---

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.

---

Composite RCS building frames integrate reinforced concrete columns with structural steel beams to provide an efficient solution for the design and construction of earthquake-resisting structures. In this paper, an optimization framework is developed for performance-based seismic design of planar RCS moment resisting frames. The objective functions are defined as minimizing the construction cost and the seismic damage. The design variables are obtained in a two-stage design optimization procedure; the elastic design in which column cross-section dimensions are determined and the inelastic design in which beam cross-sections and column reinforcements are obtained. Two design examples are presented to demonstrate the applicability and efficiency of the proposed method. Based on the obtained results, it is concluded that the proposed design optimization procedure is a viable approach in producing cost effective seismic designs of composite RCS frames, with reliable seismic performance and reduced damage potential in the event of a severe earthquake ground motion.