Search methods for building design optimization

Various optimization algorithms are available to couple with building simulation tools. Each algorithm has its own benefits as well as limitations therefore selection of

optimization algorithm directly depends on the nature of the optimization problem in consideration.

As explained previously, in simulation-based building optimization, the objective function is estimated using building simulation and since simulation tools make approximation of reality, it causes objective function to be non-linear, non-smooth and discontinuous for some parameters. As highlighted by Attia (2013) the deterministic algorithms need the evaluation functions to have particular mathematical properties like the continuity and the derivability consequently, methods might fail to contribute reliable results while handling discontinuous building and HVAC problems with highly constrained characteristics and multi-objective functions. Alternatively, gradient-free methods are based on stochastic approaches are more suitable to building applications since they allow exploration of the whole search space, eventually focusing on regions of interest only, and finally converging towards a near-optimal solution. With methods of this type, no hypothesis about the regularity of objective functions is necessary. This makes them easier to couple to building assessment tools. Therefore, as mentioned by Nguyen et al. (2014), stochastic population-based algorithms are the most frequently used methods in building performance optimization.

The performance of several optimization algorithms were tested and analysed in some studies. Wetter and Wright (2004) compared the performance of nine optimization algorithms using numerical experiments. Their study dealt with four main optimization classes: direct search algorithms (the coordinate search, the Hooke–Jeeves, and two versions of the Nelder–Mead simplex algorithm), stochastic population-based algorithms (a simple genetic algorithm (GA) and two particle swarm optimization (PSO) algorithms), a hybrid particle swarm Hooke–Jeeves algorithm and a gradient-based algorithm (the discrete Armijo gradient algorithm).

The analyses are carried out through a simple and a complex simulation model.

Direct search methods do not require any information on the derivatives of the objective function. A General Pattern Search (GPS) algorithm defines some point around the current point and aims at the point with an objective function more desirable than the current point’s and searches along each coordinate direction for a decrease in objective function.

The Hooke–Jeeves algorithm has the same convergence properties on smooth cost functions as the coordinate search algorithm. However, it makes progressively bigger steps in the direction that has reduced the cost in previous iterations.

Stochastic population-based algorithms studied in the work belong to the family of evolutionary algorithms.

Genetic algorithm (GA) is a population-based algorithm that mimics the process of natural evolution. It generates solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover.

PSO algorithm was proposed first by Eberhart and Kennedy (1995). Individuals are here called particles, and they move round in the search-space according to simple mathematical formula over the particle's position and velocity. The change of each particle from one iteration to the next is modeled based on the social behaviour of flocks of birds or schools of fish.

The hybrid global optimization algorithm does a PSO on a mesh for the first iterations. Afterwards, it starts the Hooke–Jeeves algorithm.

The Nelder Mead simplex algorithm attempts to minimize a scalar-valued nonlinear function of n real variables using only function values, without any derivative information.

Armijo is a line search method, which can be used to minimize smooth functions. It approximates gradients by finite differences, with the difference increment reduced as the optimization progresses.

The analysis by Wetter and Wright (2004) showed that the gradient-based Armijo method failed far from the optimal solution even for the simpler problem. Similarly, the Nelder–Mead algorithm did not perform well on the test problems as well. It required a high number of simulations, and in one test case, it failed far from the minimum. Neither of the algorithms is recommended for building performance optimization problems.

Moreover, according to results the coordinate search algorithm tends to fail far from the minimum if the detailed simulation model is used. On the same problems, the Hooke–Jeeves algorithm also jammed less frequently compared to the coordinate search algorithm, which may be due to the larger steps that are taken in the global

Both GA and PSO algorithms performed well, where the simple GA got close to a solution with a low number of simulations. However, the biggest cost reduction was obtained with the hybrid PSO-Hooke Jeeves algorithm but it required a greater number of simulations.

Similarly, Kämpf et al. (2010) analysed the performance of two hybrid algorithms that are Particle swarm optimization coupled with Hooke Jeeves (PSO-HJ) and covariance matrix adaptation evolution strategy coupled with hybrid differential evolution algorithms (CMAES/HDE) in optimizing 5 standard benchmark functions through EnergyPlus simulation tool. The results showed that CMAES/HDE performed better than the PSO-HJ in solving the benchmark functions with 10 dimensions or less. However, if the number of dimensions is larger than 10, the PSO-HJ performed better.

