A study of uncertain multi-objective nonlinear programming problems for rough intervals

In real conditions, the parameters of multi-objective nonlinear programming (MONLP) problem models can’t be determined exactly. Hence in this paper, we concerned with studying the uncertainty of MONLP problems. We propose algorithms to solve rough and fully-rough-interval multi-objective nonlinear programming (RIMONLP and FRIMONLP) problems, to determine optimal rough solutions value and rough decision variables, where all coefficients and decision variables in the objective functions and constraints are rough intervals (RIs). For the RIMONLP and FRIMONLP problems solving methodology are presented using the weighting method and slice-sum method with Kuhn-Tucker conditions, We will structure two nonlinear programming (NLP) problems. In the first one of this NLP problem, all of its variables and coefficients are the lower approximation (LAI) it’s RIs. The second NLP problems are upper approximation intervals (UAI) of RIs. Subsequently, both NLP problems are sliced into two crisp nonlinear problems. NLP is utilized because numerous real systems are inherently nonlinear. Also, rough intervals are so important for dealing with uncertainty and inaccurate data in decision-making (DM) problems. The suggested algorithms enable us to the optimal solutions in the largest range of possible solution. Finally, Illustrative examples of the results are given.

Optimization of S-Nitrosocaptopril Monohydrate Storage Conditions Based on Response Surface Method

From unstable crystals to relatively stable monohydrate crystals, many researchers have been working on S-nitrosocaptopril for more than two decades. S-nitrosocaptopril monohydrate (Cap-NO·H2O) is a novel crystal form of S-nitrosocaptopril (Cap-NO), and is not only a nitric oxide (NO) donor, but also an angiotensin-converting enzyme inhibitor (ACEI). Yet, a method for long-term storage has never been reported. In order to determine the optimal storage conditions, Plackett–Burman (PB) design was performed to confirm the critical factors. Response surface methodology (RSM) was employed to determine the optimal Cap-NO·H2O storage condition, based on the rough interval determined by the path of steepest ascent experiment. The optimized storage condition was denoted as nitrogen purity of 97%, temperature of −10 °C and 1.20 g deoxidizer. In this case, a final preservation rate of 97.91 ± 0.59% could be obtained. In specific storage conditions, Cap-NO·H2O was found to be stable for at least 6 months in individual PE package, procreating a potentially applicable avenue.

An Approach for Solving Multi-Objective Linear Fractional Programming Problem with fully Rough Interval Coefficients

In this paper, a multi-objective linear fractional programming (MOLFP) problem is considered where all of its coefficients in the objective function and constraints are rough intervals (RIs). At first, to solve this problem, we will construct two MOLFP problems with interval coefficients. One of these problems is a MOLFP where all of its coefficients are upper approximations of RIs and the other is a MOLFP where all of its coefficients are lower approximations of RIs. Second, the MOLFP problems are transformed into a single objective linear programming (LP) problem using a proposal given by Nuran Guzel. Finally, the single objective LP problem is solved by a regular simplex method which yields an efficient solution of the original MOLFP problem. A numerical example is given to demonstrate the results.

Optimizing a fully rough interval integer solid transportation problems

An innovative method, namely modified slice-sum method using the principle of zero point method is proposed for finding an optimal solution to fully rough interval integer solid transportation problems (FRIISTP). The proposed method yields an optimal solution to the fully rough interval integer solid transportation problem directly. In this method, there is no necessity to find an initial basic feasible solution to FRIISTP and also need not to use the existing MODI and stepping stone methods for testing the optimality to improve the basic feasible solution to the FRIISTP but directly obtain an optimal solution to the given FRIISTP by using the proposed method. The optimal values of decision variables and the objective function of the fully rough interval integer solid transportation problems provided by the proposed method are rough interval integers. The advantages of the proposed method over existing method are discussed in the context of an application example. The modified slice-sum method has been applied to calculate the optimal compromise solutions of FRIISTP, and then it was solved by using TORA software. The proposed method can be served as an appropriate tool for the decision makers when they are handling logistic models of real life situations involving three items with rough interval integer parameters.

Approaches for Solving Fully Fuzzy Rough Multi-Objective Nonlinear Programming Problems

Practical nonlinear programming problem often encounters uncertainty and indecision due to various factors that cannot be controlled. To overcome these limitations, fully fuzzy rough approaches are applied to such a problem. In this paper, an effective two approaches are proposed to solve fully fuzzy rough multi-objective nonlinear programming problems (FFRMONLP) where all the variables and parameters are fuzzy rough triangular numbers. The first, based on a slice sum technique, a fully fuzzy rough multi-objective nonlinear problem has turned into five equivalent multi-objective nonlinear programming (FFMONLP) problems. The second proposed method for solving FFRMONLP problems is α-cut approach, where the triangular fuzzy rough variables and parameters of the FFRMONLP problem are converted into rough interval variables and parameters by α-level cut, moreover the rough MONLP problem turns into four MONLP problems. Furthermore, the weighted sum method is used in both proposed approaches to convert multi-objective nonlinear problems into an equivalent nonlinear programming problem. Finally, the effectiveness of the proposed procedure is demonstrated by numerical examples.

Uncertainty Approaches for Solving Generalized Machine Maintenance Problem

In this paper, the generalized machine maintenance problem is formulated as linear programming model. The objective is to maximize the percentage production hours available per maintenance cycle of each machine. Data in many real life engineering and economic problems suffers from inexactness. There are different approaches to deal with uncertain optimization problems. In this paper two different approaches of uncertainty, Fuzzy programming and rough interval programming approaches will be introduced. We deal the concerned problem with uncertain data in coefficients of the constraints for the two approaches. A numerical example is introduced to clarify the two proposed approaches. A comparison study between the obtained results of the two proposed approaches and the results of interval approach for Samir A. and Marwa Sh [3] will be introduced.

Rough interval Max Plus Algebra for Transportation Problems

The traffic problem is an important problem which has been broadly learnt in Operations Research domain. This paper presents a new Rough Interval Max Algebra Approach (RIMAA) for solving the traffic problem with Rough Interval data. The proposed approach is simple and able to give a suitable solution to this problem. Finally, a descriptive example is given to evaluate performance of the proposed approach.