On Improvements and Applications of MVO Algorithm To Real World Problems

Abstract

The aim and of this thesis to make some improvements and solve some real word problems. The first and main objective of our thesis is to how overcome the ongoing energy crises in Pakistan and fulfill the energy demand from the given sources. The second objective of our thesis the how to minimize the errors in differential equation using evolutionary algorithm as compared to numerical technique. The ongoing load shedding and energy crises due to mismanagement of energy produced by different sources in Pakistan and increasing dependency on those sources which produce energy using expensive fuels have contributed to rise in load shedding and price of energy per kilo watt hour. In this thesis, we have presented the linear programming model of 95 energy production systems in Pakistan. An improved multiverse optimizer is implemented to generate a dataset of 100000 different solutions, which are suggesting to fulfill the overall demand of energy in the country ranging from 9587 MW to 27208 MW. We found that, if some of the power-generating systems are down due to some technical problems, still we can get our demand by following another solution from the dataset, which is partially utilizing the particular faulty power system. According to different case studies, taken in the present study, based on the reports about the electricity short falls been published in news from time to time, we have presented our solutions, respectively, for each case. It is interesting to note that it is easy to reduce the load shedding in the country, by following the solutions presented in our dataset. Graphical analysis is presented to further elaborate our findings. By comparing our results with state-of-the-art algorithms, it is interesting to note that an improved multiverse optimizer is better in getting solutions with lower power generation costs. In this thesis, we have designed a new optimization technique, which is named as the Improved Multiverse Algorithm with Levy Flights (ILFMVO) algorithm. The quality of the population is an important factor that can directly or indirectly affect the strength of an algorithm in searching for the given search space for an optimal solution. Also having an initialization of the initial population with randomly generated candidate solutions is not an effective idea in every case, especially, when the search space is large. Hence, we have updated the Levy flights based Multi-verse Optimizer (LFMVO) by dividing initialization into two parts. To investigate the ability of ILFMVO, we have solved a constrained economic dispatch problem with a non-smooth, non-convex the cost function of three, six and twenty thermal generator systems. We have compared our results with other standard algorithms. The outcome demonstrated that ILFMVO has better accuracy, stability, and convergence. This research aims at introducing a new solution finding strategy for linear and non linear ordinary differential equations representing harmonic oscillators. Our artificially intelligent technique is developed by using a general solution defined by feed-forward artificial neural network with several unknown design weights. Three heuristic technique Interior Point algorithm (IPA), Sequential quadratic programming (SQP) and active set algorithm (ASA) are combined to Multi-verse optimizer (MVO) to train the unknown weights with the help of randomly generated populations of weights. We minimize the error in approximate solutions by an unsupervised procedure. A Log sigmoid function is used for activating the neural network. To test the robustness, accuracy, efficiency, and effectiveness of our approach, we have simulated our experiments for a large number of times. Comparison with the analytical solutions of our proposed solutions suggest that our approach is suitable for ordinary differential equations representing real word phenomena.