A novel interval linear programming based on probabilistic dominance. (English) Zbl 1522.90285
Summary: This study investigates a novel interval linear programming based on probabilistic dominance. Firstly, the definition of interval linear programming is briefly reviewed. Then a new interval linear programming model is presented based on probabilistic dominance. The probabilistic dominance index treats the intervals as uniformly distributed variables and the interval inequality relation is further defined by probability. To deal with non-linearity in probabilistic dominance index, sequential quadratic programming is used to solve the problem and the performance measure approach is proposed to overcome the convergence difficulties. The determination and sensitivity analysis of the target performance measure are discussed to assess the sequential quadratic programming algorithm. Meanwhile, the extension of the proposed method to fuzzy interval linear programming is discussed. Furthermore, the proposed method is applied to the design of the plane truss structure with interval parameters. Finally, the effectiveness and rationality of the developed method are demonstrated by two mathematical examples and one interval parametric plane truss structure optimization example.
MSC:
| 90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |
| 90C05 | Linear programming |
| 90C20 | Quadratic programming |
Keywords:
interval linear programming; probabilistic dominance; sequential quadratic programming algorithm; performance measure approach; interval parametric plane truss structure optimizationReferences:
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