Continuous Distributed Constraint Optimization Problem(C-DCOP) is a constraint processing framework for continuous variables problems in multi-agent systems. There is a constraint cost function between two mutually restrictive agents in C-DCOP. The goal of the C-DCOP solving algorithm is to keep the sum of constraint cost functions in an extreme state. In a C-DCOP, each function is defined by a set of continuous variables. At present, some C-DCOP solving algorithms have been proposed, but there are some common problems such as the limitation of constraints cost function form, easy to fall into local optimum, and lack of anytime attribute. Aiming at these thorny problems, we propose a parallel optimization algorithm named Estimation of Distribution Based Algorithm for Continuous Distributed Constraint Optimization Problems (EDA-CD). In EDA-CD, each solution is regarded as an individual, and the distribution of agent value is jointly described by all outstanding individuals. Firstly, all agents cooperate to hold a distributed population. Secondly, each agent calculates the mean and variance of its variables to build probability models in parallel. Finally, the agent evaluates the fitness of samples and updates the probability model through cooperative communication on Breadth First Search (BFS) pseudo-tree. We theoretically prove that EDA-CD is an anytime algorithm. The extensive experimental results on four types of benchmark problems show that the proposed EDA-CD outperforms the state-of-the-art C-DCOP algorithms and has about 20% improvement in solution quality.

Inspired by the distributed information exchange and adaptive responsiveness of pyrosomes, this study proposes an Adaptive Pyrosome Optimization Algorithm (APOA). In APOA, each candidate solution is modeled as a pyrosome composed of interacting spores, which serve as decision-making components that update information through distributed communication and adaptive strategies. The algorithm consists of four stages: initialization (population generation), information exchange (distributed communication), adaptive decision-making (balancing exploration and exploitation via adaptive assumptions and greedy strategies to enhance convergence and solution quality), and reaction (solution update). Benchmark evaluations on 82 functions from the CEC 2014, CEC 2017, CEC 2020, and CEC 2022 test suites demonstrate that APOA achieves superior convergence speed, solution quality, and stability on 23 functions compared with 14 state-of-the-art metaheuristic algorithms. Furthermore, tests on four engineering design problems highlight its robustness and effectiveness in solving complex, high-dimensional optimization tasks.

Inspired by the spores controlling during the life cycle of pyrosomes, this paper proposes a novel swarm intelligence-based meta-heuristic adaptive pyrosome optimization algorithm named APOA, which consists of four stages: Initialization, Information Interaction, Adaptive Decision-making, and Reaction. During the interaction, spores broadcast their information to each other. The decision-making stage employs a mechanism using random and adaptive strategies to enhance global exploration and local exploitation, respectively. Comprehensive tests on 23 test functions demonstrate the superior convergence and exceptional local optima avoidance of APOA. Extensive experimental results across CEC2014, CEC2017, CEC2020, and CEC2022 standard test suites reveal that APOA statistically outperforms 14 state-of-the-art metaheuristics in convergence speed, solution quality, and algorithmic stability. Furthermore, Empirical results on four types of engineering design problems further confirm that APOA is significantly superior to the leading competing algorithms in solving complex high-dimensional optimization challenges.