Multiple Objective Nonlinear Programming Research Articles

توصيف حل البرمجة غير الخطية متعددة الأهداف ذات دوال هدف استقرابية و معلمات ضبابية في القيود

This paper presents a solution to multiple objective non-linear programming (MONLP) problems with rough objective functions and constraints with fuzzy parameters, we offer an algorithm to solve this type of problem, where we deal with multiple objective functions first, then with the fuzziness of the constraint parameter Characterizing, second and third, we deal with the roughness of the objective function. So, the problem finally turns into a non-linear programming problem with crisp objective functions and constraints. Finally, an illustrative example is given to show the application of the algorithm. Keywords: Multiobjective non-linear programming (MONLP), rough function, Fuzzy number, Ranking function.

Duality under novel generalizations of the D-type-I functions for multiple objective nonlinear programming problems

In this paper, we provide novel generalizations of the D-type-I functions by relaxing the D-Preinvexity functions using the mean-valued theorem. Under these new generalizations of the D-Preinvexity type-I functions, we also study the optimality solutions for multiple objective nonlinear programming problems. We also establish and illustrate the duality theorems (weak, strong, and converse) for the Wolf-type and Mond-Weir-type for multiple objective nonlinear programming problems using these new generalizations of the D-Preinvexity type-I functions.

Analysis The Policies Balancing Conservation and Community Interests in Maasai Mara

This paper aims to examine what policies are appropriate to balance conservation and community interests in the Maasai Mara. Grey Relational Analysis (GRA) is used to examine the relationship between indicators divided into two categories: wildlife species interests and economic industrial interests. A qualitative analysis is performed to establish a one-to-one linear correlation between the indicators. Multiple objective nonlinear programming and genetic algorithm are then applied to determine an objective function that quantizes the interests. Maximize the number of wildlife species and local community income by simulation. After the analysis of that simulation, an Fuzzy Comprehensive Evaluation (FCE) model combined with the Analytic Hierarchy Process (AHP) are employed to analyze the impact of different policies for different regions by studying the relationships between factors affecting the wildlife reserve, such as migration patterns of wildlife and the impact of human activities. This approach helps to determine the best policy decision based on the scores and pros and cons of each policy.

Second-Order Symmetric Duality for Multiple Objectives Nonlinear Programming Under Generalizations of Cone-Preinvexity Functions

In this article, we present generalizations of the cone-preinvexity functions and study a pair of second-order symmetric solutions for multiple objective nonlinear programming problems under these generalizations of the cone-preinvexity functions. In addition, we establish and prove the theorems of weak duality, strong duality, strict converse duality, and self-duality by assuming the skew-symmetric functions under these generalizations of the cone-preinvexity functions. Finally, we provide four nontrivial numerical examples to demonstrate that the results of the weak and strong duality theorems are true.

Generalizations of Higher-Order Duality for Multiple Objective Nonlinear Programming under the Generalizations of Type-I Functions

In this study, we introduce new generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions. The application of the notion of sublinear functionals to these generalizations of higher-order type-I and higher-order pseudo-convexity type-I functions is crucial to our main findings. Furthermore, under these generalizations of the higher-order type-I and higher-order pseudo-convexity type-I functions, we established and studied six new types of higher-order duality models and programs for multiple objective nonlinear programming problems. In addition, we use these generalizations of higher-order type-I functions and higher-order pseudo-convexity type-I functions, to formulate and prove the theorems of weak duality, strong duality, and strict converse duality for these new six types of higher-order model programs.

Using slacks-based model to solve inverse DEA with integer intervals for input estimation

This paper deals with an inverse data envelopment analysis (DEA) based on the non-radial slacks-based model in the presence of uncertainty employing both integer and continuous interval data. To this matter, suitable technology and formulation for the DEA are proposed using arithmetic and partial orders for interval numbers. The inverse DEA is discussed from the following question: if the output of DMU_o increases from Y_o to beta _o, such the new DMU is given by (alpha _o^*,beta ) belongs to the technology, and its inefficiency score is not less than t-percent, how much should the inputs of the DMU increase? A new model of inverse DEA is offered to respond to the previous question, whose interval Pareto solutions are characterized using the Pareto solution of a related multiple-objective nonlinear programming (MONLP). Necessary and sufficient conditions for input estimation are proposed when output is increased. A functional example is presented on data to illustrate the new model and methodology, with continuous and integer interval variables.

