Handling Technique for Four-Bar Linkage Path Generation Using Self-Adaptive Teaching-Learning Based Optimization with a Diversity Archive”,

This article proposes an alternative constraint handling technique for the four-bar linkage path generation problem. The constraint handling technique that is traditionally applied uses an exterior penalty function, and has been found to be inefficient, particularly when dealing with constraints on the input angles. The new technique deals with both input crank rotation and Grashof's criterion. Four classical path generation problems are used to test the performance of the proposed technique. A new adaptive teaching–learning-based optimization (TLBO) scheme is used to solve several optimization problems. This technique is referred to here as teaching–learning-based optimization with a diversity archive (ATLBO-DA), and was specifically developed for this design problem. The results show that this new design concept gives better results than those of previous work, and that ATLBO-DA is superior to the original version and other metaheuristic algorithms.


Position analysis and function evaluation
Step 1 Otherwise, solving Equations (2-3) for all values of 2 and solving Equation (1) for rp at each 2.
Step 2 Compute the objective function values and constraints according to Equation Step 1 If i = 1,  i 2 = 1.

D. Algorithm 4 Procedure of ATLBO-DA
Input: maximum number of generations (nit), population size (nP) Output : x best , f best Initialization: Step 0.1 Generate np initial students {x i } and perform function evaluations {f i }.

Main procedure
Step 1 While (the termination conditions are not met) do {Teacher Phase} Step 2 Calculate the mean position of solutions {x i } written as Mavg.
Step 3 Calculate the probabilities of selecting the intervals for TRR using (18).
Step 4 For i=1 to nP Step 4.1 Perform roulette wheel selection with PTRRj.
Step 4.2 Generate Pr = rand and select a teacher.
Step 4.2.1 If Pr  TRR, set the best solution as a teacher Mbest.
Step 4.2.2 Else, if Pr > TRR, randomly select a solution in AD and set it as a teacher Mbest.
Step 4.3 Create x i new using (10 -12) and perform function evaluation.
Step 4.3.1 If x i new is better than x i , add 1 point to the j-th element of TRR_Success.
Step 4.3.2 Else, add 1 point to the j-th element of TRR_Fail.
Step 5 Replace {x i } by nP best solutions from {x i }{x i new}.
{Learning Phase} Step 6 Calculate the probabilities of selecting the intervals for LRR similar to that for TRR in step 3.
Step 7 For i=1 to nP Step 7.1 Perform roulette wheel selection with PLRRj.
Step 7.2.1 If Pr  LRR, create x i new using two-student learning and perform function evaluation.
Step 7.2.2 Else, create x i new using three-student learning and perform function evaluation.
Step 7.3.1 If x i new is better than x i , add 1 point to the j-th element of LRR_Success.
Step 7.3.2 Else, add 1 point to the j-th element of LRR_Fail.
Step 8  Step 9 Update the diversity archive with the non-dominated solutions obtained from {x i }old  {x i }new.
Step 10 End While