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

2022 ◽  
pp. 1-15
Author(s):  
E. Ammar ◽  
A. Al-Asfar

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.

Author(s):  
E. Ammar ◽  
A. Al-Asfar

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.


2014 ◽  
Vol 984-985 ◽  
pp. 419-424
Author(s):  
P. Sabarinath ◽  
M.R. Thansekhar ◽  
R. Saravanan

Arriving optimal solutions is one of the important tasks in engineering design. Many real-world design optimization problems involve multiple conflicting objectives. The design variables are of continuous or discrete in nature. In general, for solving Multi Objective Optimization methods weight method is preferred. In this method, all the objective functions are converted into a single objective function by assigning suitable weights to each objective functions. The main drawback lies in the selection of proper weights. Recently, evolutionary algorithms are used to find the nondominated optimal solutions called as Pareto optimal front in a single run. In recent years, Non-dominated Sorting Genetic Algorithm II (NSGA-II) finds increasing applications in solving multi objective problems comprising of conflicting objectives because of low computational requirements, elitism and parameter-less sharing approach. In this work, we propose a methodology which integrates NSGA-II and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) for solving a two bar truss problem. NSGA-II searches for the Pareto set where two bar truss is evaluated in terms of minimizing the weight of the truss and minimizing the total displacement of the joint under the given load. Subsequently, TOPSIS selects the best compromise solution.


2015 ◽  
Vol 20 (3) ◽  
pp. 329-345 ◽  
Author(s):  
Suvasis Nayak ◽  
Akshay Ojha

This paper illustrates a procedure to generate pareto optimal solutions of multi-objective linear fractional programming problem (MOLFPP) with closed interval coefficients of decision variables both in objective and constraint functions. E-constraint method is applied to produce pareto optimal solutions comprising most preferred solution to satisfy all objectives. A numerical example is solved using our proposed method and the result so obtained is compared with that of fuzzy programming which justifies the efficiency and authenticity of the proposed method.


2015 ◽  
Vol 23 (1) ◽  
pp. 69-100 ◽  
Author(s):  
Handing Wang ◽  
Licheng Jiao ◽  
Ronghua Shang ◽  
Shan He ◽  
Fang Liu

There can be a complicated mapping relation between decision variables and objective functions in multi-objective optimization problems (MOPs). It is uncommon that decision variables influence objective functions equally. Decision variables act differently in different objective functions. Hence, often, the mapping relation is unbalanced, which causes some redundancy during the search in a decision space. In response to this scenario, we propose a novel memetic (multi-objective) optimization strategy based on dimension reduction in decision space (DRMOS). DRMOS firstly analyzes the mapping relation between decision variables and objective functions. Then, it reduces the dimension of the search space by dividing the decision space into several subspaces according to the obtained relation. Finally, it improves the population by the memetic local search strategies in these decision subspaces separately. Further, DRMOS has good portability to other multi-objective evolutionary algorithms (MOEAs); that is, it is easily compatible with existing MOEAs. In order to evaluate its performance, we embed DRMOS in several state of the art MOEAs to facilitate our experiments. The results show that DRMOS has the advantage in terms of convergence speed, diversity maintenance, and portability when solving MOPs with an unbalanced mapping relation between decision variables and objective functions.


Author(s):  
Weijun Wang ◽  
Stéphane Caro ◽  
Fouad Bennis

In the presence of multiple optimal solutions in multi-modal optimization problems and in multi-objective optimization problems, the designer may be interested in the robustness of those solutions to make a decision. Here, the robustness is related to the sensitivity of the performance functions to uncertainties. The uncertainty sources include the uncertainties in the design variables, in the design environment parameters, in the model of objective functions and in the designer’s preference. There exist many robustness indices in the literature that deal with small variations in the design variables and design environment parameters, but few robustness indices consider large variations. In this paper, a new robustness index is introduced to deal with large variations in the design environment parameters. The proposed index is bounded between zero and one, and measures the probability of a solution to be optimal with respect to the values of the design environment parameters. The larger the robustness index, the more robust the solution with regard to large variations in the design environment parameters. Finally, two illustrative examples are given to highlight the contributions of this paper.


2021 ◽  
Author(s):  
Israel Mayo-Molina ◽  
Juliana Y. Leung

Abstract The Steam Alternating Solvent (SAS) process has been proposed and studied in recent years as a new auspicious alternative to the conventional thermal (steam-based) bitumen recovery process. The SAS process incorporates steam and solvent (e.g. propane) cycles injected alternatively using the same configuration as the Steam-Assisted Gravity-Drainage (SAGD) process. The SAS process offers many advantages, including lower capital and operational cost, as well as a reduction in water usage and lower Greenhouse Gas (GHG) Emissions. On the other hand, one of the main challenges of this relatively new process is the influence of uncertain reservoir heterogeneity distribution, such as shale barriers, on production behaviour. Many complex physical mechanisms, including heat transfer, fluid flows, and mass transfer, must be coupled. A proper design and selection of the operational parameters must consider several conflicting objectives. This work aims to develop a hybrid multi-objective optimization (MOO) framework for determining a set of Pareto-optimal SAS operational parameters under a variety of heterogeneity scenarios. First, a 2-D homogeneous reservoir model is constructed based on typical Cold lake reservoir properties in Alberta, Canada. The homogeneous model is used to establish a base scenario. Second, different shale barrier configurations with varying proportions, lengths, and locations are incorporated. Third, a detailed sensitivity analysis is performed to determine the most impactful parameters or decision variables. Based on the results of the sensitivity analysis, several objective functions are formulated (e.g., minimizing energy and solvent usage). Fourth, Response Surface Methodology (RSM) is applied to generate a set of proxy models to approximate the non-linear relationship between the decision variables and the objective functions and to reduce the overall computational time. Finally, three Multi-Objective Evolutionary Algorithms (MOEAs) are applied to search and compare the optimal sets of decision parameters. The study showed that the SAS process is sensitive to the shale barrier distribution, and that impact is strongly dependent on the location and length of a specific shale barrier. When a shale barrier is located near the injector well, pressure and temperature may build up in the near-well area, preventing additional steam and solvent be injected and, consequently, reducing the oil production. Operational constraints, such as bottom-hole pressure, steam trap criterion, and bottom-hole gas rate in the producer, are among various critical decision variables examined in this study. A key conclusion is that the optimal operating strategy should depend on the underlying heterogeneity. Although this notion has been alluded to in other previous steam- or solvent-based studies, this paper is the first to utilize a MOO framework for systematically determining a specific optimal strategy for each heterogeneity scenario. With the advancement of continuous downhole fibre-optic monitoring, the outcomes can potentially be integrated into other real-time reservoir characterization and optimization work-flows.


