Nonlinear Bi-objective Problem Research Articles

Chaotic Butterfly Optimization Algorithm Applied to Multi-objective Economic and Emission Dispatch in Modern Power System

Aims : To optimize the economic and emission dispatch of the thermal power plant. Background: Considering both the economic and environmental aspects, a combined approach had made to attain a solution is known as the combined economic and emission dispatch problem. The CEED problem is a nonlinear bi-objective problem with conflicting behaviour with all the practical constraints. Objective: A new optimization method is improvised by applying the chaotic mapping to the butterfly optimization algorithm. This method is applied to the Combined Economic and Emission Dispatch (CEED) problem for optimizing consumed fuel cost and produced environment pollutant. Methods: Improved Chaotic Butterfly algorithm is applied to the optimization problem to optimize combined economic and emission dispatch. Result : The proposed technique is tested for four different test systems with various practical constraints like valve point loading, ramp rate limit and prohibited operating zones. The obtained results from the chaotic butterfly optimization algorithm (CBOA) are compared with other optimization techniques provide an optimum solution for CEED problem. Conclusion : Considering the environmental impact the novel metaheuristic swarm intelligence technique is applied with conflict of interest. Different test systems, with different practical operational constraints like valve-point loading, prohibited operating zones and ramp rate limits and emission dispatch have been analyzed to validate the implementation of the proposed algorithm in real life CEED problem situations.

An Approach for Bi-objective Optimization of Biochemical Systems

In this work, a linear approach is presented to deal with the bi-objective optimization of biochemical systems. In this approach, an S-system form of the original nonlinear bi-objective problem is first attained. We then obtain a linear bi-objective problem by the logarithmic transformations. A NBI-based approach is presented to solve the obtained linear bi-objective problem. A case study is shown to the effectiveness of the presented linear approach.

Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods

Obtaining a complete description of the efficient set of multiobjective optimization problems can be of invaluable help to the decision-maker when the objectives conflict and a solution has to be chosen. In this paper we present an interval branch-and-bound algorithm which aims at obtaining a tight outer approximation of the whole efficient set of nonlinear biobjective problems. The method enhances the performance of a previous rudimentary algorithm thanks to the use of new accelerating devices, namely, three new discarding tests. Some computational studies on a set of competitive location problems demonstrate the efficiency of the discarding tests, as well as the superiority of the new algorithm, both in time and in quality of the outer approximations of the efficient set, as compared to another method, an interval constraint-like algorithm, with the same aim. Furthermore, we also give some theoretical results of the method, which show its good properties, both in the limit (when the tolerances are set equal to zero and the algorithm does not stop) and when the algorithm stops after a finite number of steps (when we use positive tolerances). A key point in the approach is that, thanks to the use of interval analysis tools, it can be applied to nearly any biobjective problem.

Obtaining an outer approximation of the efficient set of nonlinear biobjective problems

A new method for obtaining an outer approximation of the efficient set of nonlinear biobjective optimization problems is presented. It is based on the well known `constraint method', and obtains a superset of the efficient set by computing the regions of ?-optimality of a finite number of single objective constraint problems. An actual implementation, which makes use of interval tools, shows the applicability of the method and the computational studies on a set of competitive location problems demonstrate its efficiency.