A Distributed Quantum Evolutionary Algorithm with a New Cycling Operator and Its Application in Fractal Image Compression

QUANTUM EVOLUTIONARY ALGORITHM (QEA) IS A NOVEL OPTIMIZATION ALGORITHM, PROPOSED FOR COMBINATORIAL PROBLEMS LIKE KNAPSACK AND TRAP PROBLEMS. WHILE FRACTAL IMAGE COMPRESSION IS IN THE CLASS OF NP-HARD PROBLEMS AND QEA IS HIGHLY SUITABLE FOR THE CLASS OF COMBINATORIAL PROBLEMS, QEA IS NOT WIDELY USED IN FRACTAL IMAGE COMPRESSION YET. IN ORDER TO IMPROVE THE PERFORMANCE OF FRACTAL IMAGE COMPRESSION ALGORITHMS, THIS PAPER PROPOSES A DISTRIBUTED QEA WITH A NOVEL OPERATOR CALLED CYCLING QUANTUM EVOLUTIONARY ALGORITHM. IN STANDARD QEA THE DIVERSITY IN THE POPULATION DECREASES ACROSS THE GENERATIONS. DECREASING THE DIVERSITY OF THE POPULATION DECREASES THE EXPLORATION PERFORMANCE OF THE ALGORITHM AND CAUSES THE ALGORITHM TRAPPING IN THE LOCAL OPTIMA. IN THE PROPOSED ALGORITHM, THERE ARE SOME SUBPOPULATIONS SEARCHING THE SEARCH SPACE. AFTER THE SUBPOPULATIONS ARE TRAPPED IN A LOCAL OPTIMUM, THE BEST OBSERVED POSSIBLE SOLUTIONS IN THE SUBPOPULATIONS ARE EXCHANGED IN A CYCLIC MANNER. THE PROPOSED ALGORITHM IS USED IN FRACTAL IMAGE COMPRESSION AND EXPERIMENTAL RESULTS ON SEVERAL IMAGES SHOW BETTER PERFORMANCE FOR THE PROPOSED ALGORITHM THAN GENETIC ALGORITHMS AND QEA. IN COMPARISON WITH CONVENTIONAL FRACTAL IMAGE COMPRESSION, THE PROPOSED ALGORITHM FINDS A SUITABLE SOLUTION WITH MUCH LESS COMPUTATIONAL COMPLEXITY