A new preference handling technique for interactive multiobjective optimization without trading-off

There is an increasing trend in the use of multi-objective evolutionary algorithms (MOEAs) to solve multi-objective optimization problems of the allocation of water resources. However, typically the outcome is a set of Pareto optimal solutions which make up a trade-off surface between the objective functions. For decision makers to choose a satisfactory alternative from a set of Pareto-optimal solutions, this paper suggests a new method based on least squares support vector machine (LSSVM) and k-means clustering for ranking the optimal solutions for the multi-objective allocation of water resources. First, the k-means clustering method was adopted to reduce the large set of solutions to a few representative solutions. Then, to capture and represent the decision maker's preferences as well as to select the most desirable alternative, the LSSVM method was applied to obtain the utility value for each representative solution. According to the magnitude of the utility values, the final priority orders of the representative solutions were determined. Finally, this methodology was applied to rank the Pareto optimal solution set obtained from the multi-objective optimization problems of water resources allocation for the water-receiving areas of the South-to-North Water Transfer Project in Hebei Province, China. Moreover, the comparisons of the proposed method with the information entropy method and the artificial neural network (ANN) model were given. The results of the comparison indicate that the proposed method has the ability to rank the non-dominated solutions of the multi-objective operation optimization model and that it can be employed for decision-making on water allocation and management in a river basin.

To address problems with multiple conflicting objective functions while incorporating preference information from a decision maker (a domain expert), interactive evolutionary multiobjective optimization methods have been proposed and widely adopted. To systematically assess the performance of these methods, it is desirable to have indicators that not only rely on the Pareto dominance relation, where solutions with better objective function values are preferred, but also take the decision maker's preferences into account. In this way, indicator values can meaningfully reflect the decision maker's preferences and the quality of the solutions obtained. In this paper, we propose the first performance indicator that incorporates preference information in the form of two reference points, specifically, an aspiration point, consisting of aspiration levels that represent the decision maker's full satisfaction, and a reservation point, consisting of reservation levels that represent dissatisfaction. The new indicator, termed D-PHI, translates information about reservation and aspiration points into a transformed hypervolume measure that assesses the performance of a solution set. We introduce D-PHI with an extended set of guidelines for preference-based performance evaluation, discuss its theoretical properties, and demonstrate its behavior through empirical examples. Moreover, we define a complementary indicator (CI) based on a so-called achievement scalarizing function. CI offers additional insight into whether aspiration and reservation levels have been achieved, and its usefulness is demonstrated through examples.

In reliability allocation, certain reliability values are assigned to subsystems and components to achieve the required system reliability. One big challenge in solving such reliability‐based design problems is how to handle the uncertain preferences of a decision maker on multiple attributes of interest. In this paper, we propose a new ordered weighted averaging (OWA) method based on an analytic hierarchy process to address the decision maker's uncertain preferences in reliability allocation. In the proposed OWA operator, a bi‐objective mathematical programming model considering both maximal entropy and minimal variance is transformed into a single‐objective mathematical programming model using an ideal‐point method. The maximum entropy minimal variance OWA operator takes full advantage of available information and avoids overestimating the decision maker's preferences. A detailed computational procedure is presented to facilitate the implementation of the proposed method in practice. An illustrative example about the powertrain of fuel cell vehicles is provided to demonstrate the effectiveness of this method in handling multiple attributes with uncertain preferences in reliability allocation. Copyright © 2015 John Wiley & Sons, Ltd.

Data envelopment analysis (DEA) model has been applied for evaluating bank branches and recognizing efficient and inefficient branches can help bank managers to provide appropriate strategies to improve the inefficient branches' performance. Conventional DEA models are based on the ‘black box’ approach. However, the process of providing services in banks is made up of interactive and interdependent processes. Additionally, some managers tend to incorporate their preferences in evaluation process. In this paper, best worst method (BWM) is used for incorporating decision maker (DM) preferences in two‐stage DEA model. First, BWM model is applied to obtain the weights of inputs, intermediate measures and outputs based on DM's judgement. Second, generated weights are imposed on two‐stage DEA model as additional constraints and a novel bi‐objective BWM‐two stage DEA model is introduced. Finally, the proposed bi‐objective BWM‐two stage DEA model is solved using min‐max approach. To illustrate the capability of proposed model, 45 Agricultural Bank (Agribank) branches in West Azerbaijan province of Iran are evaluated. The branches' processes are considered as two stages ‘production’ and ‘profitability’ and efficiency of branches are calculated in each stage. According to the efficiencies of each sub‐stage, branches are divided to four groups and recommendations are made for each group.

