Saja Ayad - Department of Mathematics, University of Baghdad, Baghdad ۰۰۹۶۴, Iraq
Iraq Abass - Department of Mathematics, University of Baghdad, Baghdad ۰۰۹۶۴, Iraq

Despite the fact that algorithmic strategies for dealing with Combinatorial Optimization (CO) have been available for a long time, the further application of Evolutionary Algorithms (EAs) to such problems provides a vehicle for dealing with MOPs of tremendous scope.  BAT Algorithm with Many Objectives several BAT algorithms based on R۲ Distance (MaBAT/R۲) are described, which blend the predominance notion with the R۲ marker technique. While the R۲ Indicator simplifies the multi-objective problem (MOP) by rewriting it as a series of Tchebycheff Approach problems, since this leader decision making uses the Tchebycheff Approach as a criterion, tackling these issues at the same time inside the BAT framework may lead to early converging. Predominance is important in constructing the leader's collection because it allows the chosen leaders to encompass fewer dense regions, avoiding local optima and producing a more diverse approximated Pareto front. ۹ non-linear standard functions yielded this result. MaBAT/R۲ appears to be more efficient than MOEAD, NSGAII, MPSOD, and SPEA۲. MATLAB was used to generate all of the findings (R۲۰۲۰b).