Moreover Brownlee et al. (2011) investigated the performance of five multi- objective algorithms, namely IBEA, MOCell, NSGA-II, SPEA2 and PAES on a multi-objective problem concerning window placement. The results showed that NSGA-II showed the best performance among all.

3.3.2.1 Building performance optimization tools

There are several computer tools are available to solve an optimization problem once it has been properly formulated. Numerous decent algorithms are implemented in these programs to deal with different kind of optimization issues.

Some tools include optimization algorithm libraries that can search for best design option for general optimization problems.

Nyungen et al. (2014), Machairas et al. (2014) and Attia et al. (2013) explored the stand-alone optimization tools used in building optimization studies and the most frequently mentioned tools are found to be GenOpt, Matlab Optimization Toolbox, and modeFrontier. Some less frequent tools are named as GENE_ARCH, Dakota, jEPlus, Topgui and Toplight. Moreover Nguyen et al. (2014) mentioned a new free tool, MOBO, as showing promising capabilities to become the major optimization engine in coming years.

In this study, only the tools that caught the most of the attention of research community will be introduced shortly.

GenOpt®

GenOpt is a generic optimization program developed at Lawrence Berkeley National Laboratory that has implemented a number of optimization algorithms (GenOpt, 2012). It is a stand-alone program that is designed to be coupled with any simulation program that reads from and writes to text files. GenOpt is designed to work with programs where the derivative of the cost function is not available or may not even exist. GenOpt can handle single-objective optimization with continuous and discrete variables and some constraints.

The algorithms that are available in GenOpt’s library are: Coordinate Search Algorithm, Hooke-Jeeves Algorithm, Multi-Start GPS Algorithms, Discrete Armijo Gradient, Particle Swarm Optimization, Hybrid Generalized Pattern Search Algorithm with Particle Swarm Optimization Algorithm, Simplex Algorithm of Nelder and Mead with the Extension of O’Neill, Interval Division Algorithms, and Algorithms for Parametric Runs.

Since one of GenOpt’s main application fields is building energy use or operation cost optimization, GenOpt has been designed such that it addresses the special properties of optimization problems in this area.

GenOpt has been used in several building optimization studies including Wetter and Wright (2004), Djuric et al. (2007), Coffey (2008), Hasan et al. (2008), Magnier et al. (2009), Kämpf et al. (2010), Coffey et al. (2010), Seo et al. (2011), Boonbumroong et al. (2011), Stephan et al. (2011), Asadi et al. (2012), Rapone and Saro (2012), Bigot et al. (2013), Ali et al. (2013), Cvetković and Bojić (2014), Ferrara (2014), Joe et al. (2014).

MATLAB® Optimization Toolbox

Optimization Toolbox™ extends the MATLAB® technical computing environment with tools and widely used algorithms for standard and large-scale optimization.

These algorithms solve constrained and unconstrained continuous and discrete problems. The toolbox includes functions for linear programming, quadratic programming, nonlinear optimization, nonlinear least squares, solving systems of nonlinear equations, multi-objective optimization, and binary integer programming Moreover, MATLAB Global Optimization Toolbox includes global search, multistart, pattern search, genetic algorithm, and simulated annealing solvers

MATLAB optimization environment has been used in a variety of studies including Shea et al. (2006), Jacob et al. (2010), Hamdy et al. (2011), Asadi et al. (2012), Trubiano et al. (2013), Asadi et al. (2014), Murray et al. (2014).

modeFRONTIER®

modeFRONTIER is an integration platform for objective and multi-disciplinary optimization. It provides a seamless coupling with third party engineering tools, enables the automation of the design simulation process, and facilitates analytic decision making. modeFRONTIER has a rich optimization algorithm library covering deterministic, stochastic and heuristic methods for both single and multi-objective problems including Levenberg-Marquart, Broyden–

Fletcher–Goldfarb–Shanno, Sequential quadratic programming, Multi-objective Genetic Algorithm (MOGA-II),Adaptive range Multi-objective Genetic Algorithm (ARMOGA), Fast Multi-objective Genetic Algorithm (FMOGA-II), Non-dominated Sorting Genetic Algorithm (NSGA-II), Multi-objective Particle Swarm Optimization and Multi-objective Simulated Annealing (Esteco, 2014).

MATLAB optimization environment has been used in a variety of studies including Suga et al. (2010), Hoes et al. (2011), Shi (2011), Loonen et al. (2011), Padovan and Manzan (2014), Manzan (2014), Baglivo et al. (2014).