Multi-objective Nonlinear Programming Research Articles

Optimization Design on Variable Cycle Engine Performance Based on Genetic Algorithm

The article have described the optimization of the engine performance problem as nonlinear multi-objective programming, and have analyzed the operation principle of the variable cycle engine, made models of maximum thrust , maximum unit thrust, minimum oil consumption, and then adopts the genetic algorithm to solve the model, gained the guide vane angle of CDFS,the guide vane angle of low-pressure.Turbine and the nozzle throat area when the performance is optimal . It is a problem about multi-objective optimization, obtained a series of satisfactory solution and then selected a set of approximate optimal solution as the final argument. Lastly, The matlab software is used to illustrate the effectiveness of the results.

Unified Interactive Approach for Solving Multiobjective Nonlinear Programming Problems

Unified Interactive Approach for Solving Multiobjective Nonlinear Programming Problems

Optimality and duality for nonsmooth multiobjective programming using G-type I functions

In this paper, (generalized) G-type I functions are defined for a nonlinear multiobjective programming problem where the functions involved are assumed to be locally Lipschitz. This new class of functions is a generalization of G-invex functions defined in Kang et al. (2012) [20]. Examples are given to show the existence of these functions. G-type Kuhn–Tucker necessary conditions are established for a nondifferentiable multiobjective programming problem (GMP). By using suitable G-type I functions, sufficient optimality conditions are derived for the problem (GMP). Further a Mond–Weir type dual (GMWD) is formulated and using these newly defined functions various duality results are established.

Berth and quay-crane allocation problem considering fuel consumption and emissions from vessels

Resolving the berth and quay-crane allocation problem improves the efficiency of seaside operations by optimally allocating berthing spaces and quay cranes to vessels, typically by considering a vessel’s sailing speed and arrival time at a port as constant parameters, while ignoring the impact of arrival times on fuel consumption and emissions when sailing. This work applied a novel nonlinear multi-objective mixed-integer programming model that considered a vessel’s fuel consumption and emissions, and then transformed this model into a second-order mixed-integer cone programming model to solve the problem’s computational intractability. Furthermore, the impact of number of allocated quay cranes on port operational cost, and a vessel’s fuel consumption and emissions was analyzed. Additionally, a vessel’s emissions while moored are also calculated based on wait time. Experimental results demonstrate that the new berth and quay-crane allocation strategy with a vessel’s arrival time as a decision variable can significantly improve vessels’ fuel consumption and emissions, the air quality around ports and utilization of berths and quay cranes without reducing service quality.

OPTIMIZATION OF ENERGY SAVING FOR WIRELESS SENSOR NETWORKS

Wireless sensor network (WSN) has been widely used in national defense, military and security, environmental monitoring and many other fields. It s of great significance to design WSN which consumes little energy but supports service quality flexibly and effectively. To further improve the performance of WSN, this article, focusing on aspects of low energy consumption and long life cycle of the WSN and taking energy limits and coverage requirements in WSN into account, attributes the coverage control problem of WSN to a multi-objective nonlinear programing proble. A mathematical model for multi-objective nonlinear programming problem is established and a virtual force optimization algorithm based on energy-saving is presented in this article. Sensor nodes and target coverage areas of virtual force operations and nodes of virtual force operations are carried out at the same time for energy saving so as to realize the optimization of coverage control technology. In terms of network routing optimization, taking QoS requirements, topology structure of the network and energy consumption into consideration, this article puts forward the hierarchical ecological niche ACA to optimize routing technology to analyze energy and realize simultion. Finally, advantages of the new optimization strategy on the enhancement of the network lifetime are illustrated.

A new decision-making model for solving multi-objective large-scale programming problems with a block angular structure

This paper presents a model based on a novel compromised solution method to solve the multi-objective large-scale nonlinear programming (MOLSNLP) problems with block angular structure. In this method, an aggregating function that is developed from TOPSIS and VIKOR is proposed based on the particular measure of ‘‘closeness” to the ‘‘ideal” solution. The decomposition algorithm is utilized to reduce the large-dimensional objective space into a two-dimensional space. Furthermore, two independent solution methods are proposed to solve each nonlinear sub problem respectively. In the last step of proposed method, Single objective nonlinear programming problem is solved to find the final solution. Finally, to justify the proposed method, an illustrative example is provided. Then, the sensitivity analysis is described.

