Elsevier

Energy and Buildings

Volume 34, Issue 9, October 2002, Pages 959-972
Energy and Buildings

Optimization of building thermal design and control by multi-criterion genetic algorithm

https://doi.org/10.1016/S0378-7788(02)00071-3Get rights and content

Abstract

The design of buildings is a multi-criterion optimization problem, there always being a trade-off to be made between capital expenditure, operating cost, and occupant thermal comfort. This paper investigates the application of a multi-objective genetic algorithm (MOGA) search method in the identification of the optimum pay-off characteristic between the energy cost of a building and the the occupant thermal discomfort. Results are presented for the pay-off characteristics between energy cost and zone thermal comfort, for three design days and three building weights. Inspection of the solutions indicates that the MOGA is able to find the optimum pay-off characteristic between the daily energy cost and zone thermal comfort. It can be concluded that multi-criterion genetic algorithm search methods offer great potential for the identification of the pay-off between the elements of building thermal design, and as such can help inform the building design process.

Introduction

It is common for buildings to be designed and constructed to a fixed capital cost. Within this capital expenditure, there may be some optimization of the design in an attempt to reduce running costs without prejudicing the thermal comfort of the building occupants. This approach however, pays no attention to the impact that a marginal increase in capital cost might have on the reduction in running costs or the improvement in occupant comfort. The coupling between these design criteria and its impact on the design solutions can be evaluated through the application of multi-criterion decision making (MCDM) methods. The MCDM process has two elements:

  • (1)

    the designer must make a decision as to which pay-off between the criteria results in the most desirable design solution;

  • (2)

    a procedure to search for one or more solutions that reflect the desired pay-off between the criteria.

The relationship between decision and search has three forms [1], [2].

  • •

    A priori preference articulation (decide → search), in which the decision maker (DM) defines the preferred pay-off between the criteria in advance of the search (for instance, the designer may say that the capital cost of the building is twice as important as the operating cost).

  • •

    Progressive preference articulation (decide ↔ search), in which the DM and search are intertwined, with the DM using progressive solutions to inform the decision making process and the final choice of pay-off.

  • •

    A posteriori preference articulation (search → decide), in which the DM is presented with a set of solutions and then chooses a final design solution from that set.

The most common a priori approach is one in which the DM assigns weights to each of criteria, the weighted sum of the criteria then forming a single design criterion. An optimization algorithm is then used to find the single design solution that minimizes the weighted sum of the criteria. For instance, the capital cost fc(X), and the operating cost fo(X), of a building could be transformed into a single design objective by assigning a weight (wc and wo), to each of the criteria and summing them (Eq. (1)). The sum of the criteria could then be minimized to produce a single design solution that provided a weighted pay-off between the capital and operating costs. The choice of weights may be arbitrary, although the weights could be defined through the life-cycle cost of a building since this is in principle a weighted sum of the capital and operating costs. f(X)=wofo(X)+wcfc(X)

Fig. 1 illustrates a possible pay-off between the capital and operating costs of the building. Suppose that the designer (DM), decided that minimizing capital cost was twice as important as minimizing the operating cost. Minimizing a single weighted criteria would result in one design solution on the pay-off curve. However, this does not provide the designer with information about how sensitive the operating cost is to changes in capital cost. For instance, the designer would not be able to evaluate the potential reduction in operating cost due to say a 50% increase in the capital cost.

The progressive preference articulation approach in part solves this problem, by generating at least one alternative to the single design solution (for instance, by assigning different weights and repeating the optimization). However, since the complete pay-off curve is not available, the information available to the designer is restricted to the narrow range of the solutions generated. Further, this approach is likely to be computationally too intensive for building thermal design, since each new solution would require a repeated optimization and simulation of the building thermal performance. Therefore, in this paper, the a posteriori preference articulation approach is advocated, in which the complete pay-off characteristic is determined in one optimization of the building design (thus minimizing the need for repeated optimization and associated simulation of building thermal performance).

