Article Preview
Top1. Introduction
The goal of a global optimization problem is to optimize an objective function F(x), where x is defined to be the best solution within a solution set X of all feasible solutions. Nature inspired meta-heuristic algorithms are often based on very simple concepts and hence their implementation to solve complex optimization problems is comparatively easier than classical optimization techniques. Obtaining the gradient information of the search space is not a prerequisite with these algorithms leading to their successful application in diverse real-world optimization problems. Swarm based meta-heuristic algorithms in general, loosely mimics the social behaviour of the groups of animals or birds present in the nature, e.g., Particle Swarm Optimization (PSO) (Kennedy & Eberhart, 1995), Cuckoo Search (CS) (Yang & Deb, 2009), Ant Colony Optimization (ACO) (Dorigo et al., 2006), Artificial Bee Colony (ABC) (Karaboga & Basturk, 2007), Whale Optimization Algorithm (WOA) (Mirjalili & Lewis, 2016), Grey Wolf Optimizer (GWO) (Mirjalili et al., 2014) and many more. The particles or search agents in these algorithms can share the information among themselves during the optimization process and hence can reach to the optimum or near-optimum results. These algorithms have been used in a plethora of scientific and engineering problems including image processing with deep neural networks (Bhattacharya et al, 2021).
Among all the algorithms mentioned above, the particle swarm optimization (PSO) algorithm is undoubtedly the most thoroughly researched technique for metaheuristic optimization. PSO and many of its variants are based on birds’ flocking behaviour and are used in several real-world constrained and unconstrained optimization problems. Meta-heuristic algorithms are stochastic in nature and the optimization process can be divided into two phases: exploration and exploitation. Exploration phase is the beginning stage of the optimization process in which the algorithm explores the search space for all possible solutions. This is followed by the exploitation phase which evaluates the quality of these solutions. Despite several advantages, PSO often suffer from premature convergence, i.e., trapping in a local optimum, due to an imbalance between the exploration and exploitation phases (Alba & Dorronsoro, 2005). Several methods have been proposed in the literature to overcome the stagnation problem, for example, Multi-start Particle Swarm Optimizer (MSPSO) (Kaucic, 2013), Multi-phase PSO (MPPSO) (Al-Kazemi, 2002), perturbed PSO (PPSO) (Xinchao, 2010) or binary PSO (BPSO) (Khanesar et al., 2007). New approaches have been incorporated in the standard PSO for hybridization, for example, with sine cosine algorithm and levy flight approach (Chegini, Bagheri & Najafi, 2018), Genetic algorithm (Garg, 2016), Whale Optimization Algorithm (WOA) (Trivedi et al., 2018), Grey Wolf Optimizer (Senel et al., 2019) etc.
In this study we have incorporated a spiral updating mechanism inspired from the search pattern of Whale optimization algorithm (WOA) in the standard PSO to allow more freedom in the particle movement and to reduce the chances of stagnation at local minima. Other than incorporating a randomization condition in the exploration/exploitation phase, the Spiral-PSO does not add any increased number of function evaluation in the standard PSO, keeping the computation time unchanged as described in Section 2. The modified algorithm is then tested on 23 standard benchmark functions as reported in Section 3. In Section 4 and 5, the performance of the proposed Spiral-PSO algorithm is tested for multimodal satellite image registration and the results are compared with the standard PSO. Section 6 presents the conclusion and the future directions of work.