A nonlinear mixed integer multiperiod firm model

Östermark, Ralf; Skrifvars, Hans; Westerlund, Tapio

doi:10.1016/s0925-5273(00)00019-0

Cited by 9 publications

(5 citation statements)

References 18 publications

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“…Mixed‐integer non‐linear programming (MINLP) problems occur abundantly in economics and engineering. For example, in multi‐period firm planning both discrete and continuous‐valued variables are mostly encountered when contemplating investment decisions – a factory is built or not, eventhough its financing may involve a continuous‐valued monetary spectrum (Östermark et al , 2000). Risk assessment of the firm as a generic multiperiod decision system – quantification of its risk surface – involves a MINLP formulation as a basis for Monte Carlo analysis.…”

Section: Introductionmentioning

confidence: 99%

Concurrent processing of mixed‐integer non‐linear programming problems

Östermark

2009

Kybernetes

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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.

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Section: Introductionmentioning

confidence: 99%

Concurrent processing of mixed‐integer non‐linear programming problems

Östermark

2009

Kybernetes

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“…Most of them have preferred a deterministic approach, but several works also pose models where data, for example demands, are uncertain. − Different methods have been used to formulate the corresponding models. Most of the works pose a mathematical model, generally MILP or MINLP formulations. However, there exist works that resort to simulation or heuristic approaches.…”

Section: Introductionmentioning

confidence: 99%

“…[13][14][15][16] Different methods have been used to formulate the corresponding models. Most of the works pose a mathematical model, generally MILP 17 or MINLP 18 formulations. However, there exist works that resort to simulation 19 or heuristic 20 approaches.…”

Section: Introductionmentioning

confidence: 99%

New Alternatives in the Design and Planning of Multiproduct Batch Plants in a Multiperiod Scenario

Moreno

Montagna

2007

Ind. Eng. Chem. Res.

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New alternatives for the simultaneous design and planning of multiproduct batch plants in a multiperiod scenario are presented in this article. This formulation allows the flexible configuration of the plant in every time period for each product considering the assignment of parallel units of different sizes operating either in-phase or out-of-phase. Capacity expansion during the time horizon is also allowed in order to satisfy new variable requirements. For each batch stage, following the usual procurement policy, units are selected from a set of standard and discrete sizes that are available to perform each operation. The model is formulated through a mixed-integer linear programming (MILP) formulation that maximizes the net present value of profit. From the planning point of view, product sales, raw materials purchases, inventories, waste disposal, and late deliveries are taken into account. Thus, this model simultaneously solves both design and production planning for given forecasts of product demands and pricing in each time period.

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“…The globally best individual is distributed to the mesh for further processing. A superstructure utilizing artificial intelligence is critical for solving difficult real‐world optimisation problems (Östermark et al , 2000; Östermark, 1999a‐c, 2000a; Pettersson, 1994; Westerlund et al , 1994, 1998). GHA has been integrated with a number of powerful support libraries in different tests, including the linear algebra package (LAPACK), the mixed integer linear programming (MILP) solver LP_SOLVE, the interactive mathematical and statistical library (IMSL, 1987), the feasible sequential quadratic programming (FSQP) algorithm (Lawrence et al , 1997) and the optimisation package of Quandt (cf.…”

Section: Introductionmentioning

confidence: 99%

Dynamic portfolio management under competing representations

Östermark

2005

Kybernetes

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PurposeTo solve the multi‐period portfolio management problem under transactions costs.Design/methodology/approachWe 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.FindingsSHAREX 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/valueA 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.

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A nonlinear mixed integer multiperiod firm model

Cited by 9 publications

References 18 publications

Concurrent processing of mixed‐integer non‐linear programming problems

Concurrent processing of mixed‐integer non‐linear programming problems

New Alternatives in the Design and Planning of Multiproduct Batch Plants in a Multiperiod Scenario

Dynamic portfolio management under competing representations

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