On Stability of Continuous Cooperative Static Games with Possibilistic Parameters in the Objective Functions.

The objective of this paper is to present a novel idea about the continuous possibilistic cooperative static game (Poss-CCSTG). The proposed Poss-CCSTG is a continuous cooperative static game (CCSTG) in which parameter associated with the cost functions of the players involves the possibility measures. The considered Poss-CCSTG is converted into the crisp α-CCSTG problem by using the α-cuts and hence into the multiple objective nonlinear programming problem. To solve the formulated α-CCSTG problem, an interactive approach is presented in the study with the use of the reference direction method. Further, the Lexicographic weighted Tchebycheff model is derived to obtain the weights. Also, a parametric study corresponding to the α-possibly optimal solution is defined and determined. Finally, a decision-maker can compare their desired solution with the attainable reference point and the weak efficient solution. The presented model is illustrated with a numerical example and its advantages are stated.

Carbon Emissions Abatement (CEA) Allocation Based on Inverse Slack-Based Model (SBM)

Carbon emissions abatement (CEA) is an important issue that draws attention from both academicians and policymakers. Data envelopment analysis (DEA) has been a popular tool to allocate the CEA, and most previous works are based on radial DEA models. However, as shown in our paper, these models may give biased results due to their ignorance of slackness. To avoid such problems, we propose an allocation model based on the slack-based model and multiple-objective nonlinear programming to find the CEA allocation plan, which can minimize the GDP loss. The property of nonconvexity makes the model difficult to solve. Thus, we construct an approximation algorithm to solve this model with guaranteed error bounds and complexity. In the empirical application, we take regions of china as an illustrative example and find there is a significant region gap in China. Hence, we group the regions into eastern, central, and western, and give the main results, as well as the superiority of our allocation models compared with radial models.

An outcome space algorithm for optimization over the weakly efficient set of a multiple objective nonlinear programming problem

This article presents for the first time an algorithm specifically designed for globally minimizing a finite, convex function over the weakly efficient set of a multiple objective nonlinear programming problem (V1) that has both nonlinear objective functions and a convex, nonpolyhedral feasible region. The algorithm uses a branch and bound search in the outcome space of problem (V1), rather than in the decision space of the problem, to find a global optimal solution. Since the dimension of the outcome space is usually much smaller than the dimension of the decision space, often by one or more orders of magnitude, this approach can be expected to considerably shorten the search. In addition, the algorithm can be easily modified to obtain an approximate global optimal weakly efficient solution after a finite number of iterations. Furthermore, all of the subproblems that the algorithm must solve can be easily solved, since they are all convex programming problems. The key, and sometimes quite interesting, convergence properties of the algorithm are proven, and an example problem is solved.

Inter-cell downlink co-channel interference management through cognitive sensing in heterogeneous network for LTE-A

Heterogeneous network for long term evolution advanced (LTE-A) creates severe interference. It is an urgent task to overcome the interference in macro cellular with low-power base stations (BSs), such as relay, pico, and femto called subnet nodes. In this paper, the cognitive interference model in interference zone (IZ) of the practical heterogeneous scenario is proposed. Based on investigation of interaction between the macro BS and subnet nodes in this model, the strategy framework of the cognitive critical ratio and power reward factor is set up for interference management aiming to get the maximum net saving power. The study of interference management is transformed into a multiple objective non-linear programming (MONLP) of the maximum saving power for the macro BS and subnet nodes. To facilitate the best compromise solution for both, the MONLP is changed into single objective programming and genetic algorithm (GA) is employed to obtain the global optimum solution. In addition, the practical implementation using the proposed algorithm in heterogeneous network for LTE-A is designed. Finally, numerical evaluation is used to test the applicability of the proposed algorithm, and system level simulation results demonstrate the effectiveness of the proposed interference management scheme.

A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables’ expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

The methodology of multiple-criteria decision making in the optimization of an urban transportation system: case study of Poznań City in Poland

The methodology of multiple-criteria decision making applied to the optimization of an urban transportation system is presented in the paper. Three mathematical models of different complexity are constructed to optimize the allocation of vehicles to certain routes in a mass transit system. All models take into account both passengers' and operator's objectives. The optimization problems are formulated in terms of multiple-objective fuzzy linear programming and multiple-objective non-linear programming. The sensitivity and precision analysis of the models is carried out. Two interactive multi-objective mathematical programming procedures are utilized to solve the problems. They generate samples of Pareto-optimal compromise solutions and provide the decision maker (DM) with an effective tool that supports him/her in the decision making process. Finally, the DM selects the solution that best fits his or her expectations.