Achieving Fair Spectrum Allocation and Reduced Spectrum Handoff in Wireless Sensor Networks: Modeling via Biobjective Optimization

This paper considers the problem of centralized spectrum allocations in wireless sensor networks towards the following goals: (1) maximizing fairness, (2) reflecting the priority among sensor data, and (3) avoiding unnecessary spectrum handoff. We cast this problem into a multiobjective mixed integer nonconvex nonlinear programming that is definitely difficult to solve at least globally without any aid of conversion or approximation. To tackle this intractability, we first convexify the original problem using arithmetic-geometric mean approximation and logarithmic change of the decision variables and then deploy weighted Chebyshev norm-based scalarization method in order to collapse the multiobjective problem into a single objective one. Finally, we apply simple rounding method in order to obtain approximate integer solutions. The results obtained from the numerical experiments show that, by adjusting the weight on each objective function, the proposed algorithm allocates spectrum bands fairly with well observing each sensor’s priority and reduced spectrum handoffs.

Compromise Allocation for Combined Ratio Estimates of Population Means of a Multivariate Stratified Population Using Double Sampling in Presence of Non-Response

This paper is an attempt to work out a compromise allocation to construct combined ratio estimates under multivariate double sampling design in presence of non-response when the population mean of the auxiliary variable is unknown. The problem has been formulated as a multi-objective integer non-linear programming problem. Two solution procedures are developed using goal programming and fuzzy programming techniques. A numerical example is also worked out to illustrate the computational details. A comparison of the two methods is also carried out.

Optimal Intersection Operation with Median U-Turn

The median U-turn intersection is a potential method for relieving traffic congestion at intersections. Median U-turn intersections can be classified into six types, according to the prohibited traffic movements. Although much is known about the technology of the median U-turn, efforts have focused on its geometric design, safety analysis, and evaluation. In this paper, a lane-based optimization model is proposed for the integrated design of median U-turn intersection types, lane markings, distances between the median crossovers and the main intersection, and signal timings. The capacity maximization problem is considered, and a set of constraints is determined that ensures the feasibility and safety of the optimization results. The optimization is formulated as a multi-objective mixed-integer nonlinear programming problem. It is solved by transformation to a series of mixed-integer linear programming models. The latter can be solved by the standard branch-and-bound technique. Extensive numerical analysis and a case study have shown the effectiveness of the proposed method. In addition, the method can assist transportation professionals in the proper selection of U-turn types and in the design of intersections with median U-turns.

Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming

In practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite population mean under cost constraint. An allocation of sample size becomes complicated when more than one characteristic is observed from each selected unit in a sample. In many real life situations, a linear cost function of a sample sizenhis not a good approximation to actual cost of sample survey when traveling cost between selected units in a stratum is significant. In this paper, sample allocation problem in multivariate stratified random sampling with proposed cost function is formulated in integer nonlinear multiobjective mathematical programming. A solution procedure is proposed using extended lexicographic goal programming approach. A numerical example is presented to illustrate the computational details and to compare the efficiency of proposed compromise allocation.

Optimization Model of Airplane Data Communication Network for Air Traffic Management

Aiming to better network facility deployment and reduce cost, this paper proposed an optimization model for air traffic management airplane data communication network based on multi-objective nonlinear programming to optimize the communication network trunk node and analyze user subnetwork access. Using multi-objective decomposition method, a computer-aided resolution model is presented and then simulations proved its effectiveness. This model has theoretical instruction on air traffic management plane data communication network design, and can offer reference for relate studies.

