Adaptive and Intelligent Swarms for Solving Complex Optimization Problems
Mukesh Kumar Khandelwal and Neetu Sharma
Particle Swarm Optimization (PSO) algorithms work beautifully with unimodal optimization problems but often get trapped in local optima, particularly in multi-modal problems. Due to the stagnation, premature convergence also takes place. Moreover, each swarm uses the same strategy for updating its velocity and position vector which is definitely not effective in solving different kinds of problems. This paper implements multiple movement strategies to speed up the convergence rate in unimodal problems and handles the stagnation problem by introducing a new variant of PSO named adaptive intelligence Particle Swarm Optimization (AI-PSO).
In the classical PSO algorithm, each particle updates its velocity by checking the positions of the best particles, which were received from the group and its historical data. Further, this updated velocity is used to calculate the new position of each particle. This process has been repeated for several iterations until the swarm reaches the optimal solution. Unlike PSO, in which particles’ movement was fixed and was dependent on its interaction with other swarms, AI-PSO changes its movement strategy by collecting information from the current environment.
We tried to improve the convergence of PSO by preventing it from sticking to local optima and by adding free movement towards the optimal solution when it is close to the optimum solution by defining the multiple strategies for activities in different situations. Particles that are moving in the wrong direction or start stagnating, i.e., their personal best do not improve for a fixed number of iterations, are directed towards new potential regions by defining a new movement strategy. AI-PSO algorithm has been created by improving the adaptability and intelligence of swarms in determining the path for the movement. A counter known as intelligence level is created and updated according to the action taken by the swarm. This counter variable defines the swarm’s intelligence level and guides its movement in unavoidable conditions. When the value of the counter goes minimum, the swarm assumes that it got stuck in local optima and needs to change the movement strategy.
Similarly, if the counter reaches the max value, the swarm gains sufficient information to move freely toward the best solutions. The movement strategy is updated by checking the pbest of two consecutive iterations. If the pbest of the swarm is changing in every generation, we can conclude that the swarm is improving. In such a case, the intelligence level of the swarm is increased by one, and we wait for a few generations until the counter reaches the max value. When the counter reaches the maximum value, a new movement strategy is defined to allow the swarm to move freely to improve the convergence rate. The performance of the new variant AI-PSO is established by comparing it with other versions of PSO over 24 benchmark functions provided by Black-Box Optimization Benchmarking (BBOB 2013). Results show that the proposed variant performs better than different peer algorithms.
Keywords: Adaptive, intelligent, PSO, stagnation, local optima, premature convergence