Social cognitive optimization

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Social cognitive optimization (SCO) is a population-based metaheuristic optimization algorithm which was developed in 2002.[1] This algorithm is based on the social cognitive theory, and the key point of the ergodicity is the process of individual learning of a set of agents with their own memory and their social learning with the knowledge points in the social sharing library. It has been used for solving continuous optimization,[2][3] integer programming,[4] and combinatorial optimization problems. It has been incorporated into the NLPSolver extension of Calc in Apache OpenOffice.

Algorithm[edit]

Let be a global optimization problem, where is a state in the problem space . In SCO, each state is called a knowledge point, and the function is the goodness function.

In SCO, there are a population of cognitive agents solving in parallel, with a social sharing library. Each agent holds a private memory containing one knowledge point, and the social sharing library contains a set of knowledge points. The algorithm runs in T iterative learning cycles. By running as a Markov chain process, the system behavior in the tth cycle only depends on the system status in the (t − 1)th cycle. The process flow is in follows:

  • [1. Initialization]:Initialize the private knowledge point in the memory of each agent , and all knowledge points in the social sharing library , normally at random in the problem space .
  • [2. Learning cycle]: At each cycle
    • [2.1. Observational learning] For each agent
      • [2.1.1. Model selection]:Find a high-quality model point in , normally realized using tournament selection, which returns the best knowledge point from randomly selected points.
      • [2.1.2. Quality Evaluation]:Compare the private knowledge point and the model point ,and return the one with higher quality as the base point ,and another as the reference point
      • [2.1.3. Learning]:Combine and to generate a new knowledge point . Normally should be around ,and the distance with is related to the distance between and , and boundary handling mechanism should be incorporated here to ensure that .
      • [2.1.4. Knowledge sharing]:Share a knowledge point, normally , to the social sharing library .
      • [2.1.5. Individual update]:Update the private knowledge of agent , normally replace by . Some Monte Carlo types might also be considered.
    • [2.2. Library Maintenance]:The social sharing library using all knowledge points submitted by agents to update into . A simple way is one by one tournament selection: for each knowledge point submitted by an agent, replace the worse one among points randomly selected from .
  • [3. Termination]:Return the best knowledge point found by the agents.

SCO has three main parameters, i.e., the number of agents , the size of social sharing library , and the learning cycle . With the initialization process, the total number of knowledge points to be generated is , and is not related too much with if is large.

Compared to traditional swarm algorithms, e.g. particle swarm optimization, SCO can achieving high-quality solutions as is small, even as . Nevertheless, smaller and might lead to premature convergence. Some variants [5] were proposed to guaranteed the global convergence. One can also make a hybrid optimization method using SCO combined with other optimizers. For example, SCO was hybridized with differential evolution to obtain better results than individual algorithms on a common set of benchmark problems [6].

References[edit]

  1. ^ Xie, Xiao-Feng; Zhang, Wen-Jun; Yang, Zhi-Lian (2002). Social cognitive optimization for nonlinear programming problems. International Conference on Machine Learning and Cybernetics (ICMLC), Beijing, China: 779-783.
  2. ^ Xie, Xiao-Feng; Zhang, Wen-Jun (2004). Solving engineering design problems by social cognitive optimization. Genetic and Evolutionary Computation Conference (GECCO), Seattle, WA, USA: 261-262.
  3. ^ Xu, Gang-Gang; Han, Luo-Cheng; Yu, Ming-Long; Zhang, Ai-Lan (2011). Reactive power optimization based on improved social cognitive optimization algorithm. International Conference on Mechatronic Science, Electric Engineering and Computer (MEC), Jilin, China: 97-100.
  4. ^ Fan, Caixia (2010). Solving integer programming based on maximum entropy social cognitive optimization algorithm. International Conference on Information Technology and Scientific Management (ICITSM), Tianjing, China: 795-798.
  5. ^ Sun, Jia-ze; Wang, Shu-yan; chen, Hao (2014). A guaranteed global convergence social cognitive optimizer. Mathematical Problems in Engineering: Art. No. 534162.
  6. ^ Xie, Xiao-Feng; Liu, J.; Wang, Zun-Jing (2014). "A cooperative group optimization system". Soft Computing. 18 (3): 469–495.