Fuzzy Goal Programming Approach in Selective Maintenance Reliability Model

800x600 In the present paper, we have considered the allocation problem of repairable components for a parallel-series system as a multi-objective optimization problem and have discussed two different models. In first model the reliability of subsystems are considered as different objectives. In second model the cost and time spent on repairing the components are considered as two different objectives. These two models is formulated as multi-objective Nonlinear Programming Problem (MONLPP) and a Fuzzy goal programming method is used to work out the compromise allocation in multi-objective selective maintenance reliability model in which we define the membership functions of each objective function and then transform membership functions into equivalent linear membership functions by first order Taylor series and finally by forming a fuzzy goal programming model obtain a desired compromise allocation of maintenance components. A numerical example is also worked out to illustrate the computational details of the method.  Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4

Immune optimization approach solving multi-objective chance-constrained programming

This article presents one bio-inspired immune optimization approach for linear or nonlinear multi-objective chance-constrained programming with any a prior random vector distribution. Such approach executes in order sample-allocation, evolution and memory update within a run period. In these modules, the first ensures that those high-quality elements can attach large sample sizes in the noisy environment. Thereafter, relying upon one proposed dominance probability model to justify whether one individual is superior to another one; the second attempts to find those diverse and excellent individuals. The last picks up some individuals in the evolving population to update low-quality memory cells in terms of their dominance probabilities. These guarantee that excellent and diverse individuals evolve towards the Pareto front, even if strong noises influence the process of optimization. Comparative and experimental results illustrate that the Monte Carlo simulation and important sampling make the proposed approach expose significantly different characteristics. Namely, the former ensures it a competitive optimizer, but the latter makes it effective only for uni-modal or linear chance-constrained programming. The sensitivity analysis claims that such approach performs well when two sensitive parameters takes values over specific intervals.

An Optimal Chance Constraint Multivariate Stratified Sampling Design Using Auxiliary Information

When we are dealing with multivariate problem then we need an allocation which is optimal for all the characteristics in some sense because the individual optimum allocations usually differ widely unless the characteristics are highly correlated. So an allocation called “Compromise allocation” is to be worked out suggested by Cochran. When auxiliary information is also available, it is customary to use it to increase the precision of the estimates. Moreover, for practical implementation of an allocation, we need integer values of the sample sizes. In the present paper the problem is to determine the integer optimum compromise allocation when the population means of various characteristics are of interest and auxiliary information is available for the separate and combined ratio and regression estimates. This paper considers the optimum compromise allocation in multivariate stratified sampling with non-linear objective function and probabilistic non-linear cost constraint. The probabilistic non-linear cost constraint is converted into equivalent deterministic one by using Chance Constrained programming. The formulated multi-objective nonlinear programming problem is solved by Fuzzy Goal programming approach and Chebyshev approximation. Numerical illustration is also given to show the practical utility of the approaches.

Multiobjective programming under (φ, d)-V-type I univexity

In this paper, we have introduced a new class of (φ, d)-V-type I univex, quasi (φ, d)-V-type I univex, pseudo (φ, d)-V-type I univex, quasi-pseudo (φ, d)-V-type I univex and pseudo-quasi (φ, d)-V-type I univex functions in case of nonlinear multiobjective programming problem where functions involved are nondifferentiable and illustrated through non-trivial examples that this class extends some known classes in literature. Various Karush-Kuhn-Tucker type sufficient optimality conditions are obtained under this newly introduced class of functions. Also, for mixed type multiobjective dual program, we have established weak, strong, converse and strict converse duality results in order to relate the efficient and weak efficient solutions of primal and dual problem.

Integrated Fuzzy ANP, Fuzzy VIKOR and goal programming for sourcing in a supply chain: A case study from cable industry

Article history: Received January 18, 2013 Received in revised format 10 May 2013 Accepted May 15 2013 Available online May 16 2013 In today’s competitive business environment, companies strive to increase their market shares. All companies clearly understand that they have to reach this goal by implementing cost effective methods and increase profits as much as possible. The cost of purchasing raw materials and component parts are significant portion of products in most manufacturing firms. Supplier selection and evaluation have been widely recognized to be one of the most substantial issues on material purchasing. In order to choose reliable suppliers it is necessary to have a trade-off between some tangible and intangible factors where some of them are in serious conflict. In this paper, an integrated technique of analytical network process improved by VIKOR and fuzzy sets theory and multi-objective mixed integer nonlinear programming is proposed to determine the appropriate suppliers. The proposed model of this paper also determines the order quantity allocated to each supplier in the case of multiple sourcing, multiple products and multi-period time horizon for an Iranian cable company. © 2013 Growing Science Ltd. All rights reserved.

