In dealing with constrained multi-objective optimization problems (CMOPs), a key issue of multi-objective evolutionary algorithms (MOEAs) is to balance the convergence and diversity of working populations.
The push and pull search (PPS) framework was introduced by @cite_15 . Unlike other constraint handling mechanisms, the search process of PPS is divided into two different stages: the push search and the pull search, and follows a procedure of "push first and pull second", by which the working population is pushed toward the unconstrained PF without considering any constraints in the push stage, and a constraint handling mechanism is used to pull the working population to the constrained PF in the pull stage.
@cite_15
2963115819 2963649943 2561500936 2200550062
Abstract This paper proposes a push and pull search (PPS) framework for solving constrained multi-objective optimization problems (CMOPs). To be more specific, the proposed PPS divides the search process into two different stages: push and pull search stages. In the push stage, a multi-objective evolutionary algorithm (MOEA) is used to explore the search space without considering any constraints, which can help to get across infeasible regions very quickly and to approach the unconstrained Pareto front. Furthermore, the landscape of CMOPs with constraints can be probed and estimated in the push stage, which can be utilized to conduct the parameter setting for the constraint-handling approaches to be applied in the pull stage. Then, a modified form of a constrained multi-objective evolutionary algorithm (CMOEA), with improved epsilon constraint-handling, is applied to pull the infeasible individuals achieved in the push stage to the feasible and non-dominated regions. To evaluate the performance regarding convergence and diversity, a set of benchmark CMOPs and a real-world optimization problem are used to test the proposed PPS (PPS-MOEA D) and state-of-the-art CMOEAs, including MOEA D-IEpsilon, MOEA D-Epsilon, MOEA D-CDP, MOEA D-SR, C-MOEA D and NSGA-II-CDP. The comprehensive experimental results show that the proposed PPS-MOEA D achieves significantly better performance than the other six CMOEAs on most of the tested problems, which indicates the superiority of the proposed PPS method for solving CMOPs. This paper considers the problem of distributed optimization over time-varying graphs. For the case of undirected graphs, we introduce a distributed algorithm, referred to as DIGing, based on a combination of a distributed inexact gradient method and a gradient tracking technique. The DIGing algorithm uses doubly stochastic mixing matrices and employs fixed step-sizes and, yet, drives all the agents' iterates to a global and consensual minimizer. When the graphs are directed, in which case the implementation of doubly stochastic mixing matrices is unrealistic, we construct an algorithm that incorporates the push-sum protocol into the DIGing structure, thus obtaining the Push-DIGing algorithm. Push-DIGing uses column stochastic matrices and fixed step-sizes, but it still converges to a global and consensual minimizer. Under the strong convexity assumption, we prove that the algorithms converge at R-linear (geometric) rates as long as the step-sizes do not exceed some upper bounds. We establish explicit est... We describe a simple push-pull optimization (PPO) algorithm for blue-noise sampling by enforcing spatial constraints on given point sets. Constraints can be a minimum distance between samples, a maximum distance between an arbitrary point and the nearest sample, and a maximum deviation of a sample's capacity (area of Voronoi cell) from the mean capacity. All of these constraints are based on the topology emerging from Delaunay triangulation, and they can be combined for improved sampling quality and efficiency. In addition, our algorithm offers flexibility for trading-off between different targets, such as noise and aliasing. We present several applications of the proposed algorithm, including anti-aliasing, stippling, and non-obtuse remeshing. Our experimental results illustrate the efficiency and the robustness of the proposed approach. Moreover, we demonstrate that our remeshing quality is superior to the current state-of-the-art approaches. There has been an increased growth in a number of applications that naturally generate large volumes of uncertain data. By the advent of such applications, the support of advanced analysis queries such as the skyline and its variant operators for big uncertain data has become important. In this paper, we propose the effective parallel algorithms using MapReduce to process the probabilistic skyline queries for uncertain data modeled by both discrete and continuous models. We present three filtering methods to identify probabilistic non-skyline objects in advance. We next develop a single MapReduce phase algorithm PS-QP-MR by utilizing space partitioning based on a variant of quadtrees to distribute the instances of objects effectively and the enhanced algorithm PS-QPF-MR by applying the three filtering methods additionally. We also propose the workload balancing technique to balance the workload of reduce functions based on the number of machines available. Finally, we present the brute-force algorithms PS-BR-MR and PS-BRF-MR with partitioning randomly and applying the filtering methods. In our experiments, we demonstrate the efficiency and scalability of PS-QPF-MR compared to the other algorithms.