A metaheuristic approach for multi-objective optimization of the Stirling cycle with internal irreversibilities and regenerative losses using artificial bee colony algorithm

Abstract

This study aimed to investigate the multi-objective optimization of a Stirling cycle with a mathematical model that takes into account the dead volumes, effects of regenerative losses, and internal irreversibilities on the thermodynamic performance of the cycle. The optimization was carried out using the Artificial Bee Colony algorithm, which is a population-based metaheuristic method that mimics the foraging behavior of honeybees. The developed algorithm employs the concepts of Pareto frontier and ε-dominance to find the optimal solutions in the multi-objective space which is obtained with Artificial Bee Colony algorithm. The input parameters of the system are the maximum and minimum temperatures, compression and expansion volumes, and charge pressure which affect the thermodynamic variables of the cycle. The optimization process consisted of two stages: firstly, single-objective optimization was performed separately for each objective function to obtain the baseline results. Then, three different sets of triple-objective function groups were used to perform multi-objective optimization. These are Case 1 (net work output, thermal efficiency, irreversibility parameter), Case 2 (net work output, thermal efficiency, 2nd law efficiency), and Case 3 (net work output, thermal efficiency, entropy generation). The obtained results from the single and multi-objective optimizations were compared and analyzed. Since multi-objective optimization involves conflicting objectives, it does not result in a single optimal solution, but rather a set of optimal solutions that represent different trade-offs among the objectives. In order to achieve the optimum results with a good trade-off between solutions Pareto frontier method is used. In addition, to obtain a good distribution of solutions and filter very similar solution points in the solution space, ε-dominance was used to filter them. Finally, to select the final optimal solution from the Pareto frontier solution set, LINMAP was used as a decision-making tool which is a linear programming technique that assigns weights to each solution. The weights of the solutions are achieved according to the relative distance between objectives with their single optimal values achieved by single optimization. The best solution based on the net work output is achieved with Case 3 which includes entropy generation as different from other cases. Also, Case 3 has the lowest irreversibility parameter value even though the irreversibility parameter was optimized in Case 1. Entropy generation and mean effective pressure are quite sensitive due to the multiple solutions they have at each solution step when entropy generation is not an objective function.