## 3 Methods  
The optimization algorithm proposed in this article is a hybrid of the ABC and Pareto-based approaches. This section presents a brief description of the hybridization process of the ABC algorithm with the Pareto-based approach. The main reason behind the high suitability of the ABC algorithm for this work is its good performance for difficult optimization problems, which is achieved via effective search mechanisms in a single cycle and easily implementable bee phases [33]. As noted above, the problem considered here involves a multi-objective function that requires a collection of a nondominated set of optimal values, and the Pareto approach is the most suitable approach for comparing such optimal values. This method also solves the problems of a lack of use of secondary information, the high number of objective function evaluations, and slowness during sequential processing that beset the classic ABC algorithm. The ABC algorithm modification with the Pareto approach proposed herein is a meta-heuristics application involving temporal memory, where the original answer is memorized, and unique or different optimal solutions are then found. The Pareto optimal solution set is a group of Pareto optimal solutions to the given problems that are nondominated compared with all solutions in the search space, as shown in Figure 1. Here, the optimal values obtained by the algorithm are represented by the solutions in the Pareto-optimal set. The meta-heuristic approach shown in the flowchart of Figure 2 illustrates the procedure for obtaining accurate results using the proposed hybrid ABC algorithm with the Pareto approach. Figure 1: Illustration of the Pareto-optimal set of the Pareto-based approach. The algorithm consists of seven main processes: problem formulation encoding, initialization, box arrangement using the BLF algorithm and the wall-building approach, implementation of the ABC operators, calculation of the nectar amount, roulette wheel selection, and Pareto optimal front checking. The ABC operators consist of swaps, rotations, insertions, crossovers, and mutations, through which the algorithm finds the optimal values in the local search area. These processes are described in Table 3.  
Note that, for the roulette wheel selection step, an answer is randomly selected from the answer set. The answer is then refined as the onlooker bees randomly choose a value between 0 and 1 and select the answer from Equation (3), as shown in Figure 3. Subsequently, the solutions obtained via the Pareto-based approach are compared, and the fitness values are collected [34]. Figure 2: Flowchart of proposed ABC algorithm with Pareto-based approach. Most meta-heuristic algorithms were originally proposed for solving continuous optimization problems. To solve combinatorial problems such as the container-loading problem, a solution representation is required to transform the dimension values of each box into a practical utilization solution. In this research, a solution representation with encoding and decoding schemes was developed for loading the boxes into a single container to minimize the empty space and maximize profit. The steps in the proposed heuristic filling procedure are presented in Table 4.  
In the proposed heuristic filling procedure for the solution of the SCLP, the input data include coordinate points and the dimensions of boxes and containers. The calculation step is identified based on the number of boxes, and the priority is calculated by grouping boxes of similar sizes together. The next step is to check the available space inside a container for a new layer. This is the process of checking the possibility of packing the selected boxes into the current layer. The most important step is to update the container layer regarding empty space and update the remaining box dataset to calculate the container utilization and profit margin. In the last step, the nondominated set of Pareto solutions is checked. Figure 3: Roulette wheel selection method.