Objectives In Multi-objective Optimization Research Articles

A GP-Based Hierarchical Objectives Decision-Making Method for Building Energy Efficiency Optimization

Building energy efficiency, which is critical in reducing environmental impact, has become one of the most important objectives of building designs. In order to precisely express the goals of building designs, and help decision makers estimate the ultimate performance of design schemes in advance when searching for the optimal building design, the Goal Programming Model (GPM) is introduced in this study to provide a solution for explicit design objective delivery and multi-stakeholder involved decision-making support. In this proposed method, EnergyPlusTM works as a simulation engine to search for the relationship between design parameter combinations and building energy consumption. Simultaneously, Genetic Algorithm (GA) is used to improve the efficiency of overall building energy performance optimization by processing multiple iterations. A case study with five possible design scenarios was dedicated in this study to implement the proposed optimization method, and the optimization results verified the capacity of the established GP-based optimization method to satisfy various design requirements for decision makers and/or stakeholders, especially in facing the hierarchical objectives with different priorities. In this case, the envelope-related variables, including the exterior wall and window, serve as optimization objectives. The optimization is carried out under the ideal air conditioning system, considering different energy usage patterns. Meanwhile, comparing with the vague and restricted expression of objectives in multi-objective optimization, the proposed GP-based optimization method provides explicit trade-off relationships among various objectives for designers, which improves the practical value of the optimized designs, so as to ensure the project success and facilitate the development of green buildings.

Comparison of Objectives in Multiobjective Optimization of Ultrasonic Positioning Anchor Placement

The position of anchors in an ultrasonic positioning system has a significant impact on the performance of that system. This impact on performance can be in the form of positioning error, how large of a space the system can cover, and then number of anchors required. A comparison of three different performance metrics for anchor position optimization in ultrasonic localization systems is presented. These metrics are geometric dilution of precision (GDOP), weighted GDOP (WGDOP), and simulated localization error (SLE). Each of these performance metrics is used as an objective in a multi-objective genetic algorithm. The optimal solutions found by the genetic algorithm were processed by a simulation that used a simulated received time series to localize the target position allowing a direct comparison of the three performance metrics. While the performance difference between all three metrics was small, it was found that solutions generated using WGDOP as a metric of performance outperformed those generated using the GDOP and the SLE objectives.

A New Bi-Level Planning Approach to Find Economic and Reliable Layout for Large-Scale Wind Farm

This paper presents a bi-level planning approach to find an optimal layout for a large-scale wind farm (WF) from economic and reliability perspectives. The upper level of the planning approach is formulated as constrained multi-objective optimization (MOO) to obtain the optimal WF layout, where two conflicting objectives are optimized simultaneously. Two objectives for MOO are i) yearly gross energy production and ii) annual loan repayment (for cable and land area of the WF), where the first objective is maximized and the second objective is minimized. Jensen's wake model is used to calculate the wake effect, and to evaluate the multiple wake effect within a WF, a coordinate-transformation-based approach has been adopted in this study. An efficient hybrid multi-objective metaheuristic algorithm, which is based on nondominated sorting multi-objective particle swarm optimization and improved archive multi-objective simulated annealing, has been proposed to find the optimized WF layout. The superiority of the Pareto front obtained by the proposed algorithm for the large-scale WF layout is supported by its comparison with different powerful and well-established MOO algorithms. In the lower level of the proposed approach, economic and reliability analyses of the solutions (WF layout), obtained in the Pareto front by the proposed hybrid algorithm, have been done. In this context, two performance metrics, a) generation economy index and b) expected wind energy generation (EWEG), have been considered. A sequential Monte Carlo simulation has been developed to calculate the EWEG considering random failure of both wind turbines and cables in this paper. The most suitable WF layout is selected by trading off between economy and reliability using a fuzzy decision-making approach.

