We present and analyze several definitions of Pareto optimality for multicriteria optimization or decision problems with uncertainty primarily in their objective function values. In comparison to related notions of Pa...
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We present and analyze several definitions of Pareto optimality for multicriteria optimization or decision problems with uncertainty primarily in their objective function values. In comparison to related notions of Pareto robustness, we first provide a full characterization of an alternative efficient set hierarchy that is based on six different ordering relations both with respect to the multipleobjectives and a possibly finite, countably infinite or uncountable number of scenarios. We then establish several scalarization results for the generation of the corresponding efficient points using generalized weighted-sum and epsilon-constraint techniques. Finally, we leverage these scalarization results to also derive more general conditions for the existence of efficient points in each of the corresponding optimality classes, under suitable assumptions. (C) 2019 Elsevier B.V. All rights reserved.
While the objectives of forest management vary widely and include the protection of resources in protected forests and nature reserves, the primary objective has often been the production of wood products. However, ev...
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While the objectives of forest management vary widely and include the protection of resources in protected forests and nature reserves, the primary objective has often been the production of wood products. However, even in this case, forests play a key role in the conservation of living resources. Constraining the areas of clearcuts contributes to this conservation, but if it is too restrictive, a dispersion of small clearcuts across the forest might occur, and forest fragmentation might be a serious ecological problem. Forest fragmentation leads to habitat loss, not only because the forest area is reduced, but also because the core area of the habitats and the connectivity between them decreases. This study presents a Monte Carlo tree search method to solve a bi-objective harvest scheduling problem with constraints on the clearcut area, total habitat area and total core area inside habitats. The two objectives are the maximization of both the net present value and the probability of connectivity index. The method is presented as an approach to assist the decision maker in estimating efficient alternative solutions and the corresponding trade-offs. This approach was tested with instances for forests ranging from some dozens to over a thousand stands and temporal horizons from three to eight periods. In general, multi-objective Monte Carlo tree search was able to find several efficient alternative solutions in a reasonable time, even for medium and large instances. (C) 2019 Elsevier B.V. All rights reserved.
This paper establishes a rough multiple objective programming model for a solid transportation problem. Furthermore, a general model for rough multiple objective programming problem is presented. Properties of the fea...
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This paper establishes a rough multiple objective programming model for a solid transportation problem. Furthermore, a general model for rough multiple objective programming problem is presented. Properties of the feasible and efficient solutions of rough multiple objective programming problems are investigated. In addition, compromise solutions are obtained by using the interactive fuzzy satisfying method. To solve the rough multipleobjective solid transportation problem, the rough simulation-based genetic algorithm is proposed, in which the rough simulation is embedded into the genetic algorithm. Finally, an application of the solid transportation problem at Xiluodu Hydropower Station is provided as an illustration. (C) 2011 Elsevier Inc. All rights reserved.
In this paper, a novel approach is proposed to generate set of Pareto points to represent the optimal solutions along the Pareto frontier. This approach, which introduces a new definition of dominance, can be interpre...
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This article focuses on the optimization of a complex system which is composed of several subsystems. On the one hand, these subsystems are subject to multipleobjectives, local constraints as well as local variables,...
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This article focuses on the optimization of a complex system which is composed of several subsystems. On the one hand, these subsystems are subject to multipleobjectives, local constraints as well as local variables, and they are associated with an own, subsystem-dependent decision maker. On the other hand, these subsystems are interconnected to each other by global variables or linking constraints. Due to these interdependencies, it is in general not possible to simply optimize each subsystem individually to improve the performance of the overall system. This article introduces a formal graph-based representation of such complex systems and generalizes the classical notions of feasibility and optimality to match this complex situation. Moreover, several algorithmic approaches are suggested and analyzed. (C) 2019 Elsevier B.V. All rights reserved.
In Aerial Surveillance Problem (ASP), an air platform with surveillance sensors searches a number of rectangular areas by covering the rectangles in strips and turns back to base where it starts. In this paper, we pre...
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In Aerial Surveillance Problem (ASP), an air platform with surveillance sensors searches a number of rectangular areas by covering the rectangles in strips and turns back to base where it starts. In this paper, we present a multiobjective extension to ASP, for which the aim is to help aerial mission planner to reach his/her most preferred solution among the set of efficient alternatives. We consider two conflicting objectives that are minimizing distance travelled and maximizing minimum probability of target detection. Each objective can be used to solve single objective ASPs. However, from mission planner's perspective, there is a need for simultaneously optimizing both objectives. To enable mission planner reaching his/her most desirable solution under conflicting objectives, we propose exact and heuristic methods for multiobjective ASP (MASP). We also develop an interactive procedure to help mission planner choose the most satisfying solution among all Pareto optimal solutions. Computational results show that the proposed methods enable mission planner to capture the tradeoffs between the conflicting objectives for large number of alternative solutions and to eliminate the undesirable solutions in small number of iterations.
