Particle Swarm Optimization (PSO) is an Evolutionary Algorithm (EA) that utilizes a swarm of particles to solve an optimization problem. Slow Intelligence System (SIS) is a learning framework which slowly learns the solution to a problem performing a series of operations. Moreover, Learning Automata (LA) are minuscule but effective decision making entities which are best suited to act as a controller component. In this paper, we combine two isolate populations of PSO to forge the Adaptive Intelligence Optimizer (AIO) which harnesses the advantages of a bi-population PSO to escape from the local minimum and avoid premature convergence. Furthermore, using the rich framework of SIS and the nifty control theory that LA derived from, we find the perfect matching between SIS and LA where acting slowly is the pillar of both of them. Both SIS and LA need time to converge to the optimal decision where this enables AIO to outperform standard PSO having an incomparable performance on evolutionary optimization benchmark functions.
Swarm Intelligence (SI) [1] brings a new breed of algorithms to the EA's community. Inspiring from the collective behavior of group of animals scavenging for food sources, the SI algorithms find their application in Artificial Intelligence (AI), Machine Learning (ML), social networks, Grid and Cloud computing and computer networks. SI is widely used for black box/white box optimization problems. Also, it is impressively useful for adjusting/adapting sensitive parameters of arbitrary data models.
The PSO [2] is a SI algorithm which is derived from the group movement of animal herds especially birds. PSO algorithm repeatedly try to guess the next feasible solution using its current information about each individual’s best position and the population’s best position heretofore. In PSO, the position of particles are updated using the velocity formula which contains the current position, personal best position of a particle and global best position of the swarm. Calculating the distance of each particle from its personal best position and global best position of the swarm, in each iteration of PSO algorithm, the particles move toward the latest optimal position of the swarm. This individual and social moves of each particle will eventually lead to finding the optimal result of the candidate problem.
A SIS [3] is a general framework that consists of a set of slow or quick decision cycles. In each decision cycle, SIS tries to search for new solutions within the problem space by applying a set of operators including enumeration, propagation, adaptation, elimination and concentration. In general, SIS is a slow learner but it gains performance over time by applying a sequence of operators to the problem space and producing the solution space.
LA [4] are autonomous machines designed for learning the optimal action within an unknown environment. LA roots in control theory where centralized or decentralized or even a mixture of both of these modes are used to study the behavior of a dynamic system with inputs and show how positive or negative feedback can modify the system’s behavior. LA has application in AI [5]- [7], ML [8], EA [9], [10], distributed systems [11], [12], and image processing [13].
The AIO is a new SI-based optimization algorithm which used two isolated populations of PSO. In AIO, we follow the TDR concept [14] of SIS to break the problem dimensions into three sub-dimensions that each of them is controlled by a learning automaton. The PSO populations share information through producing the reinforcement signal for the LA that control which population to run on the specific sub-dimension of the problem space. It also utilizes the slow and quick decision cycles of SIS to adopt the inertia weight parameter of PSO.
The rest of this paper is laid out organized as follows: In Section II, we discuss the related work including PSO, SIS, and LA. In Section III, we present the proposed optimization algorithm AIO. We present the experimental results in Section IV and we conclude the paper in Section V.
PSO [15] is an optimization algorithm inspires from the movement of flock of birds which often moves under the guidance of an individual leader bird to find nearby food. In PSO, a bird in the flock is simulated as a particle in the population. The population’s best position and particle’s best position mimic the leader bird and the best aviation position of each individual bird in terms of the provisioned food resource.
In an n dimensional space, the ith PSO’s individual is attributed as follows:
In each iteration, the Xi and Vi are updated using the following equations:
where in ( 1 ) and ( 2 ):
w is the inertia weight
The SIS [16] is a slow learner with multiple decision cycles. In each decision cycle a set of operations are applied to the existing solutions of the target problem. In a SIS Abstract Machine, these operations could be any combination of Enumeration, Propagation, Adaptation, Elimination, and Concentration operators. In each decision cycle of SIS, a predicate that is constructed from these operators is shielded by a guard operator which controls the flow of operation from computationally inexpensive decision cycles or quick decision cycles to expensive decision cycles or slow decision cycles.
Enumeration of the different available solutions until finding the optimal solution Propagation of the achieved new information from the new solutions within a body of feasible solutions.
Adaptation of the current solutions using the effective information gained from the elite solutions.
Elimination of the worst solutions that exist in the problem space.
Concentration on the elite solutions to produce new promising solutions.
An Abstract Machine for SIS in the nth decision cycle is defined as M = [P, S, C] where:
LA [17] are probabilistic decision making elements. Having a series of interactions with the environment, they adopt to the environment iteratively and learn the optimal acti
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