D-PHI: Desirability-Based Hypervolume Indicator for Interactive Multiobjective Optimization Using Aspiration and Reservation Levels as Preferences

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.

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.

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

Because the purpose of multiobjective optimization methods is to optimize conflicting objectives simultaneously, they mainly focus on Pareto optimal solutions, where improvement with respect to some objective is only possible by allowing some other objective(s) to impair. Bringing this idea into practice requires the decision maker to think in terms of trading-off, which may limit the ability of effective problem solving. We outline some drawbacks of this and exploit another idea emphasizing the possibility of simultaneous improvement of all objectives. Based on this idea, we propose a technique for handling decision maker's preferences, which eliminates the necessity to think in terms of trade-offs. We incorporate this technique into an interactive trade-off-free method for multiobjective optimization. We call the resulting method NAUTILUS 2, which is also suitable for negotiation support. We demonstrate the applicability of the new method with an example problem.

The cost of obtaining good information regarding the various probability distributions needed for the solution of most stochastic decision problems is considerable. It is important to consider questions such as: (1) what minimal amounts of information are sufficient to determine optimal decision rules; (2) what is the value of obtaining knowledge of the actual realization of the random vectors; and (3) what is the value of obtaining some partial information regarding the actual realization of the random vectors. This paper is primarily concerned with questions two and three when the decision maker has an a priori knowledge of the joint distribution function of the random variables. Some remarks are made regarding results along the lines of question one. Mention is made of assumptions sufficient so that knowledge of means, or of means, variances, co-variances and n-moments are sufficient for the calculation of optimal decision rules. The analysis of the second question leads to the development of bounds on the value of perfect information. For multiperiod problems it is important to consider when the perfect information is available. Jensen's inequality is the key tool of the analysis. The calculation of the bounds requires the solution of nonlinear programs and the numerical evaluation of certain functions. Generally speaking, tighter bounds may be obtained only at the expense of additional information and computational complexity. Hence, one may wish to compute some simple bounds to decide upon the advisability of obtaining more information. For the analysis of the value of partial information it is convenient to introduce the notion of a signal. Each signal represents the receipt of certain information, and these signals are drawn from a given probability distribution. When a signal is received, it alters the decision maker's perception of the probability distributions inherent in his decision problem. The choice between different information structures must then take into account these probability distributions as well as the decision maker's preference function. A hierarchy of bounds may be determined for partial information evaluation utilizing the tools of the multiperiod perfect information case. However, the calculation of these bounds is generally considerably more dicult than the calculation of similar boulids in the perfect information case. Most of the analysis is directed towards problems in which the decision maker has a linear utility function over profits, costs or some other numerical variable. However, some of the bounds generalize to the case when the utility function is strictly increasing and concave.

An approach to aid decision making for urban water management is presented that is based on the concept of trade-off sacrifice level in pairwise comparisons between criteria, modelled using fuzzy logic. This approach is illustrated by a case study - selection of alternative water supplies for a Sydney household. Four key decision making criteria covering health, economic, environment and technical aspects are selected: annual probability of infection, life cycle energy use, life cycle cost and reliability. The decision making problem is to select between cases with different volume and application of recycled greywater and rainwater in light of the four criteria. Decision maker's preference is expressed by five levels of trade-off sacrifice between pairs of criteria. The decision makers can assign their preferences for sacrifice level by linguistic assessment and the output trade-off weight (TOW). Measures of decision makers' perceived trade-off level are modelled by a rule-based fuzzy logic control system. The final analysis shows the performance for each sacrifice class for each case, to aid overall decision making with stakeholders.

Integrated, multi-scale and multi-objective design of batch food processing plants. Part 2: Application to a mobile fruit and vegetable processing unit

Multiattribute utility analysis is a set of formal procedures designed to assist a decision maker in resolving problems requiring tradeoffs among competing objectives. The approach elicits a multiattribute utility function (MAUF) intended to represent the decision maker's preferences for multivariate alternatives. While different MAUF assessment technologies are available, few studies have been conducted that compare assessment techniques. The purpose of this research was to investigate the predictive ability of four MAUF elicitation procedures. Keeney-Raiffa (KR), holistic orthogonal parameter estimation (HOPE), simple multiattribute rating technique (SMART), and mathematical programming elicited MAUFs were compared in terms of (1) ordinal preference predictions, (2) first preference predictions, and (3) ability to capture tradeoffs between competing objectives. Since actual decision tasks do not offer a "correct" solution, it is difficult to compare the performances of alternative assessment procedures in a real-world setting. Consequently, a hypothetical decision making environment was established to determine a procedure's performance in the presence of elicitation errors of known type and magnitude. The inputs necessary to implement each procedure were provided by an artificial decision maker. While behavioral influences on a technique's performance were not considered, each experimental elicitation contained one or more of the following assessment errors: noisy respondent inputs; incorrectly specified functional forms; and incompletely defined attribute sets. Validity was determined by comparing MAUF predictions to the artificial subject's known preference constructs. The four procedures were not uniformly robust within or across the elicitation scenarios considered. KR encoded models typically provided the most consistently accurate predictions. HOPE first preference predictions were sensitive to the level of noise contained in the subject's responses. SMART and mathematical programming performances were generally inferior to those of KR and HOPE. SMART offered reasonable overall preference orderings, but was less effective at predicting the subject's most desired alternative. Predictions offered by mathematical programming MAUFs were relatively unstable, at times yielding high proportions of utility loss from incorrect first preferences. This research provides an initial set of guidelines to assist a decision analyst in choosing among competing MAUF elicitation techniques.

