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Top1. Introduction
Real world optimization problems are characterized as either constrained or unconstrained optimization problems. The constraints take an important part in engineering design issues (Holland, 2010), but can cause search process to become difficult. Properly addressing the exploration and exploitation can lead to improved performance of any search algorithm. The exploration is a process in which new regions for search space is visited and in exploitation, neighborhood of previously visited points are visited (Crepinsek et al., 2013), by maintaining a balanced ratio among exploration and exploitation to achieve a successful result. Several researchers have proposed various approaches by examining the solution of specific real world engineering problems (Yao et al., 2003). As these realistic problems are nonlinear and complex, classical optimization methods are unable to attain a global optimum. Hence, over the years the application of metaheuristic approaches to address such problems has become very important (Jigang et al., 2019), e.g. genetic algorithm (GA), ant colony optimization (ACO) algorithm particle swarm optimization (PSO) algorithm, simulated annealing (SA) algorithm are used (Lin et al., 2016; Zou et al., 2013). Apart from these algorithms, the framework of differential evolution (DE) with enhanced parameters can also play a vital role to resolve the realistic optimization issues in engineering applications. In 1995, Price and Storm recommended using the complicated computing method of differential evolution (DE) algorithm (Qin et al., 2009; Zou et al., 2013). DE is considered as promising and important stochastic method because it has set of parameters that are suitable for solving engineering applications (Rahnamayan et al., 2008). For these reasons, it has been implemented into several realistic optimization problems. Available literature indicates that opposition based differential evolution (ODE), self-adaptive and adaptive algorithms of DE show faster and more reliable results than original DE algorithms without parameter control for several benchmark issues (Rahnamayan et al., 2008; Sharma & Abraham, 2019). Various applications (Ali et al., 2010; Li & Zhang, 2018) along with various modifications of DE (Jigang et al., 2019; Rastogi et al., 2017) have also been highlighted in the literature. Although there are lots of advantages of DE, there are some limitations also, these are: Unstable convergence, Easy to drop into regional optimum, for greater value of crossover rate and scaling factor there is always a high probability to skip the true solution in search area. To overcome these limitations DE is modified as described in this paper. This study presents a modified differential evolution algorithm by using the concept of external archive, logistic map (Agarwal et al., 2017) and exponential scale factor (Kashyap & Sharma, 2018). Modification is done in two ways: first is in the initialization of population using external archive and logistic map and second is in the scaling factor using exponential scaling factor. Advantage of the proposed system, considering logistic map is that, for r=3.56, logistic map performs better than random number because logistic map is a polynomial mapping of degree 2, which gives an idea of how a complex chaotic behavior can achieved from a non linear dynamic equation. Considering scaling factor, is that “during the stage of initial iteration, the value of f will be high, which helps in the search area in exploration, after drop of some iterations, exponentially the value of f will decrease, hence with reduced step size, the solution is now move and which enhances the exploitation skill of the algorithm. By using this approach, proper equilibrium between exploration and exploitation skills of the algorithm can be uphold.” The proposed method is validated by taking different benchmark functions also the outcomes are compared along with different popular state of art algorithms. Further, the study is executed and verified on real world engineering applications and also compared with some recent optimizer techniques considering one real world engineering problem. From the outcomes it can be clearly analyzed that proposed DE performed comparatively well than DCPCX and Pro DCPCX for functions f1 and f3 (Ali et al., 2010). Further from number of function evaluation which defines speeds of the algorithms, it shows that the proposed method converges faster than the other modified techniques (Ali et al., 2010). Also by comparing with some recent optimizer techniques (Sharma & Abraham, 2019) we can justify that the proposed modified technique can be compare to other different optimization algorithms and this technique is applicable to real time optimization problem.