The Parameter Space Investigation Method of Multiple Objective Nonlinear Programming: A Computational Investigation

In this paper we study the parameter space investigation method of I. M. Sobol and R. B. Statnikov. The method is a “random hitting” procedure for solving the kinds of small, but difficult, multiple objective nonlinear programming problems often encountered in engineering design and optimal control. Sobol and Statnikov have argued the effectiveness of their approach and its application possibilities. In this paper, we computationally test the parameter space investigation method to examine the extent to which claims about their method can be substantiated.

On the optimum design of Stewart platform type parallel manipulators

SummaryThis paper studies the static rigidity behaviour of a parallel manipulator with legs modelled as elastic members under axial loading. Structurally, a parallel module is more rigid compared to a serial module and is expected to take heavier payloads. Therefore, a guidance for design of such parallel manipulators is needed which leads to maximum rigidity over the workspace. In the present work, the authors propose the concept of the flexibility ellipsoid for a parallel system. Various scalar measures of rigidity are formulated on the basis of the proposed ellipsoid. An algorithm, involving multiple objective nonlinear programming technique, is implemented to decide upon some important design parameters of a generalised six degrees of freedom Stewart platform type parallel manipulator. It is observed that irrespective of the other parameters, parallel manipulators with the legs pairwise joined at the top platform possess the highest rigidity. Moreover, there exists certain kinematic dimensions for which the designed parallel system is completely free from all sorts of singularity.

Reference direction approach for solving multiple objective nonlinear programming problems

Proposes an interactive algorithm based on the reference direction approach to solve multiple objective nonlinear programming problems. The decision maker gives his/her aspiration levels in terms of the reference point in the objective function space. A number of efficient solutions are generated along the projection of the reference direction onto the efficient frontier. Each solution is an (weak) efficient solution. No special software is required to implement the proposed algorithm. The algorithm is illustrated with an example.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cone contraction method with visual interaction for multiple-objective non-linear programmes

We describe an interactive procedure, implemented on a PC, for solving multiple-objective non-linear programming (MONP) problems. The procedure is composed of two stages. The first stage consists of modelling decision maker's (DM's) preferences using a fuzzy outranking relation in a sample of non-dominated points. The relation is then translated into a preference cone defining a subset of non-dominated points of greatest interest to the DM. In the second stage the subset of non-dominated points generated by the cone is scanned interactively. A graphical interface enables a visual interaction. The DM can either reduce directly the subset of non-dominated points to be scanned or retract to the first stage and give finer preference information which results in contraction of the cone and reduction of the subset of non-dominated points scanned in the second stage. Description of the procedure is followed by presentation of its application to a didactic MONP problem.

Application of fuzzy theories to multiple objective decision making in system design

Much decision making in the real world takes place in an environment in which the goals, constraints, and consequences of possible actions are not known precisely. To deal with such imprecision in a quantitative manner, the tools of fuzzy set theory can be advantageously applied. The use and effectiveness of fuzzy theories in the formulation and solution of design problems are developed and described via an application in the engineering design of high speed mechanisms. An integrated approach to the design of high speed planar mechanisms is formulated as a multiple objective nonlinear programming problem, which combines both the kinematic and dynamic synthesis aspects of mechanism design. To model the vague and imprecise information in the problem formulation, the tools of fuzzy set theory have been used. A novel method of solving the resulting fuzzy multiple objective problem using mathematical programming techniques is presented. The outlined procedure should be useful in engineering and management design situations where uncertainty or ambiguity arises about the preciseness of permissible parameters, degree of credibility, and correctness of statements and judgements.

An Algorithm for Multiple-objective Non-linear Programming

An interactive algorithm to solve multiple-objective non-linear programming (MONLP) problems is proposed. In each iteration of the proposed algorithm, the decision-maker is presented with a solution and a set of direction (trade-off) vectors indicating possible trade-offs. Using the decision-maker's preferred trade-off vector, a new current solution and the corresponding trade-off vectors are found. The proposed algorithm is illustrated with a numerical example of a replacement model. Finally, the method is compared with four other interactive multiple-objective algorithms.

An Algorithm for Multiple-Objective Non-Linear Programming

An Algorithm for Multiple-Objective Non-Linear Programming

An Algorithm for Multiple-objective Non-linear Programming

An Algorithm for Multiple-objective Non-linear Programming