We generalize the applicability of interactive methods for solving computationally demanding, that is, time-consuming, multiobjective optimization problems. For this purpose we propose a new agent assisted interactive...
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We generalize the applicability of interactive methods for solving computationally demanding, that is, time-consuming, multiobjective optimization problems. For this purpose we propose a new agent assisted interactive algorithm. It employs a computationally inexpensive surrogate problem and four different agents that intelligently update the surrogate based on the preferences specified by a decision maker. In this way, we decrease the waiting times imposed on the decision maker during the interactive solution process and at the same time decrease the amount of preference information expected from the decision maker. The agent assisted algorithm is not specific to any interactive method or surrogate problem. As an example we implement our algorithm for the interactive NIMBUS method and the PAINT method for constructing the surrogate. This implementation was applied to support a real decision maker in solving a two-stage separation problem. (C) 2015 Elsevier Ltd. All rights reserved.
This paper deals with a class of multipleobjective linear programs (MOLP) called lexicographic multipleobjective linear programs (LMOLP). In this paper, by providing an efficient algorithm which employs the precedin...
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This paper deals with a class of multipleobjective linear programs (MOLP) called lexicographic multipleobjective linear programs (LMOLP). In this paper, by providing an efficient algorithm which employs the preceding computations as well, it is shown how we can solve the LMOLP problem if the priority of the objective functions is changed. In fact, the proposed algorithm is a kind of sensitivity analysis on the priority of the objective functions in the LMOLP problems. (C) 2010 Elsevier B.V. All rights reserved.
In robust optimization, the parameters of an optimization problem are not deterministic but uncertain. Their values depend on the scenarios which may occur. Single-objective robust optimization has been studied extens...
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In robust optimization, the parameters of an optimization problem are not deterministic but uncertain. Their values depend on the scenarios which may occur. Single-objective robust optimization has been studied extensively. Since 2012, researchers have been looking at robustness concepts for multi-objective optimization problems as well. In another line of research, single-objective uncertain optimization problems are transformed to deterministic multi-objective problems by treating every scenario as an objective function. In this paper we combine these two points of view. We treat every scenario as an objective function also in uncertain multi-objective optimization, and we define a corresponding concept of dominance which we call multi scenario efficiency. We sketch this idea for finite uncertainty sets and extend it to the general case of infinite uncertainty sets. We then investigate the relation between this dominance and the concepts of highly, locally highly, flimsily, and different versions of minmax robust efficiency. For all these concepts we prove that every strictly robust efficient solution is multi-scenario efficient. On the other hand, under a compactness condition, the set of multi-scenario efficient solutions contains a robust efficient solution for all these concepts which generalizes the Pareto robustly optimal (PRO) solutions from single-objective optimization to Pareto robust efficient (PRE) solutions in the multi-objective case. We furthermore present two results on reducing an infinite uncertainty set to a finite one which are a basis for computing multi scenario efficient solutions. (C) 2018 Elsevier B.V. All rights reserved.
In this paper we consider a simulated annealing algorithm for multiobjective optimization problems. With a suitable choice of the acceptance probabilities, the algorithm is shown to converge asymptotically, that is, t...
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In this paper we consider a simulated annealing algorithm for multiobjective optimization problems. With a suitable choice of the acceptance probabilities, the algorithm is shown to converge asymptotically, that is, the Markov chain that describes the algorithm converges with probability one to the Pareto optimal set.
One of the major issues for Markowitz mean-variance model is the errors in estimations cause "corner solutions" and low diversity in the portfolio. In this paper, we compare the mean-variance efficiency, rea...
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One of the major issues for Markowitz mean-variance model is the errors in estimations cause "corner solutions" and low diversity in the portfolio. In this paper, we compare the mean-variance efficiency, realized portfolio values, and diversity of the models incorporating different entropy measures by applying multiple criteria method. Differing from previous studies, we evaluate twenty-three portfolio over-time rebalancing strategies with considering short-sales and various transaction costs in asset diversification. Using the data of the most liquid stocks in Taiwan's market, our finding shows that the models with Yager's entropy yield higher performance because they respond to the change in market by reallocating assets more effectively than those with Shannon's entropy and with the minimax disparity model. Furthermore, including entropy in models enhances diversity of the portfolios and makes asset allocation more feasible than the models without incorporating entropy. (C) 2014 Elsevier Inc. All rights reserved.
