Using the central value operator and the semi-dispersion measure of fuzzy number, this paper proposes the definitions of the lower and upper semi-variances. A general multiperiod fuzzy portfolio optimization model wit...
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Using the central value operator and the semi-dispersion measure of fuzzy number, this paper proposes the definitions of the lower and upper semi-variances. A general multiperiod fuzzy portfolio optimization model with return demand on the portfolio at each period is proposed with the objectives of maximizing both terminal wealth and the cumulative diversification degree of portfolios over the whole investment horizon, and minimizing terminal risk. A fuzzy multiobjective nonlinear programming technique is applied to convert the proposed model into a single-objective model. A genetic algorithm (GA) is given to solve it. Besides, a numerical example is given to illustrate the application of the proposed model and the effectiveness of the designed algorithm.
In this paper, we tackle the aircraft conflict resolution problem under uncertainties. We consider errors due to the wind effect, the imprecision of aircraft speed prediction, and the delay in the execution of maneuve...
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In this paper, we tackle the aircraft conflict resolution problem under uncertainties. We consider errors due to the wind effect, the imprecision of aircraft speed prediction, and the delay in the execution of maneuvers. Using a geometrical approach, we derive an analytical expression for the minimum distance between aircraft, along with the corresponding probability of conflict. These expressions are incorporated into an existing deterministic model for conflict resolution. This model solves the problem as a maximum clique of minimum weight in a graph whose vertices represent possible maneuvers and where edges link conflict-free maneuvers of different aircraft. We then present a solution procedure focusing on two criteria, namely, fuel efficiency and the probability of reissuing maneuvers in the future: we iteratively generate Pareto front solutions to provide the controller with a set of possible solutions where she can choose the one corresponding the most to her preferences. Intensive Monte Carlo simulations validate the expressions derived for the minimum distance and the probability of conflict. Computational results highlight that up to 10 different solutions for instances involving up to 35 aircraft are generated within 3 minutes.
We propose two strategies for choosing Pareto solutions of constrained multiobjective optimization problems. The first one, for general problems, furnishes balanced optima, i.e. feasible points that, in some sense, ha...
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We propose two strategies for choosing Pareto solutions of constrained multiobjective optimization problems. The first one, for general problems, furnishes balanced optima, i.e. feasible points that, in some sense, have the closest image to the vector whose coordinates are the objective components infima. It consists of solving a single scalar-valued problem, whose objective requires the use of a monotonic function which can be chosen within a large class of functions. The second one, for practical problems for which there is a preference among the objective's components to be minimized, gives us points that satisfy this order criterion. The procedure requires the sequential minimization of all these functions. We also study other special Pareto solutions, the sub-balanced points, which are a generalization of the balanced optima.
In this paper, based on bifuzzy theory, we have studied the multiobjective programming problem under bifuzzy environment, and presented the expected-value model which is a deterministic multiobjective problem. To the ...
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ISBN:
(纸本)9783037850275
In this paper, based on bifuzzy theory, we have studied the multiobjective programming problem under bifuzzy environment, and presented the expected-value model which is a deterministic multiobjective problem. To the expected value model, the concepts of non-inferior solution are defined, and their relations are also discussed. According to practical decision-making process, a solution method, called the method of main objective function, has been studied, whose results can facilitate us to design algorithms to solve the bifuzzy multiobjective programming problem.
An algorithm to solve bi-objective quadratic fractional integer programming problems is presented in this paper. The algorithm uses epsilon-scalarization technique and a ranking approach of the integer feasible soluti...
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An algorithm to solve bi-objective quadratic fractional integer programming problems is presented in this paper. The algorithm uses epsilon-scalarization technique and a ranking approach of the integer feasible solution to find all nondominated points. In order to avoid solving nonlinear integer programming problems during this ranking scheme, the existence of a linear or a linear fractional function is established, which acts as a lower bound on the values of first objective function of the biobjective problem over the entire feasible set Numerical examples are also presented in support of the theory.
In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, ...
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In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution, and derive some Mond-Weir type duality results.
In this paper, we consider a class of multiobjective E-convex programming problems with inequality constraints, where the objective and constraint functions are E-convex functions which were firstly introduced by Youn...
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In this paper, we consider a class of multiobjective E-convex programming problems with inequality constraints, where the objective and constraint functions are E-convex functions which were firstly introduced by Youness (J. Optim. Theory Appl. 102: 439-450, 1999). Fritz-John and Kuhn-Tucker necessary and sufficient optimality theorems for the multiobjective E-convex programming are established under the weakened assumption of the theorems in Megahed et al. (J. Inequal. Appl. 2013: 246, 2013) and Youness (Chaos Solitons Fractals 12: 1737-1745, 2001). A mixed duality for the primal problem is formulated and weak and strong duality theorems between primal and dual problems are explored. Illustrative examples are given to explain the obtained results.
A bilevel optimization problem consists of minimizing an upper level objective function subject to the constraints that involve the solution mapping of the lower level optimization problem parameterized by the upper l...
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ISBN:
(纸本)9783319083773;9783319083766
A bilevel optimization problem consists of minimizing an upper level objective function subject to the constraints that involve the solution mapping of the lower level optimization problem parameterized by the upper level decision variable. The global equivalence between a general bilevel programming problem and a multiobjective optimization problem with nonconvex ordering cone is established and optimality conditions of the bilevel problem are obtained using Mordukhovich extremal principles.
Managers of modern large-scale construction projects are under pressure to meet higher customer expectations with tighter budgets. Although they deal with numerous issues in the purchasing and manufacturing processes,...
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Managers of modern large-scale construction projects are under pressure to meet higher customer expectations with tighter budgets. Although they deal with numerous issues in the purchasing and manufacturing processes, selecting effective and efficient material suppliers is among the most critical one. This selection is often very challenging when lacking precise information. Moreover, the construction contractor and the suppliers often have conflicting interests and make decisions individually. As research concerning the aforementioned issues is still relatively scarce, this paper proposes a multiobjective bilevel programming model with random fuzzy coefficients for supplier selection problem with multiple items (SSP-MI) in a large-scale construction project. The upper level problem deals with the construction contractor who selects suppliers to minimize total cost, maximize service, and item quality. The lower level problem deals with the suppliers who allocate supplied items to maximize their own total profit. For solving this complex bilevel nonlinear model with uncertainties an expected value operator method is first used to deal with the uncertain variables, and then Karush-Kuhn-Tucker (KKT) conditions and a combinatorial algorithm with a sectional genetic algorithm with fuzzy logic controller (flc-SGA) and a weighted-sum method (WSM) based on satisfactory degree (SD) denoted as flc-SGA with SD-based WSM are proposed. Finally, the proposed approach is demonstrated to be effective when carried out in the Pubugou Hydropower construction project.
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