Luus-Jaakola Optimization Procedure for Ramsey Number Lower Bounds

Ramsey numbers have been widely studied for decades, but the exact values for all but a handful are still unknown. In recent years, optimization algorithms have proven useful in calculating lower bounds for certain Ramsey numbers. In this paper, we define an optimization algorithm based on the Luus-Jaakola procedure to calculate Ramsey number lower bounds. We demonstrate the effectiveness of the algorithm for that task, show the effect of parameter selection and determine optimal parameters for the algorithm, and provide results from the implementation of the algorithm.