The classical 0-1 knapsack problem is considered with two objectives. Two methods of the "two-phases" type are developed to generate the set of efficient solutions. In the first phase, the set of supported e...
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The classical 0-1 knapsack problem is considered with two objectives. Two methods of the "two-phases" type are developed to generate the set of efficient solutions. In the first phase, the set of supported efficient solutions is determined by optimizing a parameterized single-objective knapsack problem. Two versions are proposed for a second phase, determining the non-supported efficient solutions: both versions are Branch and Bound approaches, but one is "breadth first", while the other is "depth first". Extensive numerical experiments have been realized to compare the results of both methods.
This paper proposes an exact method to solve an integer linear fractional bilevel problem with multiple objectives at the upper level, designated by IFMOBP. The proposed algorithm generates a set of efficient solution...
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This paper proposes an exact method to solve an integer linear fractional bilevel problem with multiple objectives at the upper level, designated by IFMOBP. The proposed algorithm generates a set of efficient solutions using a branch and cut algorithm based on a continuous upper level linear fractional problem. Then, the integer optimal solution obtained is tested for optimality of the lower level problem. First, the integer optimal solution of the bilevel problem is sought with a single objective function at each level. After that, an efficient cut is added and new integer solutions are determined. The efficient set is updated each time a candidate bilevel feasible solution non dominated is got and the process ends when there are no unexplored parts of the original domain. The proposed method is based on a dantzig cut to find the next best integer solution of the first objective function of the upper level, an efficient cut to get the set of efficient solutions for the main problem, and the classical branch and bound technique for integer decision variables. After the presentation of the algorithm, a numerical example and computational experiments are provided.
We propose a steepest descent method for unconstrained multicriteria optimization and a "feasible descent direction" method for the constrained case. In the unconstrained case, the objective functions are as...
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We propose a steepest descent method for unconstrained multicriteria optimization and a "feasible descent direction" method for the constrained case. In the unconstrained case, the objective functions are assumed to be continuously differentiable. In the constrained case, objective and constraint functions are assumed to be Lipshitz-continuously differentiable and a constraint qualification is assumed. Under these conditions, it is shown that these methods converge to a point satisfying certain first-order necessary conditions for Pareto optimality. Both methods do not scalarize the original vector optimization problem. Neither ordering information nor weighting factors for the different objective functions are assumed to be known. In the single objective case, we retrieve the Steepest descent method and Zoutendijk's method of feasible directions, respectively.
This paper develops a multi-objective Mixed Integer programming model for a closed-loop network design problem. In addition to the overall costs, the model optimizes overall carbon emissions and the responsiveness of ...
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This paper develops a multi-objective Mixed Integer programming model for a closed-loop network design problem. In addition to the overall costs, the model optimizes overall carbon emissions and the responsiveness of the network. An improved genetic algorithm based on the framework of NSGA II is developed to solve the problem and obtain Pareto-optimal solutions. An example with 95 cities in China is presented to illustrate the approach. Through randomly generated examples with different sizes;the computational performance of the proposed algorithm is also compared with former genetic algorithms in the literature employing the weight-sum technique as a fitness evaluation strategy. Computational results indicate that the proposed algorithm can obtain superior Pareto-optimal solutions. (C) 2016 Elsevier Inc. All rights reserved.
Nowadays, with the scarcity of water resources, competition for water resources among different levels and water sectors is growing increasingly fierce. Furthermore, uncertainties are unavoidable in the water resource...
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Nowadays, with the scarcity of water resources, competition for water resources among different levels and water sectors is growing increasingly fierce. Furthermore, uncertainties are unavoidable in the water resources system. To address the aforementioned issues, a fuzzy max-min decision bi-level multi-objective interval programming model was proposed, which can not only focus on water conflicts at the same level or between different levels, but also pay attention to optimal allocation of water resources under uncertainty. The developed model was then applied to a case study in Wuwei City, Gansu Province, China, which selected fairness of water distribution and agricultural economic benefits as planning objectives. Based on the developed model, different water resources optimal allocation schemes under different representative hydrological years were provided. From the result, as representative hydrological years changed from wet (P = 25%) to dry (P = 75%), agricultural economic benefit and Gini coefficient of agriculture would vary from [35.19, 37.78] x 108 yuan to [31.12, 31.99] x 108 yuan and from [0.468, 0.429] to [0.505, 0.503], which indicates that as available water resources decrease, agricultural economic benefit would decrease and fairness of water distribution would also decrease. And the water distribution fairness of the upper bound water allocation scheme is higher than that of the lower bound water allocation scheme when in the same representative hydrological year. In addition, no matter what representative hydrological year, the results of the established bi-level programming model are always in the middle of the results of the upper and lower level individual objective, which means that the developed bi-level programming model has great advantage to deal with water competing conflict among different levels. Furthermore, based on the results of developed model, the reasonable water resources optimization schemes can be determined by the decision-ma
In the present paper, a multi-objective goal optimization mechanism is developed by trading off between cost and variance. Both are adversaries to each other while allocating a sample size even in stratified sampling ...