Many engineering problems have multiple conflicting objectives, and they are also stochastic due to inherent uncertainties. One way to represent the multi-objective nature of problems is to use the Pareto optimality t...
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Many engineering problems have multiple conflicting objectives, and they are also stochastic due to inherent uncertainties. One way to represent the multi-objective nature of problems is to use the Pareto optimality to show the trade-off between objectives. Pareto optimality involves the identification of solutions that are not dominated by other solutions based on their respective objective functions. However, the Pareto optimality concept does not contain any information about the uncertainty of solutions. Evaluation and comparison of solutions becomes difficult when the objective functions are subjected to uncertainty. A new metric, the Pareto Uncertainty Index (PUI), is presented. This metric includes uncertainty due to the stochastic coefficients in the objective functions as part of the Pareto optimality concept to form an extended probabilistic Pareto set, we define as the p-Pareto set. The decision maker can observe and assess the randomness of solutions and compare the promising solutions according to their performance of satisfying objectives and any undesirable uncertainty. The PUI is an effective and convenient decision-making tool to compare promising solutions with multiple uncertain objectives. (C) 2020 Elsevier B.V. All rights reserved.
Preference functions have been widely used to scalarize multipleobjectives. Various forms such as linear, quasiconcave, or general monotone have been assumed. In this article, we consider a general family of function...
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Preference functions have been widely used to scalarize multipleobjectives. Various forms such as linear, quasiconcave, or general monotone have been assumed. In this article, we consider a general family of functions that can take a variety of forms and has properties that allow for estimating the form efficiently. We exploit these properties to estimate the form of the function and converge towards a preferred solution(s). We develop the theory and algorithms to efficiently estimate the parameters of the function that best represent a decision maker's preferences. This in turn facilitates fast convergence to preferred solutions. We demonstrate on a variety of experiments that the algorithms work well both in estimating the form of the preference function and converging to preferred solutions.
Natural grasslands provide important land resources in pastoral areas, and greatly contribute to ecological functioning. Overgrazing and other unreasonable exploitations have led to the degradation and desertification...
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Natural grasslands provide important land resources in pastoral areas, and greatly contribute to ecological functioning. Overgrazing and other unreasonable exploitations have led to the degradation and desertification of natural grasslands, exacerbating the forage-livestock imbalance. In areas suffering from water shortage, this imbalance gradually evolves into a water-land forage-livestock imbalance. In this study, a water-land forage-livestock balance-based model was developed to optimise the allocation of water, land, and forage resources in pastoral areas, while addressing economic and ecological benefits in a coupled manner. The model was applied in a case study of Otog Front Banner to simulate the comprehensive economic and ecological benefits to the development of water, land, and forage resources in different coupled allocations of artificial and natural grasslands. The results showed that as the duration of supplementary and barn feeding increased, local development was first constrained by the availability of natural grasslands and then by the availability of water resources. The optimal resource allocation in Otog Front Banner predicted for 2030 included a water consumption of 266,000,000 m(3), an irrigation area of 43,000 ha, a natural grassland utilisation area of 684,700 ha, and a livestock farming scale of 1,188,500 sheep units.
DsbA (disulfide bond formation protein A) is essential for disulfide bond formation directly affecting the nascent peptides folding to the correct conformation in vivo. In this paper, recombinant DsbA protein was empl...
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DsbA (disulfide bond formation protein A) is essential for disulfide bond formation directly affecting the nascent peptides folding to the correct conformation in vivo. In this paper, recombinant DsbA protein was employed to catalyze denatured lysozyme refolding and inhibit the aggregation of folding intermediates in vitro. Statistical methods, i.e., Plackett-Burman design and small central composite design, were adopted to screen out important factors affecting the refolding process and correlating these parameters with the refolding efficiency including both protein recovery and specific activity of refolded lysozyme. Four important parameters: initial lysozyme concentration, urea concentration. KCl concentration and GSSG (glutathione disulfide) concentration were picked out and operating conditions were optimized by introducing the effectiveness coefficient method and transforming the multiple objective programming into an ordinary constrained optimization issue. Finally, 99.7% protein recovery and 25,600 U/mg specific activity of lysozyme were achieved when 281.35 mu g/mL denatured lysozyme refolding was catalyzed by an equivalent molar of DsbA at the optimal settings. The results indicated that recombinant DsbA protein could effectively catalyze the oxidized formation and reduced isomerization of intramolecular disulfide bonds in the refolding of lysozyme in vitro. (C) 2012 Elsevier Ltd. All rights reserved.
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