ISSN:
 2155-3289

eISSN:
 2155-3297

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Volume 7, 2017

Volume 6, 2016

Volume 5, 2015

Volume 4, 2014

Volume 3, 2013

Volume 2, 2012

Volume 1, 2011

Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 4 issues a year in March, June, September and December.
  • Publishes both online and in print.
  • Indexed in Scopus, MathSciNet, Zentralblatt MATH and Emerging Sources Citation Index.
  • Archived in Portico and CLOCKSS.
  • NACO is a publication of the American Institute of Mathematical Sciences. All rights reserved.

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Performance evaluation of four-stage blood supply chain with feedback variables using NDEA cross-efficiency and entropy measures under IER uncertainty
Shiva Moslemi  and  Abolfazl Mirzazadeh 
2017, 7(4) : 379-401 doi: 10.3934/naco.2017024 +[Abstract](86) +[HTML](58) +[PDF](381.9KB)
Abstract:

Blood supply chain management has been considered by many managers in recent years, as one of the major challenges in health systems. In order to ensure the optimal performance of the supply chain, enable continuous improvement and create competitive advantage, establishment of a performance evaluation system is essential. For this purpose, the current study proposes a Network Data Envelopment Analysis (NDEA) model for measuring efficiency of four-stage serial network of blood supply chain in presence of feedback variables by identifying comprehensive and balanced criteria as evaluation variables. Since criteria values are obtained from subjective judgment of individuals, are uncertain. Interval Evidential Reasoning (IER) approach that deals with a variety of uncertainties such as ignorance and vagueness, has been used to control the uncertainty and provide reliable evaluation. In order to rank the units a new cross-efficiency based model is presented as a remedy for the issue of non-uniqueness of optimal weights in cross efficiency. Then, Gibbs entropy is utilized to measure the uncertainty of obtained interval cross efficiency. Finally, a numerical example is provided to illustrate the proposed model.

A new Monte Carlo based procedure for complete ranking efficient units in DEA models
Mazyar Zahedi-Seresht  , Gholam-Reza Jahanshahloo  , Josef Jablonsky  and  Sedighe Asghariniya 
2017, 7(4) : 403-416 doi: 10.3934/naco.2017025 +[Abstract](88) +[HTML](31) +[PDF](351.3KB)
Abstract:

Traditional data envelopment analysis (DEA) models split DMUs into two classes – namely efficient and inefficient. Due to the identical maximum efficiency scores of the efficient units, they cannot be ranked directly. That is why various models allowing the complete ranking of DMUs have been proposed in the past. Those models are based on different principles and have various advantages and disadvantages (infeasibility, alternative optimum, computational aspects, etc.). The method proposed in this paper uses the magnitude of the area under the efficient curve. In order to estimate this magnitude we suggest to use Monte Carlo simulation for the complete ranking originally efficient DMUs so as to overcome the problems arisen from other ranking methods and it is very simple, computationally. This method generates random weights for the inputs and outputs in the feasible region and finally derives probability the DMUs are efficient. The procedure proposed is illustrated by a numerical example and its results are compared with three of most important and popular methods for ranking efficient units (i.e. cross-efficiency evaluation, Andersen and Petersen super-efficiency model, and common set of weights method).

A robust multi-trip vehicle routing problem of perishable products with intermediate depots and time windows
Erfan Babaee Tirkolaee  , Alireza Goli  , Mani Bakhsi  and  Iraj Mahdavi 
2017, 7(4) : 417-433 doi: 10.3934/naco.2017026 +[Abstract](145) +[HTML](108) +[PDF](571.0KB)
Abstract:

Distribution of products within the supply chain with the highest quality is one of the most important competitive activities in industries with perishable products. Companies should pay much attention to the distribution during the design of their optimal supply chain. In this paper, a robust multi-trip vehicle routing problem with intermediate depots and time windows is formulated to deals with the uncertainty nature of demand parameter. A mixed integer linear programming model is presented to minimize total traveled distance, vehicles usage costs, earliness and tardiness penalty costs of services, and determine optimal routes for vehicles so that all customers' demands are covered. A number of random instances in different sizes (small, medium, and large) are generated and solved by CPLEX solver of GAMS to evaluate the robustness of the model and prove the model validation. Finally, a sensitivity analysis is applied to study the impact of the maximum available time for vehicles on the objective function value.

