An uncertain multi-objective programming problem is a special type of mathematical multi-objectiveprogramming involving uncertain variables. This type of problem is important because there are several uncertain varia...
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An uncertain multi-objective programming problem is a special type of mathematical multi-objectiveprogramming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world ***, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain ***, the uncertainmulti-objective problem is converted into an uncertain single-objectiveprogramming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objectiveprogramming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objectiveprogramming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.
The uncertain cooperative task assignment (CTA) problem based on uncertainty theory is a complex combinatorial optimization problem that cannot be effectively addressed using probability theory due to insufficient sam...
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The uncertain cooperative task assignment (CTA) problem based on uncertainty theory is a complex combinatorial optimization problem that cannot be effectively addressed using probability theory due to insufficient samples. In light of this limitation, this paper initially proposes an uncertainmultiobjective CTA (UMCTA) problem, taking into account the uncertainties present in the battlefield environment. Consequently, the expected-value standard-deviation UMCTA model (E sigma-UMCTA) model, which emphasize the minimization of expected returns and stability of the objective functions, is developed. Nonetheless, this approach may yield suboptimal assignment schemes under predetermined risk levels. To address this issue, a minimum-risk model for the UMCTA problem is introduced by maximizing the belief degree that the objective functions do not exceed the predefined risk levels, and the concept of the minimum-risk efficient assignment scheme is delineated. Given the challenges in solving the minimum-risk model due to uncertain variables, two scenarios for addressing these uncertainties in the UMCTA problem are contemplated, and the minimum-risk model is transformed into a deterministic multiobjectiveprogramming problem. Subsequently, recognizing the combinational nature and complexity of the resulting deterministic multiobjectiveprogramming problem, an enhanced discrete particle swarm optimization (PSO) algorithm with non-dominated sorting is devised, where the crossover and mutation operators are employed to sustain diversity and avert premature convergence. Finally, a simulation study is conducted to substantiate the practicability of the proposed model and assess the efficacy of the designed algorithm.
Water Saving Management Contract (WSMC) is a novel market-oriented business model, which can effectually allay the pressure of the regional water crisis. However, the imbalance of water demand and supply affecting the...
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In this paper, we discuss the formulation of the oilfield development plan in case of significant nondeterminacy in oilfield development. And the plan needs to ensure production and achieve minimum cost and maximum ne...
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In this paper, we discuss the formulation of the oilfield development plan in case of significant nondeterminacy in oilfield development. And the plan needs to ensure production and achieve minimum cost and maximum new recoverable reserves. The uncertain factors in oilfield development are analyzed in this paper, and we consider the uncertain nature of the stimulation effect of measures and new recoverable reserves per well and quantify them. On this basis, an uncertainmulti-objective optimal model of oilfield development planning is constructed. The model aims to minimize the expectation of development cost and maximize the expectation of new recoverable reserves, and optimizes the workload of each measure under the constraints including the oil production and the resources limitation. Based on uncertainty theory, the model is transformed into a deterministic model. And a nondominated sorting genetic algorithm with elite strategy is developed to solve the model and get the Pareto solution set. Then the multi-attribute decision-making is applied to select the multiple development plans, which provides the basis for the decision-making of the oilfield development plan. Finally, a numerical example is given to verify the effectiveness of the model and algorithm, and their practical application values under the background of oilfield development planning.
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