Multi-Objective Optimization of Energy Saving Control for Air Conditioning System in Data Center

A multi-objective optimization scheme is proposed to save energy for a data center air conditioning system (ACS). Since the air handling units (AHU) and chillers are the most energy consuming facilities, the proposed energy saving control scheme aims to maximize the saved energy for these two facilities. However, the rack intake air temperature tends to increase if the energy saving control scheme applied to AHU and chillers is conducted inappropriately. Both ACS energy consumption and rack intake air temperature stabilization are set as two objectives for multi-objective optimization. The non-dominated sorting genetic algorithm II (NSGA-II) is utilized to solve the multi-objective optimization problem. In order for the NSGA-II to evaluate fitness functions that are both the ACS total power consumption and AHU outlet cold air temperature deviations from a specified range, neural network models are utilized. Feedforward neural networks are utilized to learn the power consumption models for both chillers and AHUs as well as the AHU outlet cold air temperature based on the recorded data collected in the field. The effectiveness and efficiency of the proposed energy saving control scheme is verified through practical experiments conducted on a campus data center ACS.

Multi-objective optimization of thermo-acoustic devices using teaching-learning-based optimization algorithm

The current article presents three case studies based on a multi-objective optimization approach to optimize the performance of thermo-acoustic devices by obtaining the best possible set of geometrical characteristic parameters. In case study 1, the performance of a thermo-acoustic refrigerator is measured in terms of three objectives namely, acoustic cooling load (ΦC), coefficient of performance, and acoustic power loss (W02). Each objective is assigned a weight to facilitate suitable user-defined significance. The case study 2 aims to optimize a thermoacoustic prime-mover. The influence of stack position and its length, resonator length, plate thickness, and plate spacing are considered as design variables. Two objectives namely, pressure amplitude (P) and frequency (f) are considered as objectives for multi-objective optimization of the thermo-acoustic prime-mover. In case study 3, the performance of a thermo-acoustic engine is measured in terms of five objectives namely, work output (W), viscous loss (Rv), conductive heat loss (Qcond), convective heat loss (Qconv), and radiative heat loss (Qrad). Since the multiple objectives are to be optimized simultaneously, each objective is assigned a weight to facilitate suitable user-defined significance. The multi-objective optimization is carried out by the teaching-learning-based optimization algorithm. The results of application of teaching-learning-based optimization algorithm are compared with the results of General Algebraic Modeling System, response surface methodology, and experimental results. The results of the teaching-learning-based optimization algorithm are found better compared to those given by the other approaches.

On the effects of combining objectives in multi-objective optimization

In multi-objective optimization, one considers optimization problems with more than one objective function, and in general these objectives conflict each other. As the solution set of a multi-objective problem is often rather large and contains points of no interest to the decision-maker, strategies are sought that reduce the size of the solution set. One such strategy is to combine several objectives with each other, i.e. by summing them up, before employing tools to solve the resulting multi-objective optimization problem. This approach can be used to reduce the dimensionality of the objective space as well as to discard certain unwanted solutions, especially the ‘extreme’ ones found by minimizing just one of the objectives given in the classical sense while disregarding all others. In this paper, we discuss in detail how the strategy of combining objectives linearly influences the set of optimal, i.e. efficient solutions.

Uncovering relationships between environmental metrics in the multi-objective optimization of energy systems: A case study of a thermal solar Rankine reverse osmosis desalination plant

Multi-objective optimization (MOO) is increasingly being used in a wide variety of applications to identify alternatives that balance several criteria. The energy sector is not an exception to this trend. Unfortunately, the complexity of MOO grows with the number of environmental objectives. This limitation is critical in energy systems, in which several environmental criteria are typically used to assess the merits of a given technology. In this paper, we investigate the use of a rigorous dimensionality reduction method for reducing the complexity of MOO as applied to an energy system (i.e., a solar Rankine cycle coupled with reverse osmosis and thermal storage). Instead of using an aggregated environmental metric, a common approach for reducing the number of environmental objectives in MOO, we propose to optimize the system in a reduced search space of objectives that fully describe its performance and which results from eliminating redundant criteria from the analysis. Numerical results show that it is possible to reduce the problem complexity by omitting redundant environmental indicators from the optimization.

