A note on higher-order nondifferentiable symmetric duality in multiobjective programming

AbstractIn this work, we establish a strong duality theorem for Mond–Weir type multiobjective higher-order nondifferentiable symmetric dual programs. This fills some gaps in the work of Chen [X. Chen, Higher-order symmetric duality in nondifferentiable multiobjective programming problems, J. Math. Anal. Appl. 290 (2004) 423–435]

Duality in mathematical programming.

In this thesis entitled, “Duality in Mathematical Programming”, the emphasis is given on formulation and conceptualization of the concepts of second-order duality, second-order mixed duality, second-order symmetric duality in a variety of nondifferentiable nonlinear programming under suitable second-order convexity/second-order invexity and generalized second-order convexity / generalized second-order invexity. Throughout the thesis nondifferentiablity occurs due to square root function and support functions. A support function which is more general than square root of a positive definite quadratic form. This thesis also addresses second-order duality in variational problems under suitable second-order invexity/secondorder generalized invexity. The duality results obtained for the variational problems are shown to be a dynamic generalization for thesis of nonlinear programming problem.Digital copy of Thesis.University of Kashmir

Some contributions to optimality criteria and duality in Multiobjective mathematical programming.

This thesis entitled, “some contributions to optimality criteria and duality in multiobjective mathematical programming”, offers an extensive study on optimality, duality and mixed duality in a variety of multiobjective mathematical programming that includes nondifferentiable nonlinear programming, variational problems containing square roots of a certain quadratic forms and support functions which are prominent nondifferentiable convex functions. This thesis also deals with optimality, duality and mixed duality for differentiable and nondifferentiable variational problems involving higher order derivatives, and presents a close relationship between the results of continuous programming problems through the problems with natural boundary conditions between results of their counter parts in nonlinear programming. Finally it formulates a pair of mixed symmetric and self dual differentiable variational problems and gives the validation of various duality results under appropriate invexity and generalized invexity hypotheses. These results are further extended to a nondifferentiable case that involves support functions.Digital copy of Thesis.University of Kashmir

Higher-order generalized convexity and duality in nondifferentiable multiobjective mathematical programming

AbstractIn this paper, a class of generalized convexity is introduced and a unified higher-order dual model for nondifferentiable multiobjective programs is described, where every component of the objective function contains a term involving the support function of a compact convex set. Weak duality theorems are established under generalized convexity conditions. The well-known case of the support function in the form of square root of a positive semidefinite quadratic form and other special cases can be readily derived from our results

Symbolic approaches and artificial intelligence algorithms for solving multi-objective optimisation problems

Problems that have more than one objective function are of great importance in engineering sciences and many other disciplines. This class of problems are known as multi-objective optimisation problems (or multicriteria). The difficulty here lies in the conflict between the various objective functions. Due to this conflict, one cannot find a single ideal solution which simultaneously satisfies all the objectives. But instead one can find the set of Pareto-optimal solutions (Pareto-optimal set) and consequently the Pareto-optimal front is established. Finding these solutions plays an important role in multi-objective optimisation problems and mathematically the problem is considered to be solved when the Pareto-optimal set, i.e. the set of all compromise solutions is found. The Pareto-optimal set may contain information that can help the designer make a decision and thus arrive at better trade-off solutions. The aim of this research is to develop new multi-objective optimisation symbolic algorithms capable of detecting relationship(s) among decision variables that can be used for constructing the analytical formula of Pareto-optimal front based on the extension of the current optimality conditions. A literature survey of theoretical and evolutionary computation techniques for handling multiple objectives, constraints and variable interaction highlights a lack of techniques to handle variable interaction. This research, therefore, focuses on the development of techniques for detecting the relationships between the decision variables (variable interaction) in the presence of multiple objectives and constraints. It attempts to fill the gap in this research by formally extending the theoretical results (optimality conditions). The research then proposes first-order multi-objective symbolic algorithm or MOSA-I and second-order multi-objective symbolic algorithm or MOSA-II that are capable of detecting the variable interaction. The performance of these algorithms is analysed and compared to a current state-of-the-art optimisation algorithm using popular test problems. The performance of the MOSA-II algorithm is finally validated using three appropriately chosen problems from literature. In this way, this research proposes a fully tested and validated methodology for dealing with multi-objective optimisation problems. In conclusion, this research proposes two new symbolic algorithms that are used for identifying the variable interaction responsible for constructing Pareto-optimal front among objectives in multi-objective optimisation problems. This is completed based on a development and relaxation of the first and second-order optimality conditions of Karush-Kuhn-Tucker.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

A vision-based optical character recognition system for real-time identification of tractors in a port container terminal

Automation has been seen as a promising solution to increase the productivity of modern sea port container terminals. The potential of increase in throughput, work efficiency and reduction of labor cost have lured stick holders to strive for the introduction of automation in the overall terminal operation. A specific container handling process that is readily amenable to automation is the deployment and control of gantry cranes in the container yard of a container terminal where typical operations of truck identification, loading and unloading containers, and job management are primarily performed manually in a typical terminal. To facilitate the overall automation of the gantry crane operation, we devised an approach for the real-time identification of tractors through the recognition of the corresponding number plates that are located on top of the tractor cabin. With this crucial piece of information, remote or automated yard operations can then be performed. A machine vision-based system is introduced whereby these number plates are read and identified in real-time while the tractors are operating in the terminal. In this paper, we present the design and implementation of the system and highlight the major difficulties encountered including the recognition of character information printed on the number plates due to poor image integrity. Working solutions are proposed to address these problems which are incorporated in the overall identification system.postprin