Optimization Strategies Based on Sequential Quadratic Programming Applied for a Fermentation Process for Butanol Production

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Towards an intelligent graphical interface for linear programming modelling

The increase of computing power of the microcomputers has stimulated the building of direct manipulation interfaces that allow graphical representation of Linear Programming (LP) models. This work discusses the components of such a graphical interface as the basis for a system to assist users in the process of formulating LP problems. In essence, this work proposes a methodology which considers the modelling task as divided into three stages which are specification of the Data Model, the Conceptual Model and the LP Model. The necessity for using Artificial Intelligence techniques in the problem conceptualisation and to help the model formulation task is illustrated.

Design of microirrigation systems in sloping lands using linear programming

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

VAr planning using genetic algorithm and linear programming

A combined methodology consisting of successive linear programming (SLP) and a simple genetic algorithm (SGA) solves the reactive planning problem. The problem is divided into operating and planning subproblems; the operating subproblem, which is a nonlinear, ill-conditioned and nonconvex problem, consists of determining the voltage control and the adjustment of reactive sources. The planning subproblem consists of obtaining the optimal reactive source expansion considering operational, economical and physical characteristics of the system. SLP solves the optimal reactive dispatch problem related to real variables, while SGA is used to determine the necessary adjustments of both the binary and discrete variables existing in the modelling problem. Once the set of candidate busbars has been defined, the program implemented gives the location and size of the reactive sources needed, if any, to maintain the operating and security constraints.

Multi-choice mixed integer goal programming optimization for real problems in a sugar and ethanol milling company

Goal Programming (GP) is an important analytical approach devised to solve many realworld problems. The first GP model is known as Weighted Goal Programming (WGP). However, Multi-Choice Aspirations Level (MCAL) problems cannot be solved by current GP techniques. In this paper, we propose a Multi-Choice Mixed Integer Goal Programming model (MCMI-GP) for the aggregate production planning of a Brazilian sugar and ethanol milling company. The MC-MIGP model was based on traditional selection and process methods for the design of lots, representing the production system of sugar, alcohol, molasses and derivatives. The research covers decisions on the agricultural and cutting stages, sugarcane loading and transportation by suppliers and, especially, energy cogeneration decisions; that is, the choice of production process, including storage stages and distribution. The MCMIGP allows decision-makers to set multiple aspiration levels for their problems in which the more/higher, the better and the less/lower, the better in the aspiration levels are addressed. An application of the proposed model for real problems in a Brazilian sugar and ethanol mill was conducted; producing interesting results that are herein reported and commented upon. Also, it was made a comparison between MCMI GP and WGP models using these real cases. © 2013 Elsevier Inc.

Integrated cutting machine programming and lot sizing in furniture industry

In this paper a mathematical model that combines lot-sizing and cutting-stock problems applied to the furniture industry is presented. The model considers the usual decisions of the lot sizing problems, as well as operational decisions related to the cutting machine programming. Two sets of a priori generated cutting patterns are used, industry cutting patterns and a class of n-group cutting patterns. A strategy to improve the utilization of the cutting machine is also tested. An optimization package was used to solve the model and the computational results, using real data from a furniture factory, show that a small subset of n-group cutting patterns provides good results and that the cutting machine utilization can be improved by the proposed strategy.

Short-term expansion planning of radial electrical distribution systems using mixed-integer linear programming

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

MATHEMATICAL MODELS AND POLYHEDRAL STUDIES FOR INTEGRAL SHEET METAL DESIGN

We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.

Searching and retrieving in content-based repositories of formal mathematical knowledge

In this thesis, the author presents a query language for an RDF (Resource Description Framework) database and discusses its applications in the context of the HELM project (the Hypertextual Electronic Library of Mathematics). This language aims at meeting the main requirements coming from the RDF community. in particular it includes: a human readable textual syntax and a machine-processable XML (Extensible Markup Language) syntax both for queries and for query results, a rigorously exposed formal semantics, a graph-oriented RDF data access model capable of exploring an entire RDF graph (including both RDF Models and RDF Schemata), a full set of Boolean operators to compose the query constraints, fully customizable and highly structured query results having a 4-dimensional geometry, some constructions taken from ordinary programming languages that simplify the formulation of complex queries. The HELM project aims at integrating the modern tools for the automation of formal reasoning with the most recent electronic publishing technologies, in order create and maintain a hypertextual, distributed virtual library of formal mathematical knowledge. In the spirit of the Semantic Web, the documents of this library include RDF metadata describing their structure and content in a machine-understandable form. Using the author's query engine, HELM exploits this information to implement some functionalities allowing the interactive and automatic retrieval of documents on the basis of content-aware requests that take into account the mathematical nature of these documents.

Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

Mathematical models for the arrangement and the cleaning of the river basin and surroundings of the river sandy grounds to its passage by the city of Salta (Argentina)

The province of Salta is located the Northwest of Argentina in the border with Bolivia, Chile and Paraguay. Its Capital is the city of Salta that concentrates half of the inhabitants of the province and has grown to 600000 hab., from a small active Spanish town well founded in 1583. The city is crossed by the Arenales River descending from close mountains at North, source of water and end of sewers. But with actual growing it has become a focus of infection and of remarkable unhealthiness. It is necessary to undertake a plan for the recovery of the river, directed to the attainment of the well-being and to improve the life?s quality of the Community. The fundamental idea of the plan is to obtain an ordering of the river basin and an integral management of the channel and its surroundings, including the cleaning out. The improvement of the water?s quality, the healthiness of the surroundings and the improvement of the environment, must go hand by hand with the development of sport activities, of relaxation, tourism, establishment of breeding grounds, kitchen gardens, micro enterprises with clean production and other actions that contribute to their benefit by the society, that being a basic factor for their care and sustainable use. The present pollution is organic, chemical, industrial, domestic, due to the disposition of sweepings and sewer effluents that affects not only the flora and small fauna, destroying the biodiversity, but also to the health of people living in their margins. Within the plan it will be necessary to consider, besides hydric and environmental cleaning and the prevention of floods, the planning of the extraction of aggregates, the infrastructure and consolidation of margins works and the arrangement of all the river basin. It will be necessary to consider the public intervention at state, provincial and local level, and the private intervention. In the model it has been necessary to include the sub-model corresponding to the election of the entity to be the optimal instrument to reach the proposed objectives, giving an answer to the social, environmental and economic requirements. For that the authors have used multi-criteria decision methods to qualify and select alternatives, and for the programming of their implementation. In the model the authors have contemplated the short, average and long term actions. They conform a Paretooptimal alternative which secures the ordering, integral and suitable management of the basin of the Arenales River, focusing on its passage by the city of Salta.

Degrees of unsolvability in the theory of programming languages,

Bibliography: p. 120-123.

Proceedings of the symposium in linear programming.

Sponsored by Office of Scientific Research of the Air Research and Development Command and held jointly by National Bureau of Standards and the Directorate of Management Analysis, DCS/Comptroller, USAF.

Heuristic algorithm for computing reversal distance with multigene families via binary integer programming

Hannenhalli and Pevzner developed the first polynomial-time algorithm for the combinatorial problem of sorting of signed genomic data. Their algorithm solves the minimum number of reversals required for rearranging a genome to another when gene duplication is nonexisting. In this paper, we show how to extend the Hannenhalli-Pevzner approach to genomes with multigene families. We propose a new heuristic algorithm to compute the reversal distance between two genomes with multigene families via the concept of binary integer programming without removing gene duplicates. The experimental results on simulated and real biological data demonstrate that the proposed algorithm is able to find the reversal distance accurately. ©2005 IEEE