This work extends recent research in the development of a number of direct search methods in nonlinear integer programming. The various algorithms use an extension of the well-known FORTRAN MINOS code of Murtagh and Saunders as a starting point. MINOS is capable of solving quite large problems in which the objective function is nonlinear and the constraints linear. The original MINOS code has been extended in various ways by Murtagh, Saunders and co-workers since the original 1978 landmark paper. Extensions have dealt with methods to handle both nonlinear constraints, most notably MINOS/AUGMENTED and integer requirements on a subset of the variables(MINTO). The starting point for the present thesis is the MINTO code of Murtagh. MINTO is a direct descendant of MINOS in that it extends the capabilities to general nonlinear constraints and integer restrictions. The overriding goal for the work described in this thesis is to obtain a good integer-feasible or near-integer-feasible solution to the general NLIP problem while trying to avoid or at least minimize the use of the ubiquitous branch-and-bound techniques. In general, we assume a small number of nonlinearities and a small number of integer variables.Some initial ideas motivating the present work are summarised in an invited paper presented by Murtagh at the 1989 CTAC (Computational Techniques and Applications) conference in Brisbane, Australia. The approach discussed there was to start a direct search procedure at the solution of the continuous relaxation of a nonlinear mixed-integer problem by first removing integer variables from the simplex basis, then adjusting integer-infeasible superbasic variables, and finally checking for local optimality by trial unit steps in the integers. This may be followed by a reoptimization with the latest point as the starting point, but integer variables held fixed. We describe ideas for the further development of Murtagh’s direct search method. Both the old and new approaches aim to attain an integer-feasible solution from an initially relaxed (continuous) solution. Techniques such as branch-and-bound or Scarf’s neighbourhood search [84] may then be used to obtain a locally optimal solution. The present range of direct search methods differs significantly to that described by Murtagh, both in heuristics used and major and minor steps of the procedures. Chapter 5 summarizes Murtagh’s original approach while Chapter 6 describes the new methods in detail.Afeature of the new approach is that some degree of user-interaction (MINTO/INTERACTIVE) has been provided, so that a skilled user can "drive" the solution towards optimality if this is desired. Alternatively the code can still be run in "automatic" mode, where one of five available direct search methods may be specified in the customary SPECS file. A selection of nonlinear integer programming problems taken from the literature has been solved and the results are presented here in the latter chapters. Further, anewcommunications network topology and allocation model devised by Berry and Sugden has been successfully solved by the direct search methods presented herein. The results are discussed in Chapter 14, where the approach is compared with the branch-and-bound heuristic.

This work extends recent research in the development of a number of direct search methods in nonlinear integer programming. The various algorithms use an extension of the well-known FORTRAN MINOS code of Murtagh and Saunders as a starting point. MINOS is capable of solving quite large problems in which the objective function is nonlinear and the constraints linear. The original MINOS code has been extended in various ways by Murtagh, Saunders and co-workers since the original 1978 landmark paper. Extensions have dealt with methods to handle both nonlinear constraints, most notably MINOS/AUGMENTED and integer requirements on a subset of the variables(MINTO). The starting point for the present thesis is the MINTO code of Murtagh. MINTO is a direct descendant of MINOS in that it extends the capabilities to general nonlinear constraints and integer restrictions. The overriding goal for the work described in this thesis is to obtain a good integer-feasible or near-integer-feasible solution to the general NLIP problem while trying to avoid or at least minimize the use of the ubiquitous branch-and-bound techniques. In general, we assume a small number of nonlinearities and a small number of integer variables.Some initial ideas motivating the present work are summarised in an invited paper presented by Murtagh at the 1989 CTAC (Computational Techniques and Applications) conference in Brisbane, Australia. The approach discussed there was to start a direct search procedure at the solution of the continuous relaxation of a nonlinear mixed-integer problem by first removing integer variables from the simplex basis, then adjusting integer-infeasible superbasic variables, and finally checking for local optimality by trial unit steps in the integers. This may be followed by a reoptimization with the latest point as the starting point, but integer variables held fixed. We describe ideas for the further development of Murtagh’s direct search method. Both the old and new approaches aim to attain an integer-feasible solution from an initially relaxed (continuous) solution. Techniques such as branch-and-bound or Scarf’s neighbourhood search [84] may then be used to obtain a locally optimal solution. The present range of direct search methods differs significantly to that described by Murtagh, both in heuristics used and major and minor steps of the procedures. Chapter 5 summarizes Murtagh’s original approach while Chapter 6 describes the new methods in detail.Afeature of the new approach is that some degree of user-interaction (MINTO/INTERACTIVE) has been provided, so that a skilled user can "drive" the solution towards optimality if this is desired. Alternatively the code can still be run in "automatic" mode, where one of five available direct search methods may be specified in the customary SPECS file. A selection of nonlinear integer programming problems taken from the literature has been solved and the results are presented here in the latter chapters. Further, anewcommunications network topology and allocation model devised by Berry and Sugden has been successfully solved by the direct search methods presented herein. The results are discussed in Chapter 14, where the approach is compared with the branch-and-bound heuristic.

