Optimizing F6 Function Extremes Using Dual-Chain Quantum Genetic Algorithm (DCQGA)

This paper explores the application of Dual-Chain Quantum Genetic Algorithm (DCQGA) for optimizing the F6 function's extreme values. The F6 function reaches its maximum value of 1 at coordinates (0,0). We detail DCQGA's operational mechanism, which involves quantum bit encoding using dual-chain representation, quantum rotation gate operations for population evolution, and specialized crossover techniques that maintain quantum state coherence. The algorithm implementation typically includes initialization of quantum chromosomes, fitness evaluation using the F6 function landscape, and iterative updates through quantum gates that guide the solution toward optimal regions. Furthermore, we analyze DCQGA's optimization performance characteristics and applicability scope through comprehensive numerical experiments. The validation process demonstrates DCQGA's effectiveness in handling complex optimization landscapes and its superiority over conventional genetic algorithms in convergence speed and solution quality, providing practical guidance for real-world optimization applications.