Particle swarm optimization (PSO) has been shown as an effective tool for solving global optimization problems. So far, most PSO algorithms use a single learning pattern for all particles, which means that all particles in a swarm use the same strategy. This monotonic learning pattern may cause the lack of intelligence for a particular particle, which makes it unable to deal with different complex situations. This paper presents a novel algorithm, called self-learning particle swarm optimizer (SLPSO), for global optimization problems. In SLPSO, each particle has a set of four strategies to cope with different situations in the search space. The cooperation of the four strategies is implemented by an adaptive learning framework at the individual level, which can enable a particle to choose the optimal strategy according to its own local fitness landscape. The experimental study on a set of 45 test functions and two real-world problems show that SLPSO has a superior performance in comparison with several other peer algorithms.

Many real-world dynamic problems have constraints, and in certain cases not only the objective function changes over time, but also the constraints. However, there is no research in answering the question of whether current algorithms work well on continuous dynamic constrained optimization problems (DCOPs), nor is there any benchmark problem that reflects the common characteristics of continuous DCOPs. This paper contributes to the task of closing this gap. We will present some investigations on the characteristics that might make DCOPs difficult to solve by some existing dynamic optimization (DO) and constraint handling (CH) algorithms. We will then introduce a set of benchmark problems with these characteristics and test several representative DO and CH strategies on these problems. The results confirm that DCOPs do have special characteristics that can significantly affect algorithm performance. The results also reveal some interesting observations where the presence or combination of different types of dynamics and constraints can make the problems easier to solve for certain types of algorithms. Based on the analyses of the results, a list of potential requirements that an algorithm should meet to solve DCOPs effectively will be proposed.

Multipopulation methods are effective in solving dynamic optimization problems. However, to efficiently track multiple optima, algorithm designers need to address a key issue: how to adapt the number of populations. In this paper, an adaptive multipopulation framework is proposed to address this issue. A database is designed to collect heuristic information of algorithm behavior changes. The number of populations is adjusted according to statistical information related to the current evolving status in the database and a heuristic value. Several other techniques are also introduced, including a heuristic clustering method, a population exclusion scheme, a population hibernation scheme, two movement schemes, and a peak hiding method. The particle swarm optimization and differential evolution algorithms are implemented into the framework, respectively. A set of multipopulation-based algorithms are chosen to compare with the proposed algorithms on the moving peaks benchmark using four different performance measures. The effect of the components of the framework is also investigated based on a set of multimodal problems in static environments. Experimental results show that the proposed algorithms outperform the other algorithms in most scenarios.

Scalability is a crucial aspect of designing efficient algorithms. Despite their prevalence, large-scale dynamic optimization problems are not well studied in the literature. This paper is concerned with designing benchmarks and frameworks for the study of large-scale dynamic optimization problems. We start by a formal analysis of the moving peaks benchmark (MPB) and show its nonseparable nature irrespective of its number of peaks. We then propose a composite MPB suite with exploitable modularity covering a wide range of scalable partially separable functions suitable for the study of large-scale dynamic optimization problems. The benchmark exhibits modularity, heterogeneity, and imbalance features to resemble real-world problems. To deal with the intricacies of large-scale dynamic optimization problems, we propose a decomposition-based coevolutionary framework which breaks a large-scale dynamic optimization problem into a set of lower-dimensional components. A novel aspect of the framework is its efficient bi-level resource allocation mechanism which controls the budget assignment to components and the populations responsible for tracking multiple moving optima. Based on a comprehensive empirical study on a wide range of large-scale dynamic optimization problems with up to 200-D, we show the crucial role of problem decomposition and resource allocation in dealing with these problems. The experimental results clearly show the superiority of the proposed framework over three other approaches in solving large-scale dynamic optimization problems.