Industrial system ranging from a toy making system to aircraft assembly systems these days are facing huge requirement of innovation, improvement in its machinery, which requires modeling, analysis, optimization and mathematical studies of these systems. our work strong footing in this area, therefore improving the quality of analysis. our work is basically in the field of model order reduction (mor) and soft computing technique. any engineering system can be expressed mathematically as a transfer function and these transfer function are high ordered and complex, thus making it difficult to simulate and study. basic idea of mor is to bring down the order of such systems to suitable complexity and hence making system analysis and simulation easier. we have developed a novel mor technique which is a combination of analytical order reduction technique and soft computing technique i.e. we have combined the concept of time moment matching method and newly introduced soft computing technique i.e. big-bang big-crunch (bbbc) optimization to get a highly productive model order reduction algorithm. this algorithm has been applied on very high order system as well as high order time delayed system which shows highly convincing results. this technique was also tested on automatic voltage regulator model which is a sixth order system, sixth order system was converted to second order system and hence making the system analysis and controller design very easy. during this work, we came out to know various short comings of recently developed bbbc algorithm. with the aim to make it more efficient and powerful, we have proposed various structural and conceptual changes in the algorithm, and therefore proposing two new highly improved algorithms. basically, bbbc algorithm is inspired from evolution of universe and it was observed that this algorithm missed out various intricacies of the evolution of universe. we in our first improvised algorithm, have taken into account the entire shortcoming and proposed a new algorithm which is named as mbbbc i.e. modified bbbc. the simulation studies have shown great result in terms of computational efficiency and effectiveness. during this work, it was observed that mbbbc is getting stuck in local optima when used for optimization of highly nonlinear benchmark function. to solve this problem, we have introduced the concept of chaos into this algorithm therefore solving the problem of getting stuck in local optima. simulation studies have shown a highly encouraging result both in terms of computational efficiency and effectiveness. this algorithm is named as chaos mbbbc i.e. cmbbbc. as we are aware that there are many optimization algorithm these days which are used in field of engineering, but there is no solid mathematical treatment for assessing the efficiency or more appropriately comparing the efficiency of these algorithm. our work in this area has been a very important landmark, which gives a way to compare algorithms, on the basis of their computational efficiency and effectiveness. we have used inferential statistical technique to compare original algorithm i.e. bbbc, proposed algorithms i.e. mbbbc and cmbbbc and widely known and used algorithms i.e. particle swarm optimization (pso) and genetic algorithm (ga). the mathematically involved comparison has shown that cmbbbc and mbbbc have very very high performance in comparison to original algorithm, and the proposed algorithms efficiency is on par with pso and ga. this result is a major contribution to engineering sciences and field of optimization.