Multi-objective self-adaptive algorithm for highly constrained problems: Novel method and applications

As a substantive input to resolve the industrial systems and challenging optimization problems, which are multi-objective in nature, the authors introduce an emerging systematic multi-objective optimization methodology for large-scale and highly-constrained industrial production systems. The methodology uses a simulation-based optimization framework built on a novel multi-objective evolutionary algorithm that exhibits several specific innovative features to maintain genetic diversity within the population of solutions and to drive the search towards the Pareto-optimal set/front. This novel algorithm was validated using standard test functions and the results demonstrate undoubtedly that the proposed algorithm computes accurately the Pareto-optimal set for optimization problems of at least two-objective functions. Next, the algorithm was applied on a base case cogeneration optimization problem with three-objective functions named the modified CGAM problem. The modified problem includes concentrations and tax rates of pollutant emissions (i.e. CO2 and NOx). The multi-objective optimization of such a problem consists of simultaneously maximizing the exergetic efficiency of the cogeneration plant, minimizing the total cost rate (including pollutant tax rate), and minimizing the specific rate of pollutant emissions. A fuel-to-air equivalence ratio ranging from 0.5 to 1.0, and pollutant tax rates of 0.15 $/kg CO2, and 7.50 $/kg NOx were used to compute the surfaces of the Pareto fronts. The results found for the modified CGAM problem clearly demonstrate the applicability of the proposed algorithm for optimization problems of more than two-objective functions with multiple constraints. The results strengthen the fact that there is no single optimal solution but rather a set of optimal solutions that present the best trade-off alternatives from which a decision-maker can select the appropriate final decision. Also, the study emphasizes the key role of both economic and environmental issues in the optimization problem of energy systems.