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In the present paper, a multi-objective goal optimization mechanism is developed by trading off between cost and variance. Both are adversaries to each other while allocating a sample size even in stratified sampling design. Discussion section shows how these adversaries put their influence on optimal selection. This is a dual optimization procedure in which variance or mean square error is optimized in the first step and then considering some compromise on variance, cost is optimized. The process is applied to both individual and multi-objective programming models.
This paper investigates the distribution centre location problem with inaccurate information, and a general model based on a rough feasible region is established. By means of synthesizing the believable degree of the ...
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This paper investigates the distribution centre location problem with inaccurate information, and a general model based on a rough feasible region is established. By means of synthesizing the believable degree of the rough feasible region and objective functions, a solution model termed as rough multi-objective synthesis effect (RMOSE) model is developed;this constitutes a series of crisp multi-objective programming models that reflect different decision consciousness for each decision maker. The optimal solutions of the RMOSE model can be obtained by using the genetic algorithm, and it is demonstrated that the solution of the RMOSE model in proper parameters is same as that of existing model with fuzzy model information. So the proposed RMOSE model is actually an extension of a crisp multi-objective programming model. Two cases of experiments for the distribution centre location problems show that the proposed method can be directly applied to real world practices and it is better than existing methods with fuzzy model information.
Since the 1990:9, network reliability has been considered as a new index for evaluating transportation networks under uncertainty. A large number of studies have been revealed in the literature in this field, which ar...
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Since the 1990:9, network reliability has been considered as a new index for evaluating transportation networks under uncertainty. A large number of studies have been revealed in the literature in this field, which are mostly dedicated to developing relevant measures that can be utilized for the evaluation of vulnerable networks under different sources of uncertainty, such as daily traffic flow fluctuations, natural disasters, weather conditions, and so fourth. This paper addresses the resource allocation problem in vulnerable transportation networks, in which multiple performance reliability measures should be met at their desired levels, while the overall cost of upgrading links 'performances should be minimized simultaneously. For this purpose, a new approach has been considered to formulate the two well-known performance measures, connectivity and capacity reliability, along with their application in a bi-objective nonlinear mixed integer goal programming model. In order to take into account the uncertain conditions of supply, links' capacities have been assumed to be random variables and follow normal distribution functions. A computationally efficient method has been developed that allows calculating the network-wise performance indices simply by means of a set of functions of links' 'performance reliabilities. Using this approach, as the performance reliability of links are themselves functions of the random links' capacities, they can be simply calculated through numerical integration. To achieve desirable levels for both connectivity reliability and capacity reliability (as network-wise performance reliability measures) two distinct objectives have been considered. One of the objectives seeks to maximize each of the measures regardless of what is happening to the other objective function which minimizes the budget. Since optimization models with two conflicting objectives cannot be solved directly, the well-known goal attainment multi-objective decision-mak
A cost-time trade-off bulk transportation problem with the objectives to minimize the total cost and duration of bulk transportation without according priorities to them is considered. The entire requirement of each d...
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A cost-time trade-off bulk transportation problem with the objectives to minimize the total cost and duration of bulk transportation without according priorities to them is considered. The entire requirement of each destination is to be met from one source only;however a source can supply to any number of destinations subject to the availability of the commodity at it. Two new algorithms are provided to obtain the set of Pareto optimal solutions of this problem. This work extends and generalizes the work related to single-objective and prioritized two-objective bulk transportation problems done in the past while providing flexibility in decision making. (C) 2007 Elsevier B.V. All rights reserved.
This research considers a stochastic lot-sizing problem with multi-supplier and quantity discounts. The objectives are to minimise total costs, where the costs include ordering cost, holding cost, purchase cost and sh...
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This research considers a stochastic lot-sizing problem with multi-supplier and quantity discounts. The objectives are to minimise total costs, where the costs include ordering cost, holding cost, purchase cost and shortage cost, and to maximise service level of the system. In this paper, we first formulate the stochastic lot-sizing problem as a multi-objective programming (MOP) model. We then transform the model into a mixed integer programming (MIP) model. Finally, an efficient heuristic dynamic programming (HDP) model is constructed for solving large-scale stochastic lot-sizing problems. An illustrative example with two cases for a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that the proposed two models are effective and accurate tools for determining the replenishment of touch panels from multiple suppliers for multi-periods.
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