The decision maker's preference information on the importance and interaction of decision criteria can be explicitly described by the probabilistic interaction indices in the framework of the capacity based multicriteria decision analysis. In this paper, we first investigate some properties of the probabilistic interaction indices of the empty set, and propose the maximum and minimum empty set interaction principles based capacity identification methods, which can be considered as the comprehensive interaction trend preference information oriented capacity identification methods. Then, by introducing the deviation variables, the goal constraints, as well as the goal objective function, we give a new and more flexible approach to representing the decision maker's explicit preference information on the kind and degree of the interaction of any given combination of decision criteria as well as on the degree of the importance of any decision criterion, and construct the nonempty set interaction indices based capacity identification method, which can be considered as the detailed explicit preference information oriented identification method. Finally, two illustrative examples are respectively given to show the feasibility and applicability of the two kinds of methods. In addition, the comparison analysis between these two kinds of methods and some existing capacity identification methods are also mentioned.

Complex network clustering has been extensively studied in recent years, mostly through optimization approaches. In such approaches, the multi-objective optimization methods have been shown to be capable of overcoming the limitations (e.g., instability) of the single-objective methods. Nevertheless, such methods suffer from the shortcoming of incapability of maintaining a good tradeoff between exploration and exploitation, that is, to find better solutions based on the good ones obtained so far. In this paper, we present a new nature-inspired heuristic optimization method, called multi-objective discrete moth-flame optimization (DMFO) method, which achieves such a tradeoff. We describe the detailed algorithm of DMFO that utilizes the Tchebycheff decomposition approach with an \(l_2\)-norm constraint on the direction vector (2-Tch). Furthermore, we show the experimental results on synthetic and several real-world networks that verify that the proposed DMFO and the algorithm are both effective and promising for tackling the task of complex network clustering.

When solving multiobjective optimization problems, there is typically a decision maker (DM) who is responsible for determining the most preferred Pareto optimal solution based on his preferences. To gain confidence that the decisions to be made are the right ones for the DM, it is important to understand the trade-offs related to different Pareto optimal solutions. We first propose a trade-off analysis approach that can be connected to various multiobjective optimization methods utilizing a certain type of scalarization to produce Pareto optimal solutions. With this approach, the DM can conveniently learn about local trade-offs between the conflicting objectives and judge whether they are acceptable. The approach is based on an idea where the DM is able to make small changes in the components of a selected Pareto optimal objective vector. The resulting vector is treated as a reference point which is then projected to the tangent hyperplane of the Pareto optimal set located at the Pareto optimal solution selected. The obtained approximate Pareto optimal solutions can be used to study trade-off information. The approach is especially useful when trade-off analysis must be carried out without increasing computation workload. We demonstrate the usage of the approach through an academic example problem.

This paper proposes a hybrid adaptive ant colony algorithm (HAACA) to realize product family multi-objective optimization design through scale-based product platform theory model. The Pareto-optimal solution was obtained via HAACA, and then the fuzzy optimization method is presented to extract the optimal solution of multi-objective optimization problem. The multi-objective optimization method was carried out in two stages. In the first stage, each product is optimized independently via HAACA and the product platform constant parameter and its value is obtained according to the change ratio of design variables. In the second stage, the scaling variables of each product are solved via HAACA based on the optimization objectives improving the performance in constraint of restrictions and the best compromise solution is extracted based on fuzzy optimization method.

For multi-objective optimization under condition of complicated objective function, the data processing in the evaluation is sometime tediously long, special algorithm is needed to be adopted. Since the remarkable features of uniform distribution of test points within the test domain and the small number of tests, fully representative of each point, and easy to perform regression analysis, the uniform test design method is hybrid with the “intersection” method for multi-objective optimization to simplify the complicated data process in evaluation first. Furthermore, the "intersection" multi-objective optimization methodology is combined with sequential uniform design so as to get a more precise approximation for solving multi-objective optimization problem, the procedure for searching optimum of the “intersection“ multi-objective optimization methodology with sequential uniform design algorithm is put forward. A multi-objective optimization of linear programming problem with three variables is taken as our example, which involves a maximum for one objective and a minimum for another objective. The result for applying the novel approach to the example indicates the effectiveness of current hybrids.

