Heuristics applying stochastic information as tools for thermoacoustic standing-wave engine optimization
In this article, two numerical methods for solving engineering problems defined as multicriteria optimization and inverse problem are presented. In particular, this study deals with the optimization of the design of thermoacoustic engine in the frame in which both types of tasks are solved. The first proposed heuristic serves to find many p-optimal solutions simultaneously, which represents a compromise between usually mutually contradictory goals at work. Based on them, the full Pareto front is approximated. The inverse problem solution reproduces parameters for solutions located on a designated front but those that are not found in multicriteria optimization. In this article, the RACO heuristics are proposed for determining p-optimal solutions and the Bayesian approach is introduced as a method for solving ill-conditioned inverse problems. Optimization of the construction of the thermoacoustic engine is aimed at verifying proposed methodology and present the possibility of using both methods in engineering problems. The problem discussed in this article is formulated and the numerical methods used in the solution are presented in details.
Keywordsmulticriteria optimization problem, ant colony optimization, inverse problem, Bayesian approach, thermoacoustic engine optimization, numerical modelling,
References J. Andersson. Multiobjective Optimization in Engineering Design – Applications to Fluid Power Systems. Dissertation, Link¨oping Studies in Science and Technology, Dissertation No. 675, Link¨oping University, Link¨oping, Sweden, 2001.
 P. Bala Subrahmanyam, R. Sujith, M. Ramakrishna. Determination of unsteady heat release distribution from acoustic pressure measurements: a reformulation of the inverse problem, The Journal of the Acoustical Society of America, 114(2): 686–696, 2003.
 S. Bandyopadhyay, S. Saha, U. Maulik, K. Deb. A simulated annealing-based multiobjective optimization algorithm: AMOSA. IEEE Transactions on Evolutionary Computation, 12(3): 269–283, 2008.
 B. Li, J. Li, K. Tang, X. Yao. Many-objective evolutionary algorithms: A survey. ACM Computing Surveys, 48(1): 35 pages, 2015.
 U. Diwekar. Introduction to Applied Optimization. Springer, 2008.
 C. Heuberger. Inverse combinatorial optimization: a survey on problems, methods, and results. Journal of Combinatorial Optimization, 8(3): 329–361, 2004.
 J. Horn. Multicriteria decision making. In: T. Back, D.B. Fogel, Z. Michalewicz [Eds.], Handbook of Evolutionary Computation. Institute of Physics Publishing, Bristol (UK), 1997.
 B. Kaltenbacher, W. Polifke. Some regularization methods for a thermoacoustic inverse problem. Journal of Inverse and Ill-Posed Problem. 18: 997–1011, 2011.
 B.T. Knapik, A.W. van der Vaart, J.H. van Zanten. Bayesian inverse problems with Gaussian priors. The Annals of Statistics, 39(5): 2626–2657, 2011.
 J. Knowles, D. Corne, D. Kalyanmoy. Multiobjective Problem Solving from Nature: from Concepts to Applications. Springer Science & Business Media, 2007.
 S.M. Lynch. Introduction to Applied Bayesian Statistics and Estimation for Social Scientists. Springer, New York, 2007.
 I. Nowak. Bayesian approach applied for thermoacoustic inverse problem. Energy, 141: 2519–2527, 2017.
 I. Nowak, G. Nowak. Real ant colony optimization as a tool for multi-criteria problems. Computer Assisted Methods in Engineering and Science, 22: 255–265, 2015.
 H.R.B. Orlande, O. Fudym, D. Maillet, R.M. Cotta. Thermal Measurements and Inverse Techniques, CRC Press, 2011.
 V. Pareto. Manuale di Economia Politica. Societa Editrice Libraria, Milano, Italy, 1906. Translated into English by A.S. Schwier as Manual of Political Economy, Macmillan, New York, 1971.
 S.A. Saltelli, F. Tarantola. Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. John Wiley & Sons, 2004.
 K. Socha, M. Dorigo. Ant colony optimization for continuous domains. European Journal of Operational Research, 185: 1155–1173, 2008.
 S. Spoelstra, M.E.H. Tijani. Thermoacoustic Heat Pumps for Energy Savings. Presented at the seminar “Boundary crossing acoustics” of the Acoustical Society of the Netherlands, 2005.
 A.M. Stuart. Inverse problems: a Bayesian perspective. Acta Numerica, 19: 451–559, 2010.
 G.W. Swift. Thermoacoustics: a unifying perspective for some engines and refrigerators. The Journal of the Acoustical Society of America, 113(5): 2379–2381, 2003.
 O.G. Symko, E. Abdel-Rahman, Y.S. Kwon, M. Emmi, R. Behunin. Design and development of high-frequency thermoacoustic engines for thermal management in microelectronics. Microelectronics Journal, 35(2): 185–191, 2004.
 A.C. Trapp, F. Zink, O.A. Prokopyev. Thermoacoustic heat engine modelling and design optimization. Applied Thermal Engineering, 31: 2518–2528, 2011.
 O.L. de Weck. Multiobjective optimization: history and promise. Keynote Paper. The 3rd China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, Kanazawa, Japan, 2004.
 H. Werner, M. Hanke, A. Neubauer. Regularization of Inverse Problems. Vol. 375. Springer Science & Business Media, 1996.
 P.L. Yu. Cone convexity, cone extreme points, and nondominated solutions in decision problems with multiobjectives. Journal of Optimization Theory and Applications, 14(3): 319–377, 1974.
 Z. Yu, A.J. Jaworski, S. Backhaus. A low-cost electricity generator for rural areas using a travelling-wave loopedtube thermoacoustic engine. Part A: Journal of Power and Energy, 224(6): 787–795, 2010.
 E. Zitzler. Evolutionary Algorithms for Multiobjective Optimisation: Methods and Applications. PhD thesis, Eidgen¨ossische Technische Hochschule Zurich, 1999.
 E. Zitzler, K. Deb, L. Thiele. Comparison of multiobjective evolutionary algorithms: empirical results. Evolutionary Computation, 8(2): 173–195, 2000.