2004 ◽  
Vol 21 (01) ◽  
pp. 127-139 ◽  
Author(s):  
G. R. JAHANSHAHLOO ◽  
F. HOSSEINZADEH LOTFI ◽  
N. SHOJA ◽  
G. TOHIDI

In this paper, a method using the concept of l1-norm is proposed to find all the efficient solutions of a 0-1 Multi-Objective Linear Programming (MOLP) problem. These solutions are specified without generating all feasible solutions. Corresponding to a feasible solution of a 0-1 MOLP problem, a vector is constructed, the components of which are the values of objective functions. The method consists of a one-stage algorithm. In each iteration of this algorithm a 0-1 single objective linear programming problem is solved. We have proved that optimal solutions of this 0-1 single objective linear programming problem are efficient solutions of the 0-1 MOLP problem. Corresponding to efficient solutions which are obtained in an iteration, some constraints are added to the 0-1 single objective linear programming problem of the next iteration. Using a theorem we guarantee that the proposed algorithm generates all the efficient solutions of the 0-1 MOLP problem. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.


Author(s):  
Xiaojun Liu ◽  
Dongye Sun ◽  
Datong Qin ◽  
Junlong Liu

The power-cycling hydrodynamic mechanical transmissions have the advantages of continuously adjustable speed ratio and high efficiency compared with the traditional automatic transmissions, so they may be a good substitute for the prior art. For off-highway vehicles which frequently work in low speed and confront great resistance, the zero-speed-ratio torque ratio (TR) of the power-cycling hydrodynamic mechanical transmissions represents the power performance of the vehicles. Furthermore, the complexity of the transmissions is an indispensable consideration for industrial designers. The radial and axial dimensions of the power-cycling hydrodynamic mechanical transmissions are determined by the effective diameter of the torque converter’s circuit and the number of transmissions gears, respectively. In order to optimize the zero-speed-ratio TR and the complexity of the power-cycling hydrodynamic mechanical transmissions, a design methodology is proposed. Considering that there is no explicit mathematical relationship between the design variables and the multi-objective functions, the parametric design and numerical simulation for the torque converter are carried out. The intrinsic mapping between the design variables and the multi-objective functions is fitted by the radial basis function neural network. On this basis, the fast and elitist non-dominated sorting genetic algorithm (NSGA-ΙΙ) is used to solve the multi-objective optimization problem. The numerical simulation for one group of solution selected from the Pareto optimal solutions is conducted. The simulation results indicate that the design methodology proposed in this study is effective. The optimal results show that the zero-speed-ratio TR of the power-cycling hydrodynamic mechanical transmissions is heavily influenced by the radial and axial space of such transmissions. The design optimization helps to find the optimal solutions for the power-cycling HMTs, which are superior to the traditional automatic transmissions and match well the prime mover.


Transport ◽  
2013 ◽  
Vol 30 (1) ◽  
pp. 55-60
Author(s):  
Mirano Hess ◽  
Svjetlana Hess

This paper proposes a new optimization model for ship’s cargo handling operations which solution gives the structure of cargo handling resources required, along with attaining the minimum total ‘in-port’ costs and the minimum of time required for completion of cargo operations. Due to complexity of the model which consists of composite multi-objective functions together with several decision variables and constraints, the solution has been sought by utilization of an adapted genetic algorithm combined with a hybrid algorithm. Testing of the model on real world data yielded acceptable results in a short time. In the course of decision making, the ship’s operator can, on the basis of the proposed model and taking into consideration shipping market data, choose appropriate variation of the returned solution, which incorporates minimum costs, minimum of operational time and related cargo handling resources.


2012 ◽  
Vol 591-593 ◽  
pp. 15-20
Author(s):  
Jun Zhou ◽  
Jiao Long Zhang ◽  
Feng Qi Zhou

Aiming at the seriously nonlinear problems of the single nozzle thrust vector control servo system, this paper detailedly deduced the functional relations between the layout of actuators and system dynamic parameters, on the basis of which, a multi-objective optimization model was established with coupling degree, angular asymmetry, as well as length and variation degree of initial swinging arm taken into consideration. Linear weighting method was adopted to convert the multi-objective function into a uni-objective one and an improved genetic algorithm with good robustness was utilized to solve the optimization problem. Calculation results demonstrated that, with this optimization algorithm, sub-objective functions all reach the ideal effects when uni-objective function achieves optimum. The optimization method guarantees that coupling degree, angular asymmetry and swinging arm variation achieve minimum when the initial swinging arm length is at its maximum, which provides theoretical basis for the actuator layout of thrust vector control.


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