Multi-objective optimization of Organic Rankine Cycle (ORC) design considering exergy efficiency and inherent safety for LNG cold energy utilization

A novel interactive preferential evolutionary method for controller tuning in chemical processes

In this study, we developed an efficient computer-aided design tool for scaling combustor designs. From a limited number of fluid simulations, an original design is scaled while preserving most of the flow properties, using a multi-objective optimization method and deep neural network or kriging surrogate models. The accuracy and robustness of the method were first tested with a simple geometry. Investigations have shown a strong sensitivity of the surrogate models to the sample distribution, which can be reduced using a strategic sampling method. Subsequently, the geometry was scaled down to a factor of two using both surrogate models while preserving most of the flow features.

This paper designs and optimizes a new structure hybrid material B‐pillar assembly. Establish a finite element analysis model for the side impact test of an electric vehicle to verify the model's accuracy. Construct a finite element model of the hybrid material B‐pillar assembly. Combined with the static performance analysis of the B‐pillar, the laminate design of the carbon fiber composite B‐pillar reinforcement plate and optimization. For the outer and inner panels of the B‐pillar, the surrogate model method and the multiobjective optimization method are combined to set 11 design variables and 13 responses. The optimal Latin hypercube design method was used to randomly sample each design variable and fit the radial basis function (RBF) approximate model. The modified second‐generation non‐dominated sorting genetic algorithm (MNSGA‐II) was used to carry out multiobjective optimization of the mixed material B‐pillar assembly, and the multicriteria decision‐making method was used to obtain the optimal solution for the Pareto solution set. A drop weight impact test was performed on the hybrid material B‐pillar assembly. The results showed that the peak collision force of the hybrid material B‐pillar was reduced by 43.7% compared with the original steel B‐pillar, the specific energy absorption was increased by 17.5%, and the side impact safety performance was better. After optimization, the weight of the mixed material B‐column was reduced by 26.44%. The improvement rates of the intrusion amount at P2 and the intrusion speed at P1 were 23.99% and 0.63%, respectively, and the lightweight effect and side impact safety were significantly improved.Highlights The finite element analysis parameters of carbon fiber composite materials were constructed through experiments, and the basis for simulation analysis under various working conditions of the B‐pillar based on performance‐driven optimization was established. A hybrid material B‐pillar design method is proposed, which consists of a variable‐thickness high‐strength steel B‐pillar outer plate, a variable‐thickness high‐strength steel B‐pillar inner plate, and a carbon fiber composite B‐pillar reinforcement plate. The super layer of the carbon fiber composite B‐pillar reinforcement plate was optimized and the laying plan of the carbon fiber composite B‐pillar reinforcement plate was determined. Performance‐driven optimization is adopted to realize the collaboration of multilevel design and optimization methods such as B‐pillar conceptual design, detailed design, and multiobjective optimization. A modified NSGA‐II algorithm was proposed and combined with the multicriteria decision‐making method and the entropy‐weighted gray relation analysis method to determine the Pareto optimal solution and the optimal design scheme for the mixed material B‐pillar.

Multi-objective optimization of an anti-reflection AlN/VO2/AlN thermochromic window for building energy saving

This paper briefly summarizes selected published results on the Surrogate Worth Tradeoff (SWT) Method--a method for solving multiple objective optimization problems—and its extensions. The development of the SWT method is briefly discussed. Theoretical basis for the Kuhn-Tucker multipliers and trade-off functions associated with Pareto optimal solutions is presented. The SWT method is then extended to handling multiple decision-makers. The Multiobjective Statistical Method (MSM), and the analysis of risk and sensitivity in a multiobjective optimization framework using the SWT method are discussed also. A case study in water resources planning with several noncommensurable objective functions is summarized. Finally, special attributes of the SWT method are presented. Because of the very limited scope of this paper, no attempt has been made to relate the SWT method to other multiobjective optimization methods.