Alexander E. I. Brownlee

Constrained, mixed-integer and multi-objective optimisation of building designs by NSGA-II with fitness approximation

Graphical abstractDisplay Omitted HighlightsA surrogate based on radial basis function networks is adapted for mixed-type variables, multiple objectives and constraints and integrated into NSGA-II.A deterministic method to include infeasible solutions in the population is proposed.Variants of NSGA-II including these changes are applied to a typical building optimisation problem, with improvements in solution quality and convergence speed.Analysis of the constraint handling and fitness landscape of the problem is also conducted. Reducing building energy demand is a crucial part of the global response to climate change, and evolutionary algorithms (EAs) coupled to building performance simulation (BPS) are an increasingly popular tool for this task. Further uptake of EAs in this industry is hindered by BPS being computationally intensive: optimisation runs taking days or longer are impractical in a time-competitive environment. Surrogate fitness models are a possible solution to this problem, but few approaches have been demonstrated for multi-objective, constrained or discrete problems, typical of the optimisation problems in building design. This paper presents a modified version of a surrogate based on radial basis function networks, combined with a deterministic scheme to deal with approximation error in the constraints by allowing some infeasible solutions in the population. Different combinations of these are integrated with Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and applied to three instances of a typical building optimisation problem. The comparisons show that the surrogate and constraint handling combined offer improved run-time and final solution quality. The paper concludes with detailed investigations of the constraint handling and fitness landscape to explain differences in performance.

Approaches to selection and their effect on fitness modelling in an Estimation of Distribution Algorithm

Selection is one of the defining characteristics of an evolutionary algorithm, yet inherent in the selection process is the loss of some information from a population. Poor solutions may provide information about how to bias the search toward good solutions. Many estimation of distribution algorithms (EDAs) use truncation selection which discards all solutions below a certain fitness, thus losing this information. Our previous work on distribution estimation using Markov networks (DEUM) has described an EDA which constructs a model of the fitness function; a unique feature of this approach is that because selective pressure is built into the model itself selection becomes optional. This paper outlines a series of experiments which make use of this property to examine the effects of selection on the population. We look at the impact of selecting only highly fit solutions, only poor solutions, selecting a mixture of highly fit and poor solutions, and abandoning selection altogether. We show that in some circumstances, particularly where some information about the problem is already known, selection of the fittest only is suboptimal.

A fully multivariate DEUM algorithm

Distribution Estimation Using Markov network (DEUM) algorithm is a class of estimation of distribution algorithms that uses Markov networks to model and sample the distribution. Several different versions of this algorithm have been proposed and are shown to work well in a number of different optimisation problems. One of the key similarities between all of the DEUMalgorithms proposed so far is that they all assume the interaction between variables in the problem to be pre given. In other words, they do not learn the structure of the problem and assume that it is known in advance. Therefore, they may not be classified as full estimation of distribution algorithms. This work presents a fully multivariate DEUM algorithm that can automatically learn the undirected structure of the problem, automatically find the cliques from the structure and automatically estimate a joint probability model of the Markov network. This model is then sampled using Monte Carlo samplers. The proposed DEUM algorithm can be applied to any general optimisation problem even when the structure is not known.

An application of a multivariate estimation of distribution algorithm to cancer chemotherapy

Chemotherapy treatment for cancer is a complex optimisation problem with a large number of interacting variables and constraints. A number of different heuristics have been applied to it with varying success. In this paper we expand on this by applying two estimation of distribution algorithms to the problem. One is UMDA and the other is hBOA, the first EDA using a multivariate probabilistic model to be applied to the chemotherapy problem. While instinct would lead us to predict that the more sophisticated algorithm would yield better performance on a complex problem like this, we show that it is outperformed by the algorithms using the simpler univariate model. We hypothesise that this is caused by the more sophisticated algorithm being impeded by the large number of interactions in the problem which though present, do not complicate the search for optima.

Multi-objective optimization of cellular fenestration by an evolutionary algorithm

This paper describes the multi-objective optimized design of fenestration that is based on the façade of the building being divided into a number of small regularly spaced cells. The minimization of energy use and capital cost by a multi-objective genetic algorithm was investigated for: two alternative problem encodings (bit-string and integer); the application of constraint functions to control the aspect ratio of the windows; and the seeding of the search with feasible design solutions. It is concluded that the optimization approach is able to find near locally Pareto optimal solutions that have innovative architectural forms. Confidence in the optimality of the solutions was gained through repeated trail optimizations and a local search and sensitivity analysis. It was also concluded that seeding the optimization with feasible solutions was important in obtaining the optimum solutions when the window aspect ratio was constrained.

Structure learning and optimisation in a Markov-network based estimation of distribution algorithm

Structure learning is a crucial component of a multivariate Estimation of Distribution algorithm. It is the part which determines the interactions between variables in the probabilistic model, based on analysis of the fitness function or a population. In this paper we take three different approaches to structure learning in an EDA based on Markov networks and use measures from the information retrieval community (precision, recall and the F-measure) to assess the quality of the structures learned. We then observe the impact that structure has on the fitness modelling and optimisation capabilities of the resulting model, concluding that these results should be relevant to research in both structure learning and fitness modelling.

Solving the MAXSAT problem using a multivariate EDA based on Markov networks

Markov Networks (also known as Markov Random Fields) have been proposed as a new approach to probabilistic modelling in Estimation of Distribution Algorithms (EDAs). An EDA employing this approach called Distribution Estimation Using Markov Networks (DEUM) has been proposed and shown to work well on a variety of problems, using a unique fitness modelling approach. Previously DEUM has only been demonstrated on univariate and bivariate complexity problems. Here we show that it can be extended to a difficult multivariate problem and is capable of accurately modelling a fitness function and locating an optimum with a very small number of function evaluations.

Fitness Modeling With Markov Networks

Fitness modeling has received growing interest from the evolutionary computation community in recent years. With a fitness model, one can improve evolutionary algorithm efficiency by directly sampling new solutions, developing hybrid guided evolutionary operators or using the model as a surrogate for an expensive fitness function. This paper addresses several issues on fitness modeling of discrete functions, particularly how modeling quality and efficiency can be improved. We define the Markov network fitness model in terms of Walsh functions. We explore the relationship between the Markov network fitness model and fitness in a number of discrete problems, showing how the parameters of the fitness model can identify qualitative features of the fitness function. We define the fitness prediction correlation, a metric to measure fitness modeling capability of local and global fitness models. We use this metric to investigate the effects of population size and selection on the tradeoff between model quality and complexity for the Markov network fitness model.

Statistical optimisation and tuning of GA factors

This paper presents a practical methodology of improving the efficiency of genetic algorithms through tuning the factors significantly affecting GA performance. This methodology is based on the methods of statistical inference and has been successfully applied to both binary-and integer-encoded genetic algorithms that search for good chemotherapeutic schedules

A multi-objective window optimisation problem

We present an optimisation problem which seeks to locate the Pareto-optimal front of building window and shading designs minimising two objectives: projected energy use of the operational building and its construction cost. This problem is of particular interest because it has many variable interactions and each function evaluation is relatively time-consuming. It also makes use of a freely-available building simulation program EnergyPlus which may be used in many other building design optimisation problems. We describe the problem and report the results of experiments comparing the performance of a number of existing multi-objective evolutionary algorithms applied to it. We conclude that this represents a promising real-world application area.