Most real-world optimization problems often come with multiple global optima or local optima. Therefore, increasing niching metaheuristic algorithms, which devote to finding multiple optima in a single run, are developed to solve these multimodal optimization problems. However, there are two difficulties urgently to be solved for most existing niching metaheuristic algorithms: how to set the niching parameter values for different optimization problems and how to jump out of the local optima efficiently. These two difficulties limit their practicality largely. Based on Whale Swarm Algorithm (WSA) we proposed previously, this paper presents a new multimodal optimizer named WSA with Iterative Counter (WSA-IC) to address these two difficulties. On the one hand, WSA-IC improves the iteration rule of the original WSA for multimodal optimization, which removes the need of specifying different values of attenuation coefficient for different problems to form multiple subpopulations, without introducing any niching parameter. On the other hand, WSA-IC enables the identification of extreme points during the iterations relying on two new parameters (i.e., stability threshold (T_ s ) and fitness threshold (T_ f )), to jump out of the located extreme points. Moreover, the convergence of WSA-IC is proved. Finally, the proposed WSA-IC is compared with several niching metaheuristic algorithms on CEC2015 niching benchmark test functions and on five additional high-dimensional multimodal functions. The experimental results demonstrate that WSA-IC statistically outperforms other niching metaheuristic algorithms on most test functions.
The History based topological speciation (HTS) was proposed by Li and Tang @cite_1 to incorporate into the CDE with species conservation technique for multimodal optimization. HTS is a parameter-free speciation method, which captures the landscape topography relying exclusively on search history, which avoids the additional sampling and function evaluations associated with existing topology based methods. Therefore, HTS is a parameter-free speciation method. The experimental results showed that HTS performs better than existing topology-based methods when the function evaluation budget is limited.
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Evolutionary algorithms integrating various niching techniques have been widely used to find multiple optima of an optimization problem. In recent years, an increasing amount of research has been focused on the design and application of speciation-based niching techniques. These techniques rely on speciation to partition a population into subpopulations (species) such that each occupies a different region of attraction (niche) on the fitness landscape. Existing speciation methods are either distance-based or topology-based. Topology-based methods are more flexible and have fewer assumptions than distance-based methods. However, existing topology-based methods all require sampling and evaluating new individuals in order to capture the landscape topography. This incurs additional fitness evaluations (FEs), which is a drawback, especially when the FE budget is limited. In this paper, a new topology-based speciation method named history-based topological speciation (HTS) is proposed. It relies exclusively on search history to capture the landscape topography and, therefore, does not require any additional FEs to be performed. To the best of our knowledge, HTS is the only parameter-free speciation method at the moment. Both theoretical and empirical analyses have been conducted. Theoretical analysis shows that HTS incurs acceptable computational overhead. In the experimental study, HTS outperformed existing topology-based methods on benchmark functions in up to 32-D space and with as many as 50 optima, and the time overhead was practically negligible if a single FE took seconds. In this paper differential evolution is extended by using the notion of speciation for solving multimodal optimization problems. The proposed species-based DE (SDE) is able to locate multiple global optima simultaneously through adaptive formation of multiple species (or subpopulations) in an DE population at each iteration step. Each species functions as an DE by itself. Successive local improvements through species formation can eventually transform into global improvements in identifying multiple global optima. In this study the performance of SDE is compared with another recently proposed DE variant CrowdingDE. The computational complexity of SDE, the effect of population size and species radius on SDE are investigated. SDE is found to be more computationally efficient than CrowdingDE over a number of benchmark multimodal test functions. This work proposes a process for efficiently searching over combinations of individual object 6D pose hypotheses in cluttered scenes, especially in cases involving occlusions and objects resting on each other. The initial set of candidate object poses is generated from state-of-the-art object detection and global point cloud registration techniques. The best-scored pose per object by using these techniques may not be accurate due to overlaps and occlusions. Nevertheless, experimental indications provided in this work show that object poses with lower ranks may be closer to the real poses than ones with high ranks according to registration techniques. This motivates a global optimization process for improving these poses by taking into account scene-level physical interactions between objects. It also implies that the Cartesian product of candidate poses for interacting objects must be searched so as to identify the best scene-level hypothesis. To perform the search efficiently, the candidate poses for each object are clustered so as to reduce their number but still keep a sufficient diversity. Then, searching over the combinations of candidate object poses is performed through a Monte Carlo Tree Search (MCTS) process that uses the similarity between the observed depth image of the scene and a rendering of the scene given the hypothesized pose as a score that guides the search procedure. MCTS handles in a principled way the tradeoff between fine-tuning the most promising poses and exploring new ones, by using the Upper Confidence Bound (UCB) technique. Experimental results indicate that this process is able to quickly identify in cluttered scenes physically-consistent object poses that are significantly closer to ground truth compared to poses found by point cloud registration methods. The recently introduced Multi-dimensional Archive of Phenotypic Elites (MAP-Elites) is an evolutionary algorithm capable of producing a large archive of diverse, high-performing solutions in a single run. It works by discretizing a continuous feature space into unique regions according to the desired discretization per dimension. While simple, this algorithm has a main drawback: it cannot scale to high-dimensional feature spaces since the number of regions increase exponentially with the number of dimensions. In this paper, we address this limitation by introducing a simple extension of MAP-Elites that has a constant, pre-defined number of regions irrespective of the dimensionality of the feature space. Our main insight is that methods from computational geometry could partition a high-dimensional space into well-spread geometric regions. In particular, our algorithm uses a centroidal Voronoi tessellation (CVT) to divide the feature space into a desired number of regions; it then places every generated individual in its closest region, replacing a less fit one if the region is already occupied. We demonstrate the effectiveness of the new "CVT-MAP-Elites" algorithm in high-dimensional feature spaces through comparisons against MAP-Elites in a hexapod locomotion task.