A hybrid multi-objective approach based on the genetic algorithm and neural network to design an incremental cellular manufacturing system

One important issue related to the implementation of cellular manufacturing systems (CMSs) is to decide whether to convert an existing job shop into a CMS comprehensively in a single run, or in stages incrementally by forming cells one after the other, taking the advantage of the experiences of implementation. This paper presents a new multi-objective nonlinear programming model in a dynamic environment. Furthermore, a novel hybrid multi-objective approach based on the genetic algorithm and artificial neural network is proposed to solve the presented model. From the computational analyses, the proposed algorithm is found much more efficient than the fast non-dominated sorting genetic algorithm (NSGA-II) in generating Pareto optimal fronts.

Long-term multi-objective distribution network planning by DG allocation and feeders’ reconfiguration

This paper proposes a long-term planning method to maximize the benefits of network reconfiguration and distributed generation (DG) allocation in distribution networks. The proposed method handles long-term yearly load increase and seeks to define the reinforcements (i.e., line upgrades, network reconfiguration, and DG integration) and when and where they are required to meet the load rise with minimal cost and acceptable quality standards. The objectives considered in this paper are: economic (costs of line upgrades, energy losses, switching operations, and DG capital, operation and maintenance costs) and environmental (emissions from grid and DG units). The proposed method takes into consideration the uncertainty related to renewable DG output power and the load variability. The long-term planning problem is defined as multi-objective nonlinear mixed integer programming. The outcomes of the planning problem are the Pareto front, which represents different optimum operating system points. Finally, the local distribution company (LDC) can choose the system operating point based on its preferences.

A multi-objective model for designing a group layout of a dynamic cellular manufacturing system

This paper presents a multi-objective mixed-integer nonlinear programming model to design a group layout of a cellular manufacturing system in a dynamic environment, in which the number of cells to be formed is variable. Cell formation (CF) and group layout (GL) are concurrently made in a dynamic environment by the integrated model, which incorporates with an extensive coverage of important manufacturing features used in the design of CMSs. Additionally, there are some features that make the presented model different from the previous studies. These features include the following: (1) the variable number of cells, (2) the integrated CF and GL decisions in a dynamic environment by a multi-objective mathematical model, and (3) two conflicting objectives that minimize the total costs (i.e., costs of intra and inter-cell material handling, machine relocation, purchasing new machines, machine overhead, machine processing, and forming cells) and minimize the imbalance of workload among cells. Furthermore, the presented model considers some limitations, such as machine capability, machine capacity, part demands satisfaction, cell size, material flow conservation, and location assignment. Four numerical examples are solved by the GAMS software to illustrate the promising results obtained by the incorporated features.

On the Problem of Compromise Allocation in Multi-Response Stratified Sample Surveys

In stratified sample surveys, the problem of determining the optimum allocation is well known due to articles published in 1923 by Tschuprow and in 1934 by Neyman. The articles suggest the optimum sample sizes to be selected from each stratum for which sampling variance of the estimator is minimum for fixed total cost of the survey or the cost is minimum for a fixed precision of the estimator. If in a sample survey more than one characteristic is to be measured on each selected unit of the sample, that is, the survey is a multi-response survey, then the problem of determining the optimum sample sizes to various strata becomes more complex because of the non-availability of a single optimality criterion that suits all the characteristics. Many authors discussed compromise criterion that provides a compromise allocation, which is optimum for all characteristics, at least in some sense. Almost all of these authors worked out the compromise allocation by minimizing some function of the sampling variances of the estimators under a single cost constraint. A serious objection to this approach is that the variances are not unit free so that minimizing any function of variances may not be an appropriate objective to obtain a compromise allocation. This fact suggests the use of coefficient of variations instead of variances. In the present article, the problem of compromise allocation is formulated as a multi-objective non-linear programming problem. By linearizing the non-linear objective functions at their individual optima, the problem is approximated to an integer linear programming problem. Goal programming technique is then used to obtain a solution to the approximated problem.