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Article
Publication date: 1 April 1981

Arthur Meidan

Introduction Operations research, i.e. the application of scientific methodology to operational problems in the search for improved understanding and control, can be said to have…

Abstract

Introduction Operations research, i.e. the application of scientific methodology to operational problems in the search for improved understanding and control, can be said to have started with the application of mathematical tools to military problems of supply bombing and strategy, during the Second World War. Post‐war these tools were applied to business problems, particularly production scheduling, inventory control and physical distribution because of the acute shortages of goods and the numerical aspects of these problems.

Details

Management Decision, vol. 19 no. 4/5
Type: Research Article
ISSN: 0025-1747

Article
Publication date: 1 March 1984

B.H.V. Topping and D.J. Robinson

The use of three non‐linear mathematical programming techniques for the optimization of structural design problems is discussed. The methods — sequential linear programming, the…

Abstract

The use of three non‐linear mathematical programming techniques for the optimization of structural design problems is discussed. The methods — sequential linear programming, the feasible direction method and the sequential unconstrained minimization technique — are applied to a portal frame problem to enable a study of their convergence efficiency to be studied. These methods are used for both the sizing of the structural members and determining the optimum roof pitch. The sequential linear programming method is shown to be particularly efficient for application to structural design problems. Some comments on the development of computer software for structural optimization are also given.

Details

Engineering Computations, vol. 1 no. 3
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 19 June 2007

Ralf Östermark

To propose a new algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

Abstract

Purpose

To propose a new algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

Design/methodology/approach

The platform combines features from classical non‐linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around non‐integer discrete‐valued variables of local solutions, which reduces the search process significantly. In complicated problems fast feasibility restoration is achieved through concentrated Hessians. The system is programmed in strict ANSI C and can be run either stand alone or as a support library for other programs. File I/O is designed to recognize possible usage in both single and parallel processor environments.

Findings

The system has been tested on Alpha and Sun mainframes and – as a support library for a Genetic Hybrid Algorithm (GHA()) – in Linux and IBM parallel supercomputer environments. The constrained problem can, for example, be solved through a sequence of first order Taylor approximations of the non‐linear constraints and occasional feasibility restoration through Hessian information of the Lagrangian of the MINLP problem, or by invoking a nonlinear solver like SQP directly in the branch and bound tree. The system has been successfully tested on a small sample of representative continuous‐valued non‐linear programming problems.

Originality/value

It is demonstrated that – through zone‐constrained search – minlp_machine() outperforms some recent competing approaches with respect to the number of nodes in the branch and bound tree.

Details

Kybernetes, vol. 36 no. 5/6
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 12 June 2009

Ralf Östermark

To discuss a new parallel algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

Abstract

Purpose

To discuss a new parallel algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

Design/methodology/approach

The platform combines features from classical non‐linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around noninteger discrete‐valued variables at local solutions, which simplifies the local optimization problems and reduces the search process significantly. In complicated problems fast feasibility restoration may be achieved through concentrated Hessians. The system is programmed in strict ANSI C and can be run either stand alone or as a support library for other programs. File I/O is designed to recognize possible usage in both single and parallel processor environments. The system has been tested on Alpha, Sun and Linux mainframes and parallel IBM and Cray XT4 supercomputer environments. The constrained problem can, for example, be solved through a sequence of first order Taylor approximations of the non‐linear constraints and feasibility restoration utilizing Hessian information of the Lagrangian of the MINLP problem, or by invoking a nonlinear solver like SQP directly in the branch and bound tree. minlp_machine( ) has been tested as a support library to genetic hybrid algorithm (GHA). The GHA(minlp_machine) platform can be used to accelerate the performance of any linear or non‐linear node solver. The paper introduces a novel multicomputer partitioning of the discrete search space of genuine MINLP‐problems.

Findings

The system is successfully tested on a small sample of representative MINLP problems. The paper demonstrates that – through concurrent nonlinear branch and bound search – minlp_machine( ) outperforms some recent competing approaches with respect to the number of nodes in the branch and bound tree. Through parallel processing, the computational complexity of the local optimization problems is reduced considerably, an important aspect for practical applications.

Originality/value

This paper shows that binary‐valued MINLP‐problems will reduce to a vector of ordinary non‐linear programming on a suitably sized mesh. Correspondingly, INLP‐ and ILP‐problems will require no quasi‐Newton steps or simplex iterations on a compatible mesh.

Details

Kybernetes, vol. 38 no. 6
Type: Research Article
ISSN: 0368-492X

Keywords

Article
Publication date: 5 March 2018

Vincent Reinbold, Van-Binh Dinh, Daniel Tenfen, Benoit Delinchant and Dirk Saelens

This paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer…

Abstract

Purpose

This paper aims to present two mathematical models to solve the Energy Management problem of a building microgrid (MG). In particular, it proposes a deterministic mixed integer linear programming (MILP) and non-linear programming (NLP) formulations. This paper focuses on the modelling process and the optimization performances for both approaches regarding optimal operation of near-zero energy buildings connected to an electric MG with a 24-h time horizon.