Reservoir flood control decisions are often compromised by various parties with conflicting benefits, In this paper, a three-person multi-objective conflict decision model is presented for reservoir flood control. In ...
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Reservoir flood control decisions are often compromised by various parties with conflicting benefits, In this paper, a three-person multi-objective conflict decision model is presented for reservoir flood control. In order to obtain the group decision, the ideal bargaining solution is first sought by two stages satisfying programming and then the decision alternative is chosen using the fuzzy pattern recognition. The advantages of this model are simple and more adaptable to the real problem. The model is demonstrated by application to Fengman Reservoir in China. (C) 2002 Elsevier Science B.V. All rights reserved.
The problem of optimizing some contiuous function over the efficient set of a multiple objective programming problem can be formulated as a nonconvex global optimization problem with special structure. Based on the co...
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The problem of optimizing some contiuous function over the efficient set of a multiple objective programming problem can be formulated as a nonconvex global optimization problem with special structure. Based on the conical branch and bound algorithm in global optimization, we establish an algorithm for optimizing over efficient sets and discuss about the implementation of this algorithm for some interesting special cases including the case of biobjectiveprogramming problems.
We propose an interactive method for decision making under uncertainty, where uncertainty is related to the lack of understanding about consequences of actions. Such situations are typical, for example, in design prob...
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We propose an interactive method for decision making under uncertainty, where uncertainty is related to the lack of understanding about consequences of actions. Such situations are typical, for example, in design problems, where a decision maker has to make a decision about a design at a certain moment of time even though the actual consequences of this decision can be possibly seen only many years later. To overcome the difficulty of predicting future events when no probabilities of events are available, our method utilizes groupings of objectives or scenarios to capture different types of future events. Each scenario is modeled as a multiobjective optimization problem to represent different and conflicting objectives associated with the scenarios. We utilize the interactive classification-based multiobjective optimization method NIMBUS for assessing the relative optimality of the current solution in different scenarios. This information can be utilized when considering the next step of the overall solution process. Decision making is performed by giving special attention to individual scenarios. We demonstrate our method with an example in portfolio optimization.
The literature review shows research gaps into the food supply chain design. In that context, this paper deals with the design of a sustainable supply chain. A multi-objective mixed-integer linear programming model in...
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The literature review shows research gaps into the food supply chain design. In that context, this paper deals with the design of a sustainable supply chain. A multi-objective mixed-integer linear programming model includes four decisions and three sustainable criteria (economic-total network costs-, environmental-carbon emissions-, and social-work conditions and societal development-). The model aims to determine the optimal location and capacity of processing and distribution facilities, to choose the suppliers from a set of potential candidates, to determine transportation modes between all the actors, and to define the quantity of product, in order to satisfy the demand of dairy products in a set of regions. The applicability of the model is tested in a realistic case in the dairy sector in the central region of Colombia. The results show the existent trade-offs between the three dimensions of sustainability. The unweighted balance results, giving more priority to the social dimension, which obtains the least deviation, affecting the environmental performance of the chain. The analysis carried out in this paper does help decision-makers that will have at hand a set of possible configurations to be chosen in order to comply with environmental and social regulations without neglecting economic performance.
Data Envelopment Analysis is used to determine the relative efficiency of Decision Making Units as the ratio of weighted sum of outputs by weighted sum of inputs. To accomplish the purpose, a DEA model calculates the ...
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Data Envelopment Analysis is used to determine the relative efficiency of Decision Making Units as the ratio of weighted sum of outputs by weighted sum of inputs. To accomplish the purpose, a DEA model calculates the weights of inputs and outputs of each DMU individually so that the highest efficiency can be estimated. Thus, the present study suggests an innovative method using a common set of weights leading to solving a linear programming problem. The method determines the efficiency score of all DMUs and rank them too.
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