Studying Nature-based Algorithms for Solving Single and Multi-objective Optimization Problems

Research Abstract

Meta-heuristic optimization techniques have become very popular over the last two decades. Surprisingly, some of them such as Genetic Algorithm (GA), Ant Colony Optimization (ACO), and Particle Swarm Optimization (PSO) are fairly well-known among not only computer scientists but also scientists from different fields. In addition to the huge number of theoretical works, such optimization techniques have been applied in various fields of study. The last two decades witnessed fast evolution in the optimization field, and many new meta-heuristic algorithms have been developed, this evolution is related to the No Free Lunch (NFL) theorem, which states that if a meta-heuristic algorithm performs well on a set of optimization problems, there are some other optimization problems this meta-heuristic algorithm, will not perform well, which conclude that a specific optimization problem can be solved well with some meta-heuristic algorithms than others. Therefore, we used a set of meta-heuristic algorithms which, provides a better opportunity to obtain overall best optimal parameters that maximize cloning fidelity. Firstly; The Adaptive Guided Differential Evolution (AGDE) optimization algorithm employed to improve the fidelity of quantum cloning problem and the obtained parameter values minimize the cloning difference error value down to 10−8. Quantum cloning operation, started with no-go theorem which proved that there is no capability to perform a cloning operation on an unknown quantum state, however, a number of trials proved that we can make approximate quantum state cloning that is still with some errors. To the best of our knowledge, our employed method consider the first of its kind to attempt using meta-heuristic algorithm such as Adaptive Guided Differential Evolution (AGDE), to tackle the problem of quantum cloning circuit parameters to enhance the cloning fidelity. To investigate the effectiveness of the AGDE, the extensive experiments have demonstrated that the AGDE can achieve outstanding performance compared to other well-known meta-heuristics including; Enhanced LSHADE-SPACMA Algorithm (ELSHADE-SPACMA), Enhanced Differential Evolution algorithm with novel control parameter adaptation (PaDE), Improved Multi-operator Differential Evolution Algorithm (IMODE), Parameters with adaptive learning mechanism (PALM), QUasi-Affine TRansformation Evolutionary algorithm (QUATRE), Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), Cuckoo Search (CS), Bat-inspired Algorithm (BA), Grey Wolf Optimizer (GWO), and Whale Optimization Algorithm (WOA). Accordingly, the qualitative and quantitative measurements including average, standard deviation, convergence curves of the competitive algorithms over 30 independent runs, proved the superiority of AGDE to enhance the cloning fidelity. Secondly; A hybrid algorithm of SMA with Adaptive Guided Differential Evolution Algorithm (AGDE) (SMA-AGDE) to cope with the original SMA’s inherent weaknesses. The AGDE mutation method is employed to enhance the swarm agents’ local search, increase the population’s diversity, and help avoid premature convergence problem. Similar to other original metaheuristic algorithms (MAs), SMA may suffer from drawbacks, such as being trapped in minimum local regions and improper balance between exploitation and exploration phases. The SMA-AGDE’s performance is evaluated on the CEC’17 test suite, three engineering design problems include tension/compression spring, pressure vessel and rolling element bearing; additionally, a two combinatorial optimization problems include bin packing and quadratic assignment. The SMA-AGDE is compared with three categories of optimization methods: 1) the well-studied MAs, i.e., BiogeographyBased Optimizer (BBO), Gravitational Search Algorithm (GSA) and Teaching Learning-Based Optimization (TLBO); 2) recently developed MAs, i.e., Harris Hawks Optimization (HHO), Manta Ray Foraging optimization (MRFO), and the original SMA; 3) high-performance MAs and among the best of IEEE CEC competition, i.e., Evolution Strategy with Covariance Matrix Adaptation (CMA-ES), and AGDE. The overall simulation results revealed that the SMA-AGDE ranked first among the compared algorithms, and so over different function landscapes. Thus, the proposed SMA-AGDE is a promising optimization tool for global, combinatorial, and engineering optimization problems

Research Keywords

Studying Nature-based Algorithms for Solving Single and Multi-objective Optimization Problems