Previous research has documented the lack of clear relationships between the value of information and characteristics of the decision problem. This paper shows that the intensity of the decision maker's preference toward the prior choice alternatives can be regarded as the primary determinant of information value. The value of an information source, measured in utility units, is maximal when the decision maker is indifferent vis-à-vis the prior alternatives, and it is lower as the preference for one alternative over the others gets stronger. This holds under quite general conditions, which are made explicit, and for any decision maker's utility function, wealth, and background risks. The maximum buying price of information follows the same pattern for linear utility and, with a restriction, exponential utility, and this may hold approximately for other types of utility functions. The result provides a general, concise, and intuitive explanation for seemingly ill-behaved variations in the value of information. It indicates that nonmonotonic, quasi-concave relationships should generally be expected between value of information and parameters of the decision problem.

Consider a finite set of alternatives under risk which have multiple attributes. MARPI is an interactive computer-based procedure to find an efficient choice in the sense of linear expected utility. The choice is based on incomplete information about the decision maker's preferences which is elicited and processed in a sequential way. The information includes qualitative properties of the multivariate utility function such as monotonicity, risk aversion, and separability. Further, in case of an additively separable utility function, bounds on the scaling constants are elicited, and preferences (not necessarily indifferences) between sure amounts and lotteries are asked from the decision maker. The lotteries are Bernoulli lotteries generated by MARPI using special strategies. At every stage of the procedure the efficient set of alternatives is determined with respect to the information elicited so far.

This paper aims to compare two tools for decision makers that intend to support the decision of the selection of the appropriate supplier. Suppliers are crucial to both the efficiency and effectiveness of the performance of companies. A critical success factor of these companies is the selection of the appropriate supplier. A methodology is proposed to optimise the evaluation process based on different criteria. The proposed approach extends the one proposed by Ordoobadi (2009, Development of a supplier selection model using fuzzy logic. Supply Chain Management: An International Journal, 14 (4), 314–327) who proposed the application of fuzzy logic (FL) where we use the same example case study in order to compare the analytic hierarch process (AHP) with FL. In this paper we demonstrate how we can achieve the same objective of expressing human assessments in the form of linguistic expressions by using AHP. Moreover, we demonstrate the capability to run a sensitivity analysis which helps to understand the causal relationships among the different factors. We demonstrate how this capability can help us to explain and predict the different relationships among criteria and alternatives. Moreover, we provide a measure that is able to capture the consistency of the decision maker's preferences. In our approach we provide a single unit of scale that is not only capable of ranking suppliers but also provides an understanding of the difference in scale between different suppliers which can then help to allocate resources accordingly. These facilities are not offered by Ordoobadi (2009). The proposed approach here can help companies to identify the best supplier in changing environments. The paper describes a decision model that incorporates a decision maker's subjective assessments and applies a multiple criteria decision making technique to manipulate and quantify these assessments. Unlike many similar studies, two techniques have been performed on the same case study in order to improve our understanding of the differences in the proposed techniques.

ABSTRACTThe Goal Programming (GP) model is one of the first models that have been developed to deal with managerial decision‐making problems where several incommensurable and conflicting objectives are involved. The GP variants integrate the decision maker's preferences differently. This model has also been applied to group decision‐making situations. The aim of this paper is to propose a new typology based on preferences articulation of decision makers through the GP model. This typology is based on the articulation and the elucidation process of the group decision makers' preferences. Copyright © 2012 John Wiley & Sons, Ltd.

The information in data depends on the subjective value system that the receiver of the data uses to interpret them. This paper looks at the information in a theory of first order logic (a knowledge base) from the perspective of a decision maker for whom the validation of formulae (facts and rules) have varying importance. The decision maker's preferences and prior knowledge are both incorporated into the information measure. The value of information is determined by what it conveys about the formulae of importance to the decision maker. The information measure is applied as a heuristic in commonsense reasoning; in relevance assessment ; and as a preference function in belief revision.