hybrid algorithm

Graph coloring is a crucial area of research in graph theory, with numerous algorithms proposed for various types of graph coloring, particularly graph p-distance coloring‎. In this study, we employ a recently introduced graph coloring algorithm to develop a hybrid algorithm approximating the chromatic number ‎p-distance, where $p$ represents a positive integer number. We apply our algorithm to molecular graphs as practical applications of our findings.

This paper develops an efficient non-dominated sorting genetic algorithm (NSGA-II) to solve the redundancy allocation problem (RAP) of series-parallel systems. The system consists of subsystem in series, where components are used in parallel for each subsystem. Both the system and its subsystems can only take two states of complete perfect and complete failure. Identical redundant components are included to achieve a desirable reliability. The components of each subsystem, which are chosen from a list that is available in the market, are characterized by their cost, weight, and reliability. To find the optimum combination of the number of components for each subsystem, the mathematical formulation for the maximal reliability and minimal cost of the system configuration under cost constraint is first obtained. Then, a modified NSGA-II is proposed to solve the model. In this algorithm, a heuristic method of generating a primary solution is integrated to achieve better solutions. Moreover, design of experiment approach is employed to calibrate the parameters of the algorithm. At the end, some numerical examples are used to validate the solution, to assess the performance of the proposed methodology under different configurations, and to compare the performance with the ones of two other meta-heuristic algorithms. The results of experiments are generally in favor of the proposed solution algorithm.

Particle swarm optimization (PSO) is one of the practical metaheuristic algorithms which is applied for numerical global optimization‎. ‎It benefits from the nature inspired swarm intelligence‎, ‎but it suffers from a local optima problem‎. ‎Recently‎, ‎another nature inspired metaheuristic called Symbiotic Organisms Search (SOS) is proposed‎, ‎which doesn't have any parameters to set at start‎. ‎In this paper‎, ‎the PSO and SOS algorithms are combined to produce a new hybrid metaheuristic algorithm for the global optimization problem‎, ‎called PSOS‎. ‎In this algorithm‎, ‎a minimum number of the parameters are applied which prevent the trapping in local solutions and increase the success rate‎, ‎and also the SOS interaction phases are modified‎. ‎The proposed algorithm consists of the PSO and the SOS phases‎. ‎The PSO phase gets the experiences for each appropriate solution and checks the neighbors for a better solution‎, ‎and the SOS phase benefits from the gained experiences and performs symbiotic interaction update phases‎. ‎Extensive experimental results showed that the PSOS outperforms both the PSO and SOS algorithms in terms of the convergence and success ‎rates.‎

Let a graph G = (V;E) be given. In the path center problem we want to find a path P in G such that the maximum weighted distance of P to every vertex in V is minimized. In this paper a genetic algorithm and a hybrid of genetic and ant colony algorithms are presented for the path center problem. Some test problems are examined to compare the algorithms. The results show that for almost all examples the hybrid method results better solutions than genetic algorithm.