Social Cognitive Optimization

Social cognitive optimization (SCO) is a population-based metaheuristic optimization algorithm which was developed in 2002. 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, integer programming, and combinatorial optimization problems. It has been incorporated into th
NLPSolver
extension of Calc in Apache OpenOffice.

Algorithm

Let $f(x)$ be a global optimization problem, where $x$ is a state in the problem space $S$. In SCO, each state is called a ''knowledge point'', and the function $f$ is the ''goodness function''.

In SCO, there are a population of $N_c$ 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 $N_L$ knowledge points. The algorithm runs in ''T'' iterative learning cycles. By running as a Markov chain process, the system behavior in the ''t''th cycle only depends on the system status in the (''t'' − 1)th cycle. The process flow is in follows:

* . Initialization¼šInitialize the private knowledge point $x_i$ in the memory of each agent $i$, and all knowledge points in the social sharing library $X$, normally at random in the problem space $S$.
* . Learning cycle¼š At each cycle $t$ $(t = 1, \ldots, T)$：
** .1. Observational learningFor each agent $i$ $(i = 1, \ldots, N_c)$：
*** .1.1. Model selection¼šFind a high-quality ''model point'' $x_M$ in $X(t)$ , normally realized using tournament selection, which returns the best knowledge point from randomly selected $\tau_B$ points.
*** .1.2. Quality Evaluation¼šCompare the private knowledge point $x_i(t)$ and the model point $x_M$，and return the one with higher quality as the ''base point'' $x_$，and another as the ''reference point'' $x_$。
*** .1.3. Learning¼šCombine $x_$ and $x_$ to generate a new knowledge point $x_(t+1)$. Normally $x_(t+1)$ should be around $x_$，and the distance with $x_$ is related to the distance between $x_$ and $x_$, and boundary handling mechanism should be incorporated here to ensure that $x_(t+1) \in S$.
*** .1.4. Knowledge sharing¼šShare a knowledge point, normally $x_i(t+1)$, to the social sharing library $X$.
*** .1.5. Individual update¼šUpdate the private knowledge of agent $i$, normally replace $x_(t)$ by $x_(t+1)$. Some Monte Carlo types might also be considered.
** .2. Library Maintenance¼šThe social sharing library using all knowledge points submitted by agents to update $X(t)$ into $X(t+1)$. A simple way is one by one tournament selection: for each knowledge point submitted by an agent, replace the worse one among $\tau_W$ points randomly selected from $X(t)$.
* . Termination¼šReturn the best knowledge point found by the agents.

SCO has three main parameters, i.e., the number of agents $N_c$, the size of social sharing library $N_$, and the learning cycle $T$. With the initialization process, the total number of knowledge points to be generated is $N_+N_c*(T+1)$, and is not related too much with $N_$ if $T$ is large.

Compared to traditional swarm algorithms, e.g. particle swarm optimization, SCO can achieving high-quality solutions as $N_c$ is small, even as $N_c=1$. Nevertheless, smaller $N_c$ and $N_$ might lead to premature convergence. Some variants 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.

References

{{reflist,
refs=
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.

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.

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.

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.

Sun, Jia-ze; Wang, Shu-yan; chen, Hao (2014)
A guaranteed global convergence social cognitive optimizer
''Mathematical Problems in Engineering'': Art. No. 534162.

Heuristic algorithms
Optimization algorithms and methods
Collective intelligence