or final result achieved.
3.1 Investigational Situations
On the way to justify the outcomes of the planned RTLBO and for analysis its characteristics, various sets of optimization difficulties are designated for the experimentations. In each problem set, numerous familiar benchmark functions are recycled as problems to research and the search performance of the planned RTLBO & its performance is comparable with others algorithms.
Table: 1
Benchmark Functions
No Function Name Dimension Multimodal Unimodal Range Min
1 Beale 1 Not Yes [-4,4] 0
2 Matyas 2 Not Yes [-50,50] -1
Table: - 2
Data Sets Used Observation Structures Cluster
Australian Credit (AC 691 15 3
Iris 150 4 3 149 9 3
Cancer 1 700 10 3
Heart 250 12 3
Glass 350 10 3
Wine 175 8 316
4. Use of R-TLBO in Data Clustering
Some dissimilar constrained benchmark function designs for problems are given. These difficulties are used by many investigators to test the outcomes of different algorithms
Table: 3
Algorithm Data Set Used Parameter
GSA HS BBO LCA TLBO ETLBO RTLBO
Set_01 Best 16768.18 16483.61 16448.35 16431.76 16,578.42 16418.23 16295.37 Average 0.519 0.516 0.522 0.521 0.52 0.523 0.528 Set_02 Best 222.43 264.56 273.22 256.53 246.89 249.47 226.32
Average 0.426 0.412 0.402 0.416 0.422 0.426 0.434
5. Conclusion
A new optimization technique, RTLBO, is offered based on the viewpoint of the teaching–learning method & its enactment is tested by investigating with dissimilar benchmark difficulties with different features. The efficiency of RTLBO is also tested for dissimilar enactment benchmarks, i.e. best, mean solution, etc. The outcomes display the improved performance of RTLBO over additional nature-inspired optimization techniques. Also, RTLBO displays an improved performance with fewer computational determinations. This new technique can be utilized for engineering design problems and optimization applications.
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