A comparison of building energy optimization problems and mathematical test functions using static fitness landscape analysis

ABSTRACT Computational optimization is gaining popularity in energy-efficient building design. For choosing an algorithm or setting its parameters, often mathematical test functions are employed. This study, therefore, investigates differences and similarities between such test functions and building energy optimization (BEO) problems. A fitness landscape analysis (FLA) is conducted with existing and newly proposed metrics, shedding light on the characteristics of optimization problems. We use the COCO testbed and compare it to BEO problems from the literature. Results suggest that for most FLA metrics there is no statistical difference between the set of test functions and BEO problems. Also, characterizing an archetypical BEO problem appears infeasible due to the high heterogeneity we can observe in FLA metric scores. However, using hierarchical clustering we can identify similarities between test functions and groups of BEO problems. Such knowledge may be exploited for selecting or calibrating an algorithm, thus facilitating its effective use in practice.

[1]  Raymond Ros,et al.  Real-Parameter Black-Box Optimization Benchmarking 2009: Experimental Setup , 2009 .

[2]  Zhongming Shi,et al.  A review of simulation-based urban form generation and optimization for energy-driven urban design , 2017 .

[3]  Julian Francis Miller,et al.  Information Characteristics and the Structure of Landscapes , 2000, Evolutionary Computation.

[4]  Edmund K. Burke,et al.  The Genetic and Evolutionary Computation Conference , 2011 .

[5]  Aris Tsangrassoulis,et al.  Algorithms for optimization of building design: A review , 2014 .

[6]  Lazaros Elias Mavromatidis,et al.  A review on hybrid optimization algorithms to coalesce computational morphogenesis with interactive energy consumption forecasting , 2015 .

[7]  Andries Petrus Engelbrecht,et al.  A survey of techniques for characterising fitness landscapes and some possible ways forward , 2013, Inf. Sci..

[8]  Paola Annoni,et al.  Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , 2010, Comput. Phys. Commun..

[9]  Sean N. Murray,et al.  Multi-variable optimization of thermal energy efficiency retrofitting of buildings using static modelling and genetic algorithms – A case study , 2014 .

[10]  Nikolaos V. Sahinidis,et al.  Derivative-free optimization: a review of algorithms and comparison of software implementations , 2013, J. Glob. Optim..

[11]  László Pál,et al.  A Comparison of Global Search Algorithms for Continuous Black Box Optimization , 2012, Evolutionary Computation.

[12]  D. Shahsavani,et al.  Variance-based sensitivity analysis of model outputs using surrogate models , 2011, Environ. Model. Softw..

[13]  Michael Affenzeller,et al.  A Comprehensive Survey on Fitness Landscape Analysis , 2012, Recent Advances in Intelligent Engineering Systems.

[14]  Wei Tian,et al.  A review of sensitivity analysis methods in building energy analysis , 2013 .

[15]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[16]  Vojislav Novakovic,et al.  Optimization of energy consumption in buildings with hydronic heating systems considering thermal comfort by use of computer-based tools , 2007 .

[17]  Anh Tuan Nguyen,et al.  A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems , 2016 .

[18]  Andries Petrus Engelbrecht,et al.  Quantifying ruggedness of continuous landscapes using entropy , 2009, 2009 IEEE Congress on Evolutionary Computation.

[19]  Godfried Augenbroe,et al.  Multi-criteria decision making under uncertainty in building performance assessment , 2013 .

[20]  Gregorio Toscano Pulido,et al.  Multi-objectivization, fitness landscape transformation and search performance: A case of study on the hp model for protein structure prediction , 2015, Eur. J. Oper. Res..

[21]  Garrison W. Greenwood,et al.  On the use of random walks to estimate correlation in fitness landscapes , 1998 .

[22]  I. Sobol.  On the distribution of points in a cube and the approximate evaluation of integrals , 1967 .

[23]  E. Weinberger,et al.  Correlated and uncorrelated fitness landscapes and how to tell the difference , 1990, Biological Cybernetics.

[24]  Steffen Petersen,et al.  Choosing the appropriate sensitivity analysis method for building energy model-based investigations , 2016 .

[25]  Lisa Guan,et al.  Ant colony algorithm for building energy optimisation problems and comparison with benchmark algorithms , 2017 .

[26]  J. Hensen,et al.  Integrating robustness indicators into multi-objective optimization to find robust optimal low-energy building designs , 2018, Journal of Building Performance Simulation.

[27]  William W. Braham,et al.  An integrated energy–emergy approach to building form optimization: Use of EnergyPlus, emergy analysis and Taguchi-regression method , 2015 .

[28]  Terry Jones,et al.  Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms , 1995, ICGA.

[29]  Zong Woo Geem,et al.  Sustainable Building Design: A Review on Recent Metaheuristic Methods , 2015, Recent Advances in Swarm Intelligence and Evolutionary Computation.

[30]  I. Sobol.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[31]  Saman K. Halgamuge,et al.  Similarity of Continuous Optimization Problems from the Algorithm Performance Perspective , 2019, 2019 IEEE Congress on Evolutionary Computation (CEC).

[32]  Anh Tuan Nguyen,et al.  Passive designs and strategies for low-cost housing using simulation-based optimization and different thermal comfort criteria , 2014 .

[33]  Christina J. Hopfe,et al.  Robust Building Scheme Design Optimization for Uncertain Performance Prediction , 2017, Building Simulation Conference Proceedings.

[34]  Lars Junghans,et al.  Hybrid single objective genetic algorithm coupled with the simulated annealing optimization method for building optimization , 2015 .

[35]  P. Stadler.  Fitness Landscapes , 1993 .

