1D Bin Packing Problem Dual-Algorithm Solver: Comparative Implementation of Backtracking and Cultural Algorithms

This article introduces the Bin-Packing-Solver project released by RamyAI55 on GitHub in June 2026. The project implements two methods via Python: backtracking algorithm (exact solution) and cultural algorithm (heuristic solution), and builds a graphical interface based on Tkinter to support visual comparison of the two algorithms. Originating from a course assignment for Logic and Artificial Intelligence at the British University in Egypt, the project aims to demonstrate the performance differences of different algorithms in solving the 1D bin packing problem.

The bin packing problem is a classic NP-hard combinatorial optimization problem, with the goal of packing all items into the minimum number of fixed-capacity bins. Its application scenarios are wide-ranging, including cargo loading in logistics transportation, virtual machine allocation in cloud computing, file packaging in data storage, etc. Solving this problem requires a trade-off between solution quality and computational efficiency, so comparing exact and heuristic algorithms has important practical value.

The backtracking algorithm uses a depth-first search strategy, combined with multiple optimizations: 1. Descending order sorting of items (first-fit decreasing strategy); 2. Branch pruning (prune if the current number of bins exceeds the known optimal); 3. Lower bound estimation (the ratio of remaining item volume to bin capacity as the lower bound). This algorithm guarantees a globally optimal solution, but its time complexity grows exponentially with the number of items, so it is only suitable for small-scale problems.

The cultural algorithm is based on evolutionary computation and simulates knowledge dissemination in human society. Its core components include: individuals (candidate solutions), population (set of candidate solutions), and belief space (storing knowledge from excellent individuals, such as high-frequency items and minimum filling rate). The algorithm flow is: initialize population → evaluate and select excellent individuals → update belief space → use beliefs to guide new individual generation → genetic operations (crossover, mutation) → termination. Compared to genetic algorithms, it converges to high-quality solutions faster through knowledge guidance.

The project's Tkinter GUI supports: parameter input (item size range, quantity, bin capacity), algorithm selection (run individually or simultaneously), ASCII visualization (using █ for filled space and - for empty space), and performance metrics (execution time, number of bins). Users can intuitively observe: the backtracking algorithm's solution is better but takes longer, while the cultural algorithm is faster but not globally optimal.

Practical application scenarios include logistics warehousing, cloud computing resource scheduling, ad space allocation, file packaging and compression, etc. The project's expansion directions include: optimizing algorithm performance (more advanced pruning, adaptive parameters), adding more algorithms (first-fit, simulated annealing), extending to multi-dimensional bin packing, adding constraints (item weight, mutual exclusion constraints), and migrating to a web interface.

As a teaching demonstration, this project embodies the characteristics of combining theory and practice, and modular design. For the bin packing problem, the backtracking algorithm can be chosen for small-scale scenarios to obtain optimal solutions; for large-scale practical problems, heuristic methods like the cultural algorithm are more suitable. The project's value lies in helping to understand the trade-off between exact and heuristic algorithms, providing a reference for selecting appropriate strategies for practical problems.