Design/methodology/approach

A general architecture of a MG is detailed, involving energy storage systems, distributed generation and a thermal reduced model of the grid-connected building. A continuous non-linear model is detailed along with linearizations for the mixed-integer liner formulation. Multi-physic, non-linear and non-convex phenomena are detailed, such as ventilation and air quality models.

Findings

Results show that both approaches are relevant for solving the energy management problem of the building MG.

Originality/value

Introduction and modelling of the thermal loads within the MG. The resulting linear program handles the mutli-objective trade-off between discomfort and the cost of use taking into account air quality criterion. Linearization and modelling of the ventilation system behaviour, which is generally non-linear and non-convex equality constraints, involving air quality model, heat transfer and ventilation power. Comparison of both MILP and NLP methods on a general use case provides a solution that can be interpreted for implementation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 37 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 October 1995

B.A. Murtagh and J.W. Sims

Describes a procedure for modelling the costs of production anddistribution between several production facilities with economies ofscale and many customers who are widely…

1174

Abstract

Describes a procedure for modelling the costs of production and distribution between several production facilities with economies of scale and many customers who are widely dispersed. The problem takes the form of a large transportation problem on which is superimposed a cost minimization problem involving variable production quantities. These costs involve fixed costs for initiating production and variable costs with diminishing returns to scale. Models the problem as a non‐linear integer programming problem and then solves it using a recently developed non‐linear integer algorithm. Describes two applications in Australia and New Zealand and illustrates how comparison with a mixed‐integer linear programming formulation shows a significant improvement.

Details

International Journal of Physical Distribution & Logistics Management, vol. 25 no. 8
Type: Research Article
ISSN: 0960-0035

Keywords

Article
Publication date: 1 October 2005

Ralf Östermark

To solve the multi‐period portfolio management problem under transactions costs.

1650

Abstract

Purpose

To solve the multi‐period portfolio management problem under transactions costs.

Design/methodology/approach

We apply a recently designed super genetic hybrid algorithm (SuperGHA) – an integrated optimisation system for simultaneous parametric search and non‐linear optimisation – to a recursive portfolio management decision support system (SHAREX). The parametric search machine is implemented as a genetic superstructure, producing tentative parameter vectors that control the ultimate optimisation process.

Findings

SHAREX seems to outperform the buy and hold‐strategy on the Finnish stock market. The potential of a technical portfolio system is best exploitable under favorable market conditions.

Originality/value

A number of robust engines for matrix algebra, mathematical programming and numerical calculus have been integrated with SuperGHA. The engines expand its scope as a general‐purpose algorithm for mathematical programming.

Details

Kybernetes, vol. 34 no. 9/10
Type: Research Article
ISSN: 0368-492X

Keywords

Book part
Publication date: 1 January 1991

Abstract

Details

Operations Research for Libraries and Information Agencies: Techniques for the Evaluation of Management Decision Alternatives
Type: Book
ISBN: 978-0-12424-520-4

Abstract

Details

Optimal Growth Economics: An Investigation of the Contemporary Issues and the Prospect for Sustainable Growth
Type: Book
ISBN: 978-0-44450-860-7

Article
Publication date: 4 February 2022

Arezoo Gazori-Nishabori, Kaveh Khalili-Damghani and Ashkan Hafezalkotob

A Nash bargaining game data envelopment analysis (NBG-DEA) model is proposed to measure the efficiency of dynamic multi-period network structures. This paper aims to propose…

Abstract

Purpose

A Nash bargaining game data envelopment analysis (NBG-DEA) model is proposed to measure the efficiency of dynamic multi-period network structures. This paper aims to propose NBG-DEA model to measure the performance of decision-making units with complicated network structures.

Design/methodology/approach

As the proposed NBG-DEA model is a non-linear mathematical programming, finding its global optimum solution is hard. Therefore, meta-heuristic algorithms are used to solve non-linear optimization problems. Fortunately, the NBG-DEA model optimizes the well-formed problem, so that it can be solved by different non-linear methods including meta-heuristic algorithms. Hence, a meta-heuristic algorithm, called particle swarm optimization (PSO) is proposed to solve the NBG-DEA model in this paper. The case study is Industrial Management Institute (IMI), which is a leading organization in providing consulting management, publication and educational services in Iran. The sub-processes of IMI are considered as players where their pay-off is defined as the efficiency of sub-processes. The network structure of IMI is studied during multiple periods.

Findings

The proposed NBG-DEA model is applied to measure the efficiency scores in the IMI case study. The solution found by the PSO algorithm, which is implemented in MATLAB software, is compared with that generated by a classic non-linear method called gradient descent implemented in LINGO software.

Originality/value

The experiments proved that suitable and feasible solutions could be found by solving the NBG-DEA model and shows that PSO algorithm solves this model in reasonable central process unit time.

Details

Journal of Modelling in Management, vol. 18 no. 2
Type: Research Article
ISSN: 1746-5664

Keywords

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