Providing an algorithm for solving general optimization problems based on Domino theory

Optimization is a very important process in engineering. Engineers can create better production only if they make use of optimization tools in reduction of its costs including consumption time. Many of the engineering real-word problems are of course non-solvable mathematically (by mathematical programming solvers). Therefore, meta-heuristic optimization algorithms are needed to solve these problems. Based on this assumption, many new meta-heuristic optimization algorithms have been proposed inspired by natural phenomena, such as IWO [58], BBO [59], WWO [61], and so on. Inspired by domino toppling theory, we proposed an optimization algorithm. Using domino pieces, we can create countless complex structures. To simulate the domino movement in the search space of a problem, we consider the particles in the search space as the domino pieces and, by creating an optimal path, we will try to direct the dominoes to the optimal path. The optimal paths will be updated in each iteration. After initializing the dominoes randomly at the beginning of each evaluation, the picking piece or the first moving piece will be identified and then the particles will be selected by the optimal path. Applying a motion equation to each domino will move the dominoes forward in that direction. At first, a predefined dominoes will be randomly distributed in the problem space. Choosing the optimal path will accelerate the convergence of the domino particles towards the target. After choosing the path in current iteration, we now have to do the domino movement. The particles will move to a new location by applying the new location equation. By applying this equation, each domino piece will sit on the track ahead of itself. The front piece will also move to a new location by applying an equation separate from the rest. After moving the dominoes to the new location, the worst iteration of the previous iteration will be removed from the problem space. In the new iteration, the optimal domino path, the new locations of domino pieces and the global optimum will be updated. At the end of the algorithm, the global optimum will be determined as the optimal solution. This method is implemented in a simulator environment. To evaluate the performance of the Domino Optimization algorithm, we use a complete benchmark including 30 objective functions called CEC 2014 [67] that are single-objective numerical functions. In all cases, we set the population size to 50, the dimension size to 30, and the number of fitness function evaluation to 150,000. We compare the proposed Domino Optimization algorithm (DO) with the algorithms LOA [57], ICS [62], NPSO [63], MOHS [64], BCSO [65] and FFFA [66]. The results obtained from the 3 unimodal functions show that the proposed method is able to achieve a better solution than any of the state of the art algorithms at the equal resources. Results in the multimodal functions show that the proposed method has the best performance in finding the optimal solution in all of the available 13 functions in this section. In all of 6 functions in the hybrid section, the quality of the proposed method is better than all of the state of the art algorithms at the equal resources. The standard deviation values ​​of the proposed method, which are often small numbers, indicate algorithm convergence around the optimal solution. Also among the available methods, two algorithms, named NPSO and LOA, have good results after the proposed method. In the convergence analysis of dominoes, the diversity of objective functions in 100 distinct iterations shows a big value at the beginning of the algorithm, and a low value at the end of the algorithm.