Opposition-based learning was first introduced as a solution for machine learning; however, it is being extended to other artificial intelligence and soft computing fields including metaheuristic OPTIMIZATION. It not only utilizes an estimate of a solution but also enters its counter-part information into the search process. The present work applies such an approach to COLLIDING BODIES OPTIMIZATION as a powerful meta-heuristic with several engineering applications. Special combination of static and dynamic opposition-based operators are hybridized with CBO so that its performance is enhanced. The proposed OCBO is validated in a variety of benchmark test functions in addition to structural OPTIMIZATION and optimal clustering. According to the results, the proposed method of opposition-based learning has been quite effective in performance enhancement of parameter-less COLLIDING BODIES OPTIMIZATION.

COLLIDING BODIES OPTIMIZATION (CBO) is a new population-based stochastic OPTIMIZATION algorithm based on the governing laws of one dimensional collision between two BODIES from the physics. Each agent is modeled as a body with a specified mass and velocity. A collision occurs between pairs of objects to find the global or near-global solutions. Enhanced COLLIDING BODIES OPTIMIZATION (ECBO) uses memory to save some best solutions and utilizes a mechanism to escape from local optima. The performances of the CBO and ECBO are shown through truss and frame design OPTIMIZATION problems. The codes of these methods are presented in MATLAB and C++.

This paper describes the application of the recently developed metaheuristic algorithm for simultaneous analysis, design and OPTIMIZATION of Water Distribution Systems (WDSs). In this method, analysis is carried out using COLLIDING BODIES OPTIMIZATION algorithm (CBO). The CBO is a population-based search approach that imitates nature’s ongoing search for better solutions. Also, design and cost OPTIMIZATION of WDSs are performed simultaneous with analysis process using a new objective function in order to satisfying the analysis criteria, design constraints and cost OPTIMIZATION. A number of practical examples of WDSs are selected to demonstrate the efficiency of the presented algorithm. Comparison of obtained results clearly signifies the efficiency of the CBO method in reducing the WDSs construction cost and computational time of the analysis.

In this paper, optimal design of arch dams is performed under frequency limitations. COLLIDING BODIES OPTIMIZATION (CBO), a recently developed meta-heuristic OPTIMIZATION method, which has been successfully applied to several structural problems, is revised and utilized for finding the best feasible shape of arch dams. The formulation of CBO is derived from one-dimensional collisions between BODIES, where each agent solution is considered as the massed object or body. The design procedure aims to obtain minimum weight of arch dams subjected to natural frequencies, stability and geometrical limitations. Two arch dam examples from the literature are examined to verify the suitability of the design procedure and to demonstrate the effectiveness and robustness of the CBO in creating optimal design for arch dams. The results of the examples show that CBO is a powerful method for optimal design of arch dams.

Stochastic nature of earthquake has raised a challenge for engineers to choose which record for their analyses. Clustering is offered as a solution for such a data mining problem to automatically distinguish between ground motion records based on similarities in the corresponding seismic attributes. The present work formulates an OPTIMIZATION problem to seek for the best clustering measures. In order to solve this problem, the well-known Kmeans algorithm and COLLIDING BODIES OPTIMIZATION are employed. The latter acts like a parameter-less meta-heuristic while the former provides strong intensification.Consequently, a hybrid algorithm is proposed by combining features of both the algorithms to enhance the search and avoid premature convergence. Numerical simulations show competative performance of the proposed method in the treated example of optimal ground motion clustering, regarding global OPTIMIZATION and quality of final solutions.

