Dynamic multi-objective heating optimization

doi:10.1016/S0377-2217(01)00282-X

European Journal of Operational Research

Volume 142, Issue 1, 1 October 2002, Pages 1-15

https://doi.org/10.1016/S0377-2217(01)00282-X Get rights and content

Abstract

We develop a multicriteria approach to the problem of space heating under a time varying price of electricity. In our dynamic goal programming model the goals are ideal temperature intervals and the other criteria are the costs and energy consumption. We discuss the modelling requirements in multicriteria problems with a dynamic structure and present a new relaxation method combining the traditional ϵ-constraint and goal programming (GP) methods. The multi-objective heating optimization (MOHO) application in a spreadsheet environment with numerical examples is described.

Introduction

In this paper we introduce an application of multicriteria optimization from our everyday environment. The problem is to optimize the indoor temperature, i.e., thermal comfort in a residential house. The problem is methodologically quite interesting as decision support is clearly needed due to the system dynamics and the necessity to tradeoff preferences which are costs and comfort over time. The definition of comfort is a complex issue in itself [13]. This paper develops a new goal programming (GP) approach. The dynamics of the problem arises from three factors: the house acts as a heat storage, the price of electricity is time varying and the outdoor temperature changes over the day. The criteria included in the model are the total heating costs, the energy consumed and the living comfort implicitly defined through the levels and variations of hourly indoor temperature. The model is implemented on a spreadsheet application multi-objective heating optimization (MOHO) [18] which is used to illustrate the solutions. A setting of this kind is a realistic one both for small residential and large commercial electricity users. With the introduction of deregulated energy markets [37] the possibilities of a consumer to be offered innovative pricing contracts is increasing. In the old regulated environment there could exist national legislation determining the acceptable types of time varying prices (such as time of use, TOU). Today the situation has changed, at least in the Nordic countries, where the distribution and selling of electricity are separated by law. You can buy electricity from any supplier and not only from your local distributor [19], [37]. There can be brokers who can have different kinds of dynamic pricing policies to offer. Customers are also willing to subscribe to such policies and act reactively in their use of electricity. It is this setting which is of interest in the model presented here. The implementation described remains still a research effort which is not yet available commercially. However, it has successfully been tested with consumers by the utility of Helsinki Energy. There are no technical reasons why a system like this could not be implementable in real life. In fact, the authors do believe that this will be an optional direction for future pricing policies as part of the so-called smart house concept. Environmental issues are also related to the avoidance of demand peaks. They are often met with more polluting reserve generation units. Naturally, policies of this kind become increasingly interesting in larger commercial and community buildings.

Section snippets

Goal programming

GP is a widely used [47] multicriteria method originally presented in 1955 by Charnes and Cooper [9]. The name GP was introduced only later in a book from 1961 [7], where it was described as an extension to linear programming (LP). Today there are new textbooks, e.g., by Ignizio [21], [22]. Some modelling and critical issues of GP are discussed in [41] and more recent developments can be found in [4], [51].

In the multicriteria setting the special characteristic of GP models is the way the

Dynamic multicriteria problems and interval GP

This paper discusses modelling approach needed when dynamics are involved in multicriteria problems and provides a real life example of such problem, namely heating optimization. In particular we study the use of intervals in the definition of the goals. Already in [6], [10] and in the survey paper of Charnes and Cooper [8] the possibility of using goal intervals, i.e., goal sets, was presented. Some related early applications include financial planning [27] and water reservoir management [5].

GPϵ method

In multi-objective analysis one often wants to study the effects of relaxing some goal constraints. This is particularly relevant in dynamic GP where the DM needs to provide goal values for each criterion at each stage. Therefore, we will introduce a method combining the ϵ-constraint method of Haimes [15], [16] and GP in the heating problem. For simplicity, we consider minimization of all the criteria, i.e., $min_{x∈S} {f_{1} (x),f_{2} (x),…,f_{k} (x)},$ where x=(x₁,x₂,…,x_n) is the n-dimensional vector of decision

Multi-objective heating optimization

The objective of residential heating systems is to keep the indoor temperature within comfortable limits. The traditional control device is a thermostat which keeps the indoor temperature close to the preset level. However, if the price of electricity is time dependent, there is a possibility to save in heating costs by using the house as a heat storage. This leads to a multicriteria problem of maximizing the living comfort and minimizing the heating costs under a given price of electricity,

The spreadsheet application MOHO

The overall setting for the heating is shown in Figs. 4 and 5 shows the interfaces of the related spreadsheet application MOHO. The house parameters consist of the dynamic heat transfer model of the house and the maximum heating power. The variable planning parameters include electricity price for each hour and the outdoor temperatures at five time points.

Before the optimization takes place the DM needs to give his or her preferences. In the first step the DM specifies his indoor temperature

Conclusions

We show how the space heating of a house can be formulated as a dynamic multicriteria optimization problem, and that one can successfully use the spreadsheet as a modelling environment for finding the solution. Instead of directly dealing with the tradeoffs between criteria, we suggest a stepwise procedure. It starts by first minimizing the costs or energy consumption and continues then by respecifying the goal or relaxing the temperature limits. We present a new GPϵ method combining the ϵ

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R.P. Hämäläinen, J. Mäntysaari, Power Agents v. 1.0, Computer Software, Systems Analysis Laboratory, Helsinki...

R.P. Hämäläinen, J. Mäntysaari, MOHO – Multi-Objective Heating Optimization v. 1.0, Computer Software, Systems Analysis...

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Continuous OptimizationDynamic multi-objective heating optimization

Abstract

Introduction

Section snippets

Goal programming

Dynamic multicriteria problems and interval GP

GPϵ method

Multi-objective heating optimization

The spreadsheet application MOHO

Conclusions

Socio-Economic Planning Sciences

Omega

Energy – The International Journal

European Journal of Operational Research

European Journal of Operational Research

Omega

International Transactions in Operational Research

Automatica

Energy Policy

Energy Economics

European Journal of Operational Research

Fuzzy Sets and Systems

Valuing the future: A MADA example involving nuclear waste storage

Journal of Multi-Criteria Decision Analysis

Existence of efficient solutions for vector maximization problems

Journal of Optimization Theory and Applications

Goal programming with dynamic goals

Journal of Multi-Criteria Decision Analysis

Real-time reservoir operations by goal programming

Journal of Water Resources Planning and Management

Management Models and Industrial Applications of Linear Programming

Goal programming and multiple objective optimization

European Journal of Operational Research

Optimal estimation of executive compensation by linear programming

Management Science

A goal interval programming model for resource allocation in a marine environmental protection program

Journal of Environmental Economics and Management

Saving energy using market-based control

Multiobjective energy generation planning under uncertainty

Transactions of Institute of Industrial Engineers

Thermal Comfort

On a bicriterion formulation of the problems of integrated systems identification and system optimization

IEEE Transactions on Systems, Man, and Cybernetics

Hierarchical Multiobjective Analysis of Large-Scale Systems

Continuous Optimization
Dynamic multi-objective heating optimization