Revisiting the Evolution and Application of Assignment Problem: A Brief Overview

The assignment problem (AP) is incredibly challenging that can model many real-life problems. This paper provides a limited review of the recent developments that have appeared in the literature, meaning of assignment problem as well as solving techniques and will provide a review on   a lot of research studies on different types of assignment problem taking place in present day real life situation in order to capture the variations in different types of assignment techniques. Keywords: Assignment problem, Quadratic Assignment, Vehicle Routing, Exact Algorithm, Bound, Heuristic etc

A unified framework for model-based multi-objective linear process and energy optimisation under uncertainty

Process and energy models provide an invaluable tool for design, analysis and optimisation. These models are usually based upon a number of assumptions, simplifications and approximations, thereby introducing uncertainty in the model predictions. Making model based optimal decisions under uncertainty is therefore a challenging task. This issue is further exacerbated when more than one objective is to be optimised simultaneously, resulting in a Multi-Objective Optimisation (MO2MO2) problem. Even though, some methods have been proposed for MO2MO2 problems under uncertainty, two separate optimisation techniques are employed; one to address the multi-objective aspect and another to take into account uncertainty. In the present work, we propose a unified optimisation framework for linear MO2MO2 problems, in which the uncertainty and the multiple objectives are modelled as varying parameters. The MO2MO2 under uncertainty problem (MO2U2)(MO2U2) is thus reformulated and solved as a multi-parametric programming problem. The solution of the multi-parametric programming problem provides the optimal solution as a set of parametric profiles

Energy Crop Supply in France: A Min-Max Regret Approach

This paper attempts to estimate energy crop supply using an LP model comprising hundreds of representative farms of the arable cropping sector in France. In order to enhance the predictive ability of such a model and to provide an analytical tool useful to policy makers, interval linear programming (ILP) is used to formalise bounded rationality conditions. In the presence of uncertainty related to yields and prices it is assumed that the farmer minimises the distance from optimality once uncertainty resolves introducing an alternative criterion to the classic profit maximisation rationale. Model validation based on observed activity levels suggests that about 40% of the farms adopt the min-max regret criterion. Then energy crop supply curves, generated by the min-max regret model, are proved to be upward sloped alike classic LP supply curves.interval linear programming, min-max regret, energy crops, France, Crop Production/Industries, Resource /Energy Economics and Policy, C61, D81, Q18,

Nonlinear modelling and optimal control via Takagi-Sugeno fuzzy techniques: A quadrotor stabilization

Using the principles of Takagi-Sugeno fuzzy modelling allows the integration of flexible fuzzy approaches and rigorous mathematical tools of linear system theory into one common framework. The rule-based T-S fuzzy model splits a nonlinear system into several linear subsystems. Parallel Distributed Compensation (PDC) controller synthesis uses these T-S fuzzy model rules. The resulting fuzzy controller is nonlinear, based on fuzzy aggregation of state controllers of individual linear subsystems. The system is optimized by the linear quadratic control (LQC) method, its stability is analysed using the Lyapunov method. Stability conditions are guaranteed by a system of linear matrix inequalities (LMIs) formulated and solved for the closed loop system with the proposed PDC controller. The additional GA optimization procedure is introduced, and a new type of its fitness function is proposed to improve the closed-loop system performance.Web of Science71110

Priority Events Determination For The Risk-oriented Management Of Electric Power System

The task of risk-oriented management of the electric power system in conditions of multi-criteria choice is considered. To determine the most effective measures, the implementation of which will reduce the magnitude of the risk of an emergency situation, multi-criteria analysis methods are applied. A comparative analysis of the multi-criteria alternative (ELECTRE) ranking method based on utility theory and the Pareto method, which defines a subset of non-dominant alternatives, is carried out. The Pareto method uses in its algorithm only qualitative characteristics of the advantage and allows only to distinguish a group of competitive solutions with the same degrees of non-dominance. Given the large number of evaluation criteria, the Pareto method is ineffective because the resulting subset of activities is in the field of effective trade-offs, when no element of the set of measures can be improved without degrading at least one of the other elements. The ELECTRE method is a pairwise comparison of multi-criteria alternatives based on utility theory. This method allows to identify a subset of the most effective activities. The number of elements of the resultant subset is regulated by taking into account the coefficients of importance of optimization criteria and expert preferences