An optimum pay-off characteristic may be represented by the Pareto set of solutions. Each solution in the set is said to be non-dominated by any other solution. This concept is illustrated in Fig. 2, which shows a set of seven sample solutions for two criteria (f1(X) and f2(X)). The non-dominated solutions in the set are indicated by a ranking of 0. For each of the non-dominated solutions, there is no other solution in the set that has a lower value in any criterion. The solution ranked 3 however, is “dominated” by three other solutions in the set; i.e. three other solutions have a lower value in both criteria.

Pareto multi-criterion optimization has been applied previously to the design of buildings [3]. The criteria considered were the thermal load, daylight availability, planning efficiency, and capital cost. The optimization problem was solved using a dynamic programming optimization algorithm, which although solutions where obtained, did not provide a sufficient number of solutions to allow the pay-off between the criteria to be examined. A potential solution to this deficiency is examined in this paper through the use of a multi-criterion genetic algorithm optimization method.

Note that the focus of this paper is on the search element of the MCDM process rather than the decision making element. The effectiveness of the search method is examined in relation to the optimum sizing of a heating, ventilating and air conditioning (HVAC) system, simultaneously with the optimization of its supervisory control strategy; identification of the pay-off between the system energy use and occupant comfort being the aim of the optimization.

Section snippets

Optimization algorithm

The search method advocated for finding the Pareto, non-dominated, set of solutions is based on a genetic algorithm (GA). Although several “traditional” multi-criterion optimization methods exist [2], they often require a sequential and therefore computationally intensive approach to finding the Pareto set of solutions. Rather than progressively minimizing a single possible solution, GAs operate with a set of possible solutions (known as the population). This enables several members (if not all

Example problem formulation

The multi-criterion optimization of building thermal systems is investigated here through the design of a single zone “all outside air” HVAC system. The system consists of a regenerative heat exchanger, cooling coil, heating coil, and supply fan (Fig. 3). The control system is open loop to the zone, since the optimization seeks to determine the supply air temperature (θs), and flow rate (Ms), in each hour such that the zone conditions remain comfortable. This control configuration has been

Results and analysis

The performance of the multi-criterion genetic algorithm has been investigated here for the solution of two optimization problems. In each case, for a given building construction, the pay-off is sort between the energy cost and occupant thermal discomfort. However, in the first optimization problem, only the summer design day of operation is considered, which reduces the scale of the optimization problem and consequently makes it easier to solve. In the second optimization problem, all three

Conclusions

The design of buildings is a multi-criterion optimization problem, there always being a trade-off to be made between capital expenditure, operating cost, and occupant thermal comfort. Such a design process can be informed by the application of MCDM techniques. The MCDM process has two elements, the search for viable solutions, and the decision as to which solution is the most desirable.

This paper investigates that application of a multi-criterion genetic algorithm in the search for a

Acknowledgments

The authors acknowledge the UK Engineering and Physical Science Research Council for funding this work. The authors would also like to acknowledge Professor Peter Fleming and Dr. Andrew Chipperfield of the University of Sheffield for the advice they have given on multi-objective genetic algorithm optimization.

References (17)

  • N.A. D’Cruz et al.

    Multi-criteria model for building performance and design

    Building and Environment

    (1987)
  • M.J. Ren et al.

    A ventilated slab thermal storage system model

    Building and Environment

    (1998)
  • D.A. Van Veldhuizen et al.

    Multi-objective evolutionary algorithms: analyzing the state-of-the-art

    Evolutionary Computation

    (2000)
  • K. Miettinen, Some methods for non-linear multi-objective optimization, Lecture Notes in Computer Science: Evolutionary...
  • C.A. Coello Coello, A short tutorial on evolutionary multi-objective optimization, Lecture Notes in Computer Science:...
  • D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley,Reading, MA,...
  • C.M. Fonesca, P.J. Fleming, Multi-objective Genetic Algorithms Made Easy: Selection, Sharing and Mating Restriction,...
  • C.M. Fonseca et al.

    Multi-objective optimization and multiple constraint handling with evolutionary algorithms. Part 1. A unified formulation

    IEEE Transactions on Systems and Cybernetics Part A: Systems and Humans

    (1998)
There are more references available in the full text version of this article.

Cited by (419)

View all citing articles on Scopus
View full text