Šio bakalauro darbo tikslas - realizuoti tiesioginės paieškos metodą (lyderio ir pasekėjo uždaviniui). Šiam tikslui pasiekti buvo nagrinėjama tiesioginio paieškos metodo (lyderio ir pasekėjo uždaviniui) matematinė formuluotė ir algoritmas pateikti Dali Zhang ir Gui-Hua Lin darbe„Dviejų lygių tiesioginės paieškos metodas lyderio – pasekėjo uždaviniui ir taikymams“ (angl. „Bilevel Direct Search Method for Leader – Follower Equilibrium Problems and Applications“). Darbo metu buvo sukurta programa, realizuojanti metodą, metodas pritaikytas oligopolinės rinkos modeliui (deterministiniam, nedeterministiniam, stochastiniam) spręsti, taip pat metodas pritaikytas oligopolinės rinkos modeliui, kai algoritmo parametrai generuojami atsitiktinai. / The purpose of this bachelor work – to realize the Direct Search Method (for Leader - Follower problem). To achieve this aim was analyzed the mathematical formulation of direct search method and algorithm that were submitted at paper of Dali Zhang and Gui-Hua Lin „Bilevel Direct Search Method for Leader – Follower Equilibrium Problems and Applications“. During this work was developed a program for realizing the method. The method was adapted for oligopolistic market model (deterministic, non-deterministic, stochastic), also, method was adapted for oligopolistic market model, when the parameters of algorithm are generated randomly.

Today's modern aerospace systems exhibit strong interdisciplinary coupling and require a multidisciplinary, collaborative approach. Analysis methods that were once considered feasible only for advanced and detailed design are now available and even practical at the conceptual design stage. This changing philosophy for conducting conceptual design poses additional challenges beyond those encountered in a low fidelity design of aircraft. This thesis takes some steps towards bridging the gaps in existing technologies and advancing the state-of-the-art in aircraft design. The first part of the thesis proposes a new Pareto front approximation method for multiobjective optimization problems. The method employs a hybrid optimization approach using two derivative free direct search techniques, and is intended for solving blackbox simulation based multiobjective optimization problems with possibly nonsmooth functions where the analytical form of the objectives is not known and/or the evaluation of the objective function(s) is very expensive (very common in multidisciplinary design optimization). A new adaptive weighting scheme is proposed to convert a multiobjective optimization problem to a single objective optimization problem. Results show that the method achieves an arbitrarily close approximation to the Pareto front with a good collection of well-distributed nondominated points. The second part deals with the interdisciplinary data communication issues involved in a collaborative mutidisciplinary aircraft design environment. Efficient transfer, sharing, and manipulation of design and analysis data in a collaborative environment demands a formal structured representation of data. XML, a W3C recommendation, is one such standard concomitant with a number of powerful capabilities that alleviate interoperability issues. A compact, generic, and comprehensive XML schema for an aircraft design markup language (ADML) is proposed here to provide a common language for data communication, and to improve efficiency and productivity within a multidisciplinary, collaborative environment. An important feature of the proposed schema is the very expressive and efficient low level schemata. As a proof of concept the schema is used to encode an entire Convair B58. As the complexity of models and number of disciplines increases, the reduction in effort to exchange data models and analysis results in ADML also increases. / Ph. D.