The research contribution focuses in the area of self-optimization of PSO based on a “to be defined” Multi Self-Adaptive Particle Swarm Optimization (MSAPSO) approach. The purpose of the new algorithm is the dynamic adaption on multiple levels at the same time.
These levels of MSAPSO are:
• Bidirectional learning strategy (social & cognition) with varying strength between the individual particle and the swarm itself
• Adaptive inertia weight strategy along different classes of benchmarks
• Dynamic detection of balanced exploration and exploitation points (optimal triples of inertia weight, social and cognition parameters)
• Use of adaptive randomization model with different probability distributions • Finding dependencies between inertia weight and social & cognition parameters
The MSAPSO behavior can vary by self-adaptive social and cognitive parameters, dynamic inertia weight and the adaptive randomization strategy of the algorithm, during the runtime. The overall intent is to accelerate the convergence speed, while keeping the diversity of the search to avoid trapping into local minima or maxima. The multi-level self- optimization approach promises to generate positive synergies on both aspects (exploration and exploitation behavior of the algorithm) at the same time.
The concept of the dissertation will fall into four parts, where the first part takes care about the definition of a bidirectional learning approach, which is dynamic in nature because the strength of this cooperation strategy depends on the individual and group success of the particles in a varying problem search space (unimodal/multimodal and combinations of it).
An analogy to this aspect is the learning within social groups where it is of course beneficial to learn from the actual best, but still the question remains open to what degree this should happen. Although an individual might be not the best as of now, it could be that in the future very good personal success is possible and because of that, the individual should not just purely believe in the actual best in the group. In addition, the question is, if there is a natural limit of bidirectional learning which makes the overall convergence optimal, independent what the optimization problem is about. Also, the question can be raised how the variation of social collaboration and cognition changes with the increase of the dimensionality of the problem.
The second part will evaluate the concept of optimal balance points between exploration and exploitation, which should be agnostic from the underlying benchmark problem, so it is fully self-adaptive. In this context, there is a need to better understand the dynamics of MSAPSO in general, the convergence behavior, the influence of the problem benchmarks dimensionality and the applied probability distributions in the algorithm as influence factors to the optimal “balance point”.
parameters influence the inertia weight parameter and vice versa and if rules can be found such that it can be applied to the overall self-adaptive model of MSAPSO.
The last aspect is the adaptive randomization during the algorithmic runtime. The idea here is that when convergence matures over time, there is decreasing need to equally distribute the particles all over the search space. The overall goal is to find very good solutions at the final convergence. So, based on this fact, there is the option to choose better fitting probability distributions to draw random numbers from, when the algorithm matures as there is better “knowledge” from the examined search space towards the end of the algorithmic runtime.
The MSAPSO algorithm does not limit itself to the four self-optimization aspects as proposed. In the future, many other aspects with regard to self-optimization might appear. If that happens, there is the question which of them contributes to the success, which are contradictory and which are synergetic to each other. Finally, this raises the question of which self-optimization strategy or combinations of it to use for a certain type of a problem surface. It is finally similar to the problem what also a human brain has to solve, which needs to decide dynamically which “algorithms” to use and also the need to dynamically parametrize the respective algorithms in order to best approach the actual faced problem scope.
„ …. that the algorithm simply has to tell what the best answer is to any given problem in one step! “4 Such algorithm surprisingly does exist in reality. For the special case of a
quadratic function, this actually works with a root finding method called Newton-Raphson, which is able to find the global optimum within one-step. As mentioned, this is a special case and of course cannot be generalized. Today, there is no known way to create one universal algorithm that can provide the “one-step” answer to complex problems. On the other side, there should be still enough room for improvement in order to shorten the time of convergence (iterative steps) while still be able to work on a broad set of problems with the “same” algorithm. When we consider the self-optimization as a way to continuously adapt to the given underlying structure of the problem, then there is a chance to reduce the iteration steps dramatically in average. To translate this into the view of a particle, the following graph describes the “ideal” convergence with regard to a hypothetical self- optimization PSO algorithm:
Figure 3: Ideal convergence behavior of a particle with self-optimization
In the graph at time point one, the different PSO variants takes a random and initial guess. In the following iterations, the two self-adaptive strategies realize improvements over the original “PSO algorithm without Self-Opt” (dark line). In iteration t PSO with “Self-Opt 2” (brighter dark line) realizes a benefit over the PSO “Self-Opt 1” strategy (brighter line). The resulting dashed black line would be the “ideal” convergence behavior of a to be defined multi self-adaptive algorithm.
On one hand, the nature of self-optimizing approaches should lead into broader applicability of the algorithm with regard to optimization problems. On the other hand, the
hybridization of different self-optimization strategies is more complex to understand with respect to their specific system and convergence behavior improvements and contributions.