COLLIDING BODIES OPTIMIZATION (CBO) is a population-based metaheuristic algorithm that complies physics laws of momentum and energy. Due to the stagnation susceptibility of CBO by premature convergence and falling into local optima, some meritorious methodologies based on Sine Cosine Algorithm and a mutation operator were considered to mitigate the shortcomings mentioned earlier. Sine Cosine Algorithm (SCA) is a stochastic OPTIMIZATION method that employs sine and cosine based mathematical models to update a randomly generated initial population. In this paper, we developed a new hybrid approach called hybrid CBO with SCA (HCBOSCA) to obtain reliable structural design OPTIMIZATION of discrete and continuous variable structures, where a memory was defined to intensify the convergence speed of the algorithm. Finally, three structural problems were studied and compared to some state of the art OPTIMIZATION methods. The experimental results confirmed the competence of the proposed algorithm.

This study presents a robust hybrid meta-heuristic OPTIMIZATION algorithm by merging Modified COLLIDING BODIES OPTIMIZATION and Genetic Algorithm that is called GMCBO. One of the inabilities of COLLIDING BODIES OPTIMIZATION (CBO) is collapsing into the trap of local minima and not finding global optima. In this paper, to rectify this weak point, at first, some modifications are accomplished on the CBO process and then by using the concept of the genetic algorithm able to enhance the convergence rate, establishing a balance between the feature exploration and exploitation processes, the increasing power of finding global optimal design and escaping of local optimal. For evaluating the performance of the proposed method, the optimal design of laminated composite materials has been considered. Compare the results of structural analysis with GMCBO and other OPTIMIZATION methods shows a high convergence rate and its ability to find the global optimal solution of the proposed algorithm for structural OPTIMIZATION problems.

This paper investigates discrete design OPTIMIZATION of reinforcement concrete frames using the recently developed meta-heuristic called Enhanced COLLIDING BODIES OPTIMIZATION (ECBO) and the Non-dominated Sorting Enhanced COLLIDING BODIES OPTIMIZATION (NSECBO) algorithm. The objective function of algorithms consists of construction material costs of reinforced concrete structural elements and carbon dioxide (CO2) emissions through different phases of a building life cycle that meets the standards and requirements of the American Concrete Institute’s Building Code. The proposed method uses predetermined section database (DB) for design variables that are taken as the area of steel and the geometry of cross-sections of beams and columns. A number of benchmark test problems are optimized to verify the good performance of this methodology. The use of ECBO algorithm for designing reinforced concrete frames indicates an improvement in the computational efficiency over the designs performed by Big Bang-Big Crunch (BB-BC) algorithm. The analysis also reveals that the two objective functions are quite relevant and designs focused on mitigating CO2 emissions could be achieved at an acceptable cost increment in practice. Pareto results of the NSECBO algorithm indicate that both objective yield similar solutions.

In this paper two recently developed meta-heuristic OPTIMIZATION methods, known as COLLIDING BODIES OPTIMIZATION (CBO) and Enhanced COLLIDING BODIES OPTIMIZATION (ECBO), are used for optimum nodal ordering to minimize bandwidth of sparse matrices. The CBO is a simple OPTIMIZATION algorithm which is inspired by a collision between two objects in one-dimension. Each agent is modeled as a body with a specified velocity and mass. A collision happens between pairs of BODIES and the new positions of the COLLIDING BODIES are updated based on the collision laws. The enhanced COLLIDING BODIES OPTIMIZATION (ECBO) utilizes memory to save some best so-far-solution to improve the performance of the CBO without increasing the computational cost. This algorithm utilizes a mechanism to escape from local optima. The bandwidth of some graph matrices, which have equivalent pattern to structural matrices, is minimized using these approaches. Comparison of the obtained results with those of some existing methods shows the robustness of these two new meta-heuristic algorithms for bandwidth OPTIMIZATION.

This paper presents the application of metaheuristic methods to the minimum crossing number problem for the first time. These algorithms including particle swarm OPTIMIZATION, improved ray OPTIMIZATION, COLLIDING BODIES OPTIMIZATION and enhanced COLLIDING BODIES OPTIMIZATION. For each method, a pseudo code is provided. The crossing number problem is NP-hard and has important applications in engineering. The proposed algorithms are tested on six complete graphs and eight complete bipartite graphs and their results are compared with some existing methods.