Enhanced-interval linear programming

Zhou, Feng; Huang, Guohe; Chen, Guo-Xian; Guo, Hao

doi:10.1016/j.ejor.2008.12.019

Cited by 51 publications

(24 citation statements)

References 32 publications

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“…, (i = 1, 2..., n). In other words, x  is Pareto optimal if there exists no feasible vector of decision variables in the search space which would decrease some objectives without causing an increase in at least one other objective simultaneously (Zhou et al, 2009). …”

Section: Solution Approachmentioning

confidence: 99%

“…In order to overcome this problem some researchers have applied interval programming. In really using interval programming does not require the specification or the assumption of probabilistic distribution (as in stochastic programming) or possibility distributions (as in fuzzy programming) (Zhou et al, 2009). Hence, it is a good idea for the decision makers to determine the uncertain as intervals.…”

Section: Introductionmentioning

confidence: 99%

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An approach for solving multi-objective assignment problem with interval parameters

Salehi¹

2014

10.5267/j.msl

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This paper presents a multi-objective assignment problem (MAP) with interval parameters. Here, the model concentrates on three criteria: total cost, total profit and total operation time of assignment. The proposed model is classified as a nonlinear programming, in which it is difficult to solve. Hence, the model is converted into crisp linear programming problem by applying a substitution variables approach. In addition, a weighted min-max method is applied to transform the multi-objective problem into a single objective optimization problem. Finally, several numerical examples are provided to illustrate the implementation of the proposed approach. The results clearly provide some evidences that the proposed approach was easier to contrast compared with other approaches. The results also indicate that decision makers' preferences over various objectives could influence on solutions.

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Section: Solution Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An approach for solving multi-objective assignment problem with interval parameters

Salehi¹

2014

10.5267/j.msl

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show abstract

“…However, the increasing data requirements for specifying probability density or parameter membership functions have become a big challenge for TMDL allocations [7,14]. Even when many data are available, the computational algorithms for stochastic or fuzzy optimization models, such as nonlinear programming (NP) or modern heuristic global searches, may face complex or nonlinear problems [19,20]. For example, traditional NP algorithms, including both gradient and non-gradient based ones, were limited to local optima upon solving the aforementioned SOM framework [11,21].…”

Section: Introductionmentioning

confidence: 99%

“…The SOM framework under uncertainty can be grouped into four broad categories: namely stochastic optimization models, fuzzy optimization models, interval optimization models and hybrids of the above three model types [15][16][17][18][19]. However, the increasing data requirements for specifying probability density or parameter membership functions have become a big challenge for TMDL allocations [7,14].…”

Section: Introductionmentioning

confidence: 99%

“…Based on Huang's cluster analysis [16], Zhou et al [23] proposed a modified interval linear programming (MILP) model to establish strict mathematical relationships between decision variables and uncertain constraint coefficients, which also provides sufficient conditions to obtain an absolutely feasible solution space. Zhou et al [19] further defined a new uncertainty type, the enhanced-interval number, and developed an enhanced-interval linear programming (EILP) model, as well as a computationally-efficient solution algorithm, which provides insight into both extreme and non-extreme tradeoffs between system benefits and the different risk levels of constraint violations due to parametric uncertainties in the objective functions and constraints [15,18].…”

Section: Introductionmentioning

confidence: 99%

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An Indirect Simulation-Optimization Model for Determining Optimal TMDL Allocation under Uncertainty

Zhou

Dong

et al. 2015

Water

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An indirect simulation-optimization model framework with enhanced computational efficiency and risk-based decision-making capability was developed to determine optimal total maximum daily load (TMDL) allocation under uncertainty. To convert the traditional direct simulation-optimization model into our indirect equivalent model framework, we proposed a two-step strategy: (1) application of interval regression equations derived by a Bayesian recursive regression tree (BRRT v2) algorithm, which approximates the original hydrodynamic and water-quality simulation models and accurately quantifies the inherent nonlinear relationship between nutrient load reductions and the credible interval of algal biomass with a given confidence interval; and (2) incorporation of the calibrated interval regression equations into an uncertain optimization framework, which is further converted to our indirect equivalent framework by the enhanced-interval linear programming (EILP) method and provides approximate-optimal solutions at various risk levels. The proposed strategy was applied to the Swift Creek Reservoir's nutrient TMDL allocation (Chesterfield County, VA) to identify the minimum OPEN ACCESSWater 2015, 7 6635 nutrient load allocations required from eight sub-watersheds to ensure compliance with user-specified chlorophyll criteria. Our results indicated that the BRRT-EILP model could identify critical sub-watersheds faster than the traditional one and requires lower reduction of nutrient loadings compared to traditional stochastic simulation and trial-and-error (TAE) approaches. This suggests that our proposed framework performs better in optimal TMDL development compared to the traditional simulation-optimization models and provides extreme and non-extreme tradeoff analysis under uncertainty for risk-based decision making.

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Methodology for Interval-Valued Matrix Games with 2-Tuple Fuzzy Linguistic Information

Malhotra

Gupta

Singh³

2020

Lecture Notes in Computer Science

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Enhanced-interval linear programming

Cited by 51 publications

References 32 publications

An approach for solving multi-objective assignment problem with interval parameters

An approach for solving multi-objective assignment problem with interval parameters

An Indirect Simulation-Optimization Model for Determining Optimal TMDL Allocation under Uncertainty

Methodology for Interval-Valued Matrix Games with 2-Tuple Fuzzy Linguistic Information

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