An investigation of the most important factors for sustainable product development using evidential reasoning
Farzaneh Ahmadzadeh  , Kathrina Jederström  , Maria Plahn  , Anna Olsson  and  Isabell Foyer 
2017, 7(4) : 435-455 doi: 10.3934/naco.2017027 +[Abstract](72) +[HTML](104) +[PDF](542.2KB)
Abstract:

Those working in product development need to consider sustainability, being careful not to compromise the future generation's ability to satisfy its needs. Several strategies guide companies towards sustainability. This paper studies six of these strategies: eco-design, green design, cradle-to-cradle, design for environment, zero waste, and life cycle approaches. Based on a literature review and semi-structured interviews, it identifies 22 factors of sustainability from the perspective of manufacturers. The purpose is to determine which are the most important and to use them as a foundation for a new design strategy. A survey based on the 22 factors was given to people working with product development; they graded each factor by importance. The resulting qualitative data were analyzed using evidential reasoning. The analysis found the factors "minimize use of toxic substances, " "increase competitiveness, " "economic benefits, " "reduce material usage, " "material selection, " "reduce emissions, " and "increase product functionality" are more important and should serve as the foundation for a new approach to sustainable product development.

A study of numerical integration based on Legendre polynomial and RLS algorithm
Hongguang Xiao  , Wen Tan  , Dehua Xiang  , Lifu Chen  and  Ning Li 
2017, 7(4) : 457-464 doi: 10.3934/naco.2017028 +[Abstract](70) +[HTML](27) +[PDF](291.3KB)
Abstract:

A quadrature rule based on Legendre polynomial functions is proposed to find approximate values of definite integrals in this paper. This method uses recursive least squares (RLS) algorithm to compute coefficients of Legendre polynomial fitting functions, and then approximately computes values of definite integrals by using obtained the coefficients. The main advantage of this approach is its efficiency and simple applicability. Finally some examples are given to test the convergence and accuracy of the method.

A hybrid meta-heuristic algorithm to minimize the number of tardy jobs in a dynamic two-machine flow shop problem
Mostafa Abouei Ardakan  , A. Kourank Beheshti  , S. Hamid Mirmohammadi  and  Hamed Davari Ardakani 
2017, 7(4) : 465-480 doi: 10.3934/naco.2017029 +[Abstract](58) +[HTML](75) +[PDF](437.8KB)
Abstract:

In this paper, first, the problem of dynamic two-machine flow shop scheduling with the objective of minimizing the number of tardy jobs is investigated. Second, a hybrid algorithm based on genetic algorithm and parallel simulated annealing algorithm is presented. In order to solve large scale instances of the problem and to generate the initial population for the hybrid approach, a heuristic algorithm is also presented. To evaluate the efficiency of the proposed algorithms, they are compared with an optimal branch-and-bound algorithm which has been already developed in the literature. Computational experiments demonstrate that the proposed hybrid algorithm can solve the entire small-sized problems and more than 95% of medium-sized problems optimally.

Numerical method for solving optimal control problems with phase constraints
Alexander Tyatyushkin  and  Tatiana Zarodnyuk 
2017, 7(4) : 481-492 doi: 10.3934/naco.2017030 +[Abstract](256) +[HTML](28) +[PDF](541.6KB)
Abstract:

The main idea of the method consists in successive solving auxiliary problems, which minimizes a special constructed Lagrange function, subject to linearized phase constraints. The linearly constrained auxiliary problems are more simple than the original ones because linear constraints can be easily processed. We shall discuss different aspects connected with approximating control problems and using the program system for solving them. We shall then pay attention to optimal control problems with constraints on inertia of control functions. For illustrations, four control problems will be solved using the proposed software.

