## 1 Introduction
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Study** & **Research Focus** & **Method** & **Key Contributions** \\ \hline \multirow{3}{*}{Multi-Objective Evolutionary Algorithms [11; 12; 13; 18]} & \multirow{3}{*}{Solving Bi-Objective TTP using evolutionary algorithms} & Establishes new benchmarks, demonstrates robust performance, and improves Pareto set & \multirow{3}{*}{ \begin{tabular}{c} Databases and improves Pareto set \\ approximations \\ \end{tabular}  } \\  & & & \\ \hline \multirow{3}{*}{Dynamic Programming and Hybrid Approaches [12; 16; 19]} & \multirow{3}{*}{ \begin{tabular}{c} Integrating dynamic \\ programming within evolutionary \\ algorithms for TTP \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} Combines exact and approximate \\ algorithms, leveraging DP for \\ packing problems \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} Outperforms state-of-the-art \\ results and enhances solution \\ quality in large instances \\ \end{tabular}  } \\  & & & \\ \hline \multirow{3}{*}{Adaptive and Specialized Algorithms [11; 13; 20]} & \multirow{3}{*}{ \begin{tabular}{c} Dynamic multi-objective \\ optimization of TTP \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} Combination of dynamic \\ programming and evolutionary \\ algorithms \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} Improves algorithm performance, \\ particularly in specialized and \\ adaptive contexts \\ \end{tabular}  } \\  & & & \\ \hline \multirow{3}{*}{Metaheuristic and Weighted-Sum Methods [14; 15]} & \multirow{3}{*}{ \begin{tabular}{c} Utilizing metaheuristic \\ approaches like VNS and \\ weighted-sum methods \\ \end{tabular}  } & \multirow{3}{*}{\ \begin{tabular}{c} Includes randomized heuristics \\ and Variable Neighbourhood \\ Search \\ \end{tabular}  } & \multirow{3}{*}{ \begin{tabular}{c} Provides competitive \\ performance, improves \\ best-known solutions in \\ competitions \\ \end{tabular}  } \\ \cline{1-1} \cline{3-3} \cline{5-5}  & Ant Colony Optimization and & & \\ \cline{1-1} \cline{3-3} \cline{5-5}  & & & \\ \cline{1-1} \cline{3-3} \cline{5-5} ICA References [16; 17; 21] & & \\ \cline{1-1} \cline{3-3} \cline{5-5 This paper introduces a novel heuristic multi-objective optimization algorithm for solving BITTP, leveraging the Five-element Cycle Optimization algorithm (FECO). FECO, grounded in the Five-element Cycle Model (FECM), has effectively addressed combinatorial optimization problems [22]. Building upon this framework, we devise a fresh individual evaluation criterion and integrate it with FECO's distinctive optimization mechanism to formulate an innovative individual update strategy. This strategy aims to harmonize global exploration and local exploitation, enhancing search capabilities and facilitating more effective solutions to BITTP. The remaining sections of the paper are organized as follows: Section 2 provides a comprehensive explanation of BITTP and FECO. The methodology for solving BITTP using the proposed algorithm is delineated in Section 3. Section 4 introduces the experimental conditions, including the experimental operating environment, benchmark problems, and algorithm performance metrics. Section 5 details the algorithm's parameter settings, experimental results, and analysis. Finally, Section 6 offers concluding remarks and outlines avenues for future research.