[36]  Jan Carmeliet,et al.  Why We Need a Testbed for Black-Box Optimization Algorithms in Building Simulation , 2020 .

[37]  Louis Gosselin,et al.  Comparison between two genetic algorithms minimizing carbon footprint of energy and materials in a residential building , 2018, Journal of Building Performance Simulation.

[38]  Burcin Becerik-Gerber,et al.  HVAC system energy optimization using an adaptive hybrid metaheuristic , 2017 .

[39]  Judyta Maria Browne Will Neil and Rodriguez Edgar Cichocka.  Optimization in the Architectural Practice - An International Survey , 2017 .

[40]  Christian L. Müller,et al.  Energy Landscapes of Atomic Clusters as Black Box Optimization Benchmarks , 2012, Evolutionary Computation.

[41]  Saman K. Halgamuge,et al.  Exploratory Landscape Analysis of Continuous Space Optimization Problems Using Information Content , 2015, IEEE Transactions on Evolutionary Computation.

[42]  Charles Audet,et al.  Derivative-Free and Blackbox Optimization , 2017 .

[43]  Kenichi Tamura,et al.  Quantitative measure of nonconvexity for black-box continuous functions , 2019, Inf. Sci..

[44]  Jan Carmeliet,et al.  Development and test application of the UrbanSOLve decision-support prototype for early-stage neighborhood design , 2018, Building and Environment.

[45]  Sébastien Vérel,et al.  ParadisEO-MO: from fitness landscape analysis to efficient local search algorithms , 2013, Journal of Heuristics.

[46]  Bernd Bischl,et al.  Exploratory landscape analysis , 2011, GECCO '11.

[47]  Richard A. Watson,et al.  Reducing Local Optima in Single-Objective Problems by Multi-objectivization , 2001, EMO.

[48]  Drury B. Crawley,et al.  EnergyPlus: Energy simulation program , 2000 .

[49]  John S. Gero,et al.  On optimization in computer aided architectural design , 1980 .

[50]  I. Sobol.  Uniformly distributed sequences with an additional uniform property , 1976 .

[51]  Wim Hordijk,et al.  A Measure of Landscapes , 1996, Evolutionary Computation.

[52]  Giacomo Nannicini,et al.  Introduction to Architectural Design Optimization , 2017 .

[53]  Alfonso P. Ramallo-González,et al.  Using self-adaptive optimisation methods to perform sequential optimisation for low-energy building design , 2014 .

[54]  Jan Carmeliet,et al.  Clustering and Ranking Based Methods for Selecting Tuned Search Heuristic Parameters , 2019, 2019 IEEE Congress on Evolutionary Computation (CEC).

[55]  Navid Delgarm,et al.  Multi-objective optimization of building energy performance and indoor thermal comfort: A new method using artificial bee colony (ABC) , 2016 .

[56]  Ralph Evins,et al.  A review of computational optimisation methods applied to sustainable building design , 2013 .

[57]  Xing Shi,et al.  A review on building energy efficient design optimization rom the perspective of architects , 2016 .

[58]  David RUTTEN.  NAVIGATING MULTI-DIMENSIONAL LANDSCAPES IN FOGGY WEATHER AS AN ANALOGY FOR GENERIC PROBLEM SOLVING , 2014 .

[59]  Stefano Tarantola,et al.  Estimating the approximation error when fixing unessential factors in global sensitivity analysis , 2007, Reliab. Eng. Syst. Saf..

[60]  Patrick Siarry,et al.  A survey on optimization metaheuristics , 2013, Inf. Sci..

[61]  Philippe Rigo,et al.  A review on simulation-based optimization methods applied to building performance analysis , 2014 .

[62]  Fabio Schoen,et al.  Global Optimization: Theory, Algorithms, and Applications , 2013 .

[63]  Jonathan A. Wright,et al.  Constrained, mixed-integer and multi-objective optimisation of building designs by NSGA-II with fitness approximation , 2015, Appl. Soft Comput..

[64]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[65]  Shengwei Wang,et al.  Design optimization and optimal control of grid-connected and standalone nearly/net zero energy buildings , 2015 .

[66]  Salvatore Carlucci,et al.  Assessing gaps and needs for integrating building performance optimization tools in net zero energy buildings design , 2013 .

[67]  J. Kämpf,et al.  A comparison of global optimization algorithms with standard benchmark functions and real-world applications using EnergyPlus , 2009 .

[68]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[69]  Galina Merkuryeva,et al.  Simulation-based fitness landscape analysis and optimisation of complex problems , 2015 .

[70]  Jan Carmeliet,et al.  Building energy optimization: An extensive benchmark of global search algorithms , 2019, Energy and Buildings.

[71]  Jonathan A. Wright,et al.  A comparison of deterministic and probabilistic optimization algorithms for nonsmooth simulation-based optimization , 2004 .

[72]  Michael Affenzeller,et al.  Fitness Landscape Analysis of a Simulation Optimisation Problems with HeuristicLab , 2011, 2011 UKSim 5th European Symposium on Computer Modeling and Simulation.

[73]  Saman K. Halgamuge,et al.  Quantifying Variable Interactions in Continuous Optimization Problems , 2017, IEEE Transactions on Evolutionary Computation.

[74]  Weili Xu,et al.  Improving evolutionary algorithm performance for integer type multi-objective building system design optimization , 2016 .

[75]  Jean-Paul Watson,et al.  An Introduction to Fitness Landscape Analysis and Cost Models for Local Search , 2010 .

[76]  Jason Brownlee,et al.  Clever Algorithms: Nature-Inspired Programming Recipes , 2012 .