On the use of Principal Component Analysis for reducing the number of environmental objectives in multi-objective optimization: Application to the design of chemical supply chains

Multi-objective optimization (MOO) has recently attracted an increasing interest in environmental engineering. One major limitation of the existing solution methods for MOO is that their computational burden tends to grow rapidly in size with the number of environmental objectives. In this paper, we study the use of Principal Component Analysis (PCA) to identify redundant environmental metrics in MOO that can be omitted without disturbing the main features of the problem, thereby reducing the associated complexity. We show that, besides its numerical usefulness, the use of PCA coupled with MOO provides valuable insights on the relationships between environmental indicators of concern for decision-makers. The capabilities of the proposed approach are illustrated through its application to the design of environmentally conscious chemical supply chains (SCs).

A novel MILP-based objective reduction method for multi-objective optimization: Application to environmental problems

Abstract Multi-objective optimization has recently emerged as a useful technique in sustainability analysis, as it can assist in the study of optimal trade-off solutions that balance several criteria. The main limitation of multi-objective optimization is that its computational burden grows in size with the number of objectives. This computational barrier is critical in environmental applications in which decision-makers seek to minimize simultaneously several environmental indicators of concern. With the aim to overcome this limitation, this paper introduces a systematic method for reducing the number of objectives in multi-objective optimization with emphasis on environmental problems. The approach presented relies on a novel mixed-integer linear programming formulation that minimizes the error of omitting objectives. We test the capabilities of this technique through two environmental problems of different nature in which we attempt to minimize a set of life cycle assessment impacts. Numerical examples demonstrate that certain environmental metrics tend to behave in a non-conflicting manner, which makes it possible to reduce the dimension of the problem without losing information.

G-dominance: Reference point based dominance for multiobjective metaheuristics

One of the main tools for including decision maker (DM) preferences in the multiobjective optimization (MO) literature is the use of reference points and achievement scalarizing functions [A.P. Wierzbicki, The use of reference objectives in multiobjective optimization, in: G. Fandel, T. Gal (Eds.), Multiple-Criteria Decision Making Theory and Application, Springer-Verlag, New York, 1980, pp. 469–486.]. The core idea in these approaches is converting the original MO problem into a single-objective optimization problem through the use of a scalarizing function based on a reference point. As a result, a single efficient point adapted to the DM’s preferences is obtained. However, a single solution can be less interesting than an approximation of the efficient set around this area, as stated for example by Deb in [K. Deb, J. Sundar, N. Udaya Bhaskara Rao, S. Chaudhuri, Reference point based multiobjective optimization using evolutionary algorithms, International Journal of Computational Intelligence Research, 2(3) (2006) 273–286]. In this paper, we propose a variation of the concept of Pareto dominance, called g-dominance, which is based on the information included in a reference point and designed to be used with any MO evolutionary method or any MO metaheuristic. This concept will let us approximate the efficient set around the area of the most preferred point without using any scalarizing function. On the other hand, we will show how it can be easily used with any MO evolutionary method or any MO metaheuristic (just changing the dominance concept) and, to exemplify its use, we will show some results with some state-of-the-art-methods and some test problems.

Optimization strategy based on genetic algorithms and neural networks applied to a polymerization process

AbstractThe article presents a simple and general methodology, especially destined to the optimization of complex, strongly nonlinear systems, for which no extensive knowledge or precise models are available. The optimization problem is solved by means of a simple genetic algorithm, and the results are interpreted both from the mathematical point of view (the minimization of the objective function) and technological (the estimation of the achievement of individual objectives in multiobjective optimization). The use of a scalar objective function is supported by the fact that the genetic algorithm also computes the weights attached to the individual objectives along with the optimal values of the decision variables. The optimization strategy is accomplished in three stages: (1) the design and training of the neural model by a new method based on a genetic algorithm where information about the network is coded into the chromosomes; (2) the actual optimization based on genetic algorithms, which implies testing different values for parameters and different variants of the algorithm, computing the weights of the individual objectives and determining the optimal values for the decision variables; (3) the user's decision, who chooses a solution based on technological criteria. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008