Recent advances in numerical methods for nonlinear equations and nonlinear least squares
Ya-Xiang Yuan 
2011, 1(1) : 15-34 doi: 10.3934/naco.2011.1.15 +[Abstract](110) +[PDF](445.3KB) Cited By(27)
Control parameterization for optimal control problems with continuous inequality constraints: New convergence results
Ryan Loxton  , Qun Lin  , Volker Rehbock  and  Kok Lay Teo 
2012, 2(3) : 571-599 doi: 10.3934/naco.2012.2.571 +[Abstract](48) +[PDF](325.0KB) Cited By(18)
A modified Fletcher-Reeves-Type derivative-free method for symmetric nonlinear equations
Dong-Hui Li  and  Xiao-Lin Wang 
2011, 1(1) : 71-82 doi: 10.3934/naco.2011.1.71 +[Abstract](60) +[PDF](194.9KB) Cited By(16)
Univariate geometric Lipschitz global optimization algorithms
Dmitri E. Kvasov  and  Yaroslav D. Sergeyev 
2012, 2(1) : 69-90 doi: 10.3934/naco.2012.2.69 +[Abstract](128) +[PDF](602.3KB) Cited By(15)
Optimal control strategies for tuberculosis treatment: A case study in Angola
Cristiana J. Silva  and  Delfim F. M. Torres 
2012, 2(3) : 601-617 doi: 10.3934/naco.2012.2.601 +[Abstract](52) +[PDF](342.2KB) Cited By(13)
Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions
Walter Alt  , Robert Baier  , Matthias Gerdts  and  Frank Lempio 
2012, 2(3) : 547-570 doi: 10.3934/naco.2012.2.547 +[Abstract](128) +[PDF](298.8KB) Cited By(13)
Noether's symmetry Theorem for variational and optimal control problems with time delay
Gastão S. F. Frederico  and  Delfim F. M. Torres 
2012, 2(3) : 619-630 doi: 10.3934/naco.2012.2.619 +[Abstract](56) +[PDF](199.0KB) Cited By(12)
Towards globally optimal operation of water supply networks
Ambros M. Gleixner  , Harald Held  , Wei Huang  and  Stefan Vigerske 
2012, 2(4) : 695-711 doi: 10.3934/naco.2012.2.695 +[Abstract](91) +[PDF](810.5KB) Cited By(12)
An unconstrained optimization approach for finding real eigenvalues of even order symmetric tensors
Lixing Han 
2013, 3(3) : 583-599 doi: 10.3934/naco.2013.3.583 +[Abstract](54) +[PDF](442.5KB) Cited By(12)
Linearized alternating direction method of multipliers with Gaussian back substitution for separable convex programming
Bingsheng He  and  Xiaoming Yuan 
2013, 3(2) : 247-260 doi: 10.3934/naco.2013.3.247 +[Abstract](62) +[PDF](461.8KB) Cited By(11)
Performance evaluation of four-stage blood supply chain with feedback variables using NDEA cross-efficiency and entropy measures under IER uncertainty
Shiva Moslemi  and  Abolfazl Mirzazadeh 
2017, 7(4) : 379-401 doi: 10.3934/naco.2017024 +[Abstract](86) +[HTML](58) +[PDF](381.9KB) PDF Downloads(28)
A study of numerical integration based on Legendre polynomial and RLS algorithm
Hongguang Xiao  , Wen Tan  , Dehua Xiang  , Lifu Chen  and  Ning Li 
2017, 7(4) : 457-464 doi: 10.3934/naco.2017028 +[Abstract](70) +[HTML](27) +[PDF](291.3KB) PDF Downloads(20)
Numerical method for solving optimal control problems with phase constraints
Alexander Tyatyushkin  and  Tatiana Zarodnyuk 
2017, 7(4) : 481-492 doi: 10.3934/naco.2017030 +[Abstract](256) +[HTML](28) +[PDF](541.6KB) PDF Downloads(12)
A robust multi-trip vehicle routing problem of perishable products with intermediate depots and time windows
Erfan Babaee Tirkolaee  , Alireza Goli  , Mani Bakhsi  and  Iraj Mahdavi 
2017, 7(4) : 417-433 doi: 10.3934/naco.2017026 +[Abstract](145) +[HTML](108) +[PDF](571.0KB) PDF Downloads(10)
A new Monte Carlo based procedure for complete ranking efficient units in DEA models
Mazyar Zahedi-Seresht  , Gholam-Reza Jahanshahloo  , Josef Jablonsky  and  Sedighe Asghariniya 
2017, 7(4) : 403-416 doi: 10.3934/naco.2017025 +[Abstract](88) +[HTML](31) +[PDF](351.3KB) PDF Downloads(10)
A hybrid meta-heuristic algorithm to minimize the number of tardy jobs in a dynamic two-machine flow shop problem
Mostafa Abouei Ardakan  , A. Kourank Beheshti  , S. Hamid Mirmohammadi  and  Hamed Davari Ardakani 
2017, 7(4) : 465-480 doi: 10.3934/naco.2017029 +[Abstract](58) +[HTML](75) +[PDF](437.8KB) PDF Downloads(9)
Topological properties of Henig globally efficient solutions of set-valued problems
Guolin Yu 
2014, 4(4) : 309-316 doi: 10.3934/naco.2014.4.309 +[Abstract](167) +[PDF](290.7KB) PDF Downloads(9)
An investigation of the most important factors for sustainable product development using evidential reasoning
Farzaneh Ahmadzadeh  , Kathrina Jederström  , Maria Plahn  , Anna Olsson  and  Isabell Foyer 
2017, 7(4) : 435-455 doi: 10.3934/naco.2017027 +[Abstract](72) +[HTML](104) +[PDF](542.2KB) PDF Downloads(7)
A simplex grey wolf optimizer for solving integer programming and minimax problems
Mohamed A. Tawhid  and  Ahmed F. Ali 
2017, 7(3) : 301-323 doi: 10.3934/naco.2017020 +[Abstract](101) +[HTML](4) +[PDF](600.9KB) PDF Downloads(5)
A unified maximum entropy method via spline functions for Frobenius-Perron operators
Jiu Ding  and  Noah H. Rhee 
2013, 3(2) : 235-245 doi: 10.3934/naco.2013.3.235 +[Abstract](107) +[PDF](355.4KB) PDF Downloads(4)

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