Exploration and Analysis of Heuristics a

This study provides a comprehensive overview of various heuristics and meta-heuristics employed to address the classic Bin Packing Problem in one dimension (BPP-1D). The exploration begins with the implementation of greedy construction techniques, such as Next-Fit and First-Fit, to initialize solutions. Subsequently, local search procedures, including Hill-Climbing and Simulated Annealing, are applied. Initially, a single mapping function, either Swap(1,0) or insertion, is utilized. The approach is then enhanced by incorporating two additional mapping functions to broaden the search space. A noteworthy finding is achieved by applying a variable neighborhood, specifically swap(1,1), swap(2,1), and swap(1,0) in this order (VN-11-21-10), to an initial Next-Fit solution, yielding superior outcomes. The study further investigates the Greedy Randomized Adaptive Search Procedure with Hill Climbing as the local search. The subsequent section introduces two population-based searches: a Grouping Genetic Algorithm (GGA) and Ant Colony Optimization (ACO). Finally, the application of a variable neighborhood, VN-11-21-10, as a local search to ACO is explored. This comprehensive examination provides insights into the efficacy of these methodologies, offering a nuanced understanding of their applications in solving the BPP-1D. The results highlight the importance of considering diverse heuristic and meta-heuristic approaches for optimizing solutions in complex combinatorial problems, thereby contributing valuable knowledge to the field of optimization algorithms.