Ideological Sublations: Resolution of Dialectic in Population-based Optimization

We propose a population-based optimization algorithm inspired by two main thinking modes in philosophy. Particles are regarded as thinkers and their locations are interpreted as the theses. Both thinking modes are based on the concept of dialectic and thesis-antithesis paradigm. Idealistic and materialistic antitheses are formulated as optimization models. Based on the models, the population is coordinated for dialectical interactions. At the population-based context, the formulated optimization models are reduced to simple detection problems. According to the assigned thinking mode to each thinker, dialectic quantities of each thinker with two other specified thinkers are measured. One of them at maximum dialectic is selected and its position is called the available antithesis for the considered thesis. Thesis-antithesis interactions are defined by meaningful distribution of the step-sizes for each thinking mode. In fact, the thinking modes are regarded as exploration and exploitation elements of the proposed algorithm. The result is a delicate balance between the thinkers without any requirement for adjustment of the step-size coefficients. Main parameter of the proposed algorithm is the number of particles appointed to each thinking modes. An additional integer parameter is defined to boost the stability of the final algorithm in facing with some specific problems. The proposed algorithm is evaluated on different problems. First, a testbed of 12 single objective continuous functions in low and high dimensions is considered. Then, proposed algorithm is tested for sparse reconstruction problem in the context of compressed sensing. The results indicate efficiency and in some cases superiority of performance of the proposed algorithm in comparison with a variety of well-known algorithms. Low runtime is another remarkable advantage of the proposed algorithm.