Solving 0-1 knapsack and bin packing problem using Logical Social Group Optimization

The 0-1 Knapsack Problem (KP) and Bin Packing Problem (BPP) are NP-hard combinatorial optimization challenges often tackled using metaheuristics. Both problems have prominent utilization in the real world such as in resource allocation, logistics, decision-making, etc. The binarized variant of metaheuristics available in the literature mostly uses transfer functions for conversion of the domain from continuous to binary. Generally, the conversion functions are computationally expensive which demands more utilization of computational resources. Whereas the boolean functions are performed using bitwise operations which are inherent to the digital computer hardware and are less computationally expensive. This prominent research gap has been addressed in this paper by introducing Logical Social Group Optimization (LSGO), a logic-based binarized variant of Social Group Optimization (SGO) that leverages Boolean logic for improved efficiency. In LSGO, after the binarization by replacing the arithmetic operators with logical operators, one of the variables gets cancelled out. To preserve that variable, two versions of LSGO have been proposed. The first one is LSGO-Reduc where one of the initial operands in the equation is removed or reduced and after reducing it, no variables disappear. The second one is LSGO-Rever, where the boolean operators in the equation are reversed or exchanged and hence, no variables are lost. The three algorithms have been simulated with various datasets of knapsack and its variant problems and bin-packing problem for thorough testing on different problem types and scalability. Experimental results demonstrate that LSGO variants outperform conventional algorithms, achieving an average profit of 970 units on the P07 dataset for single knapsack problems, surpassing SGO (950 units) and Genetic Algorithm (GA) (930 units) with greater stability. In multiple knapsack problems, LSGO variants reach a profit of 1925 units, exceeding Particle Swarm Optimization (PSO) (1850 units). For bin packing problems, the binary splitting strategy optimally minimizes bin usage, achieving 5 bins on the P04 dataset, while maintaining solution quality. Unlike conventional methods that rely on transfer functions to solve binary problems, LSGO employs logical operators instead of arithmetic ones, eliminating the need for external functions. This approach significantly reduces computational overhead and offers potential improvements in large-scale instances. LSGO-Rever outperforms LSGO and LSGO-Reduc for most computationally complex problems. The results highlight the effectiveness of LSGO in enhancing solution quality, stability, scalability, and efficiency for discrete optimization problems where Knapsack has been taken as a case study in this paper. Moreover, the practical application of the proposed algorithm for simulation of path finding robots has been discussed to shed some light on the applicability of the algorithm. The results have been validated with ranking algorithm, Nemenyei post hoc statistical test and friedman chi square test which shows promising results with adequate graphs and tables derived from the simulations.