Generation of Pareto optimal solutions for multi-objective optimization problems via a reduced interior-point algorithm

In this paper, a reduced interior-point (RIP) algorithm is introduced to generate a Pareto optimal front for multi-objective constrained optimization (MOCP) problem. A weighted Tchebychev metric approach is used together with achievement scalarizing function approach to convert MOCP problem to a single-objective constrained optimization (SOCO) problem. An active-set technique is used together with a Coleman–Li scaling matrix and a decrease interior-point method to solve SOCO problem. A Matlab implementation of RIP algorithm was used to solve three cases and application. The results showed that the RIP algorithm is promising when compared with well-known algorithms and the computations may be superior relevant for comprehending real-world application problems

An active-set trust-region algorithm for solving warehouse location problem

In this paper, an active-set strategy is used together with a penalty method and a trust-region technique to solve a warehouses location problem. The trust region is used to modify the local method in such a way that it is guaranteed to converge at all even if the starting point is far away from the solution. The trust-region method is a well-accepted technique in nonlinear optimization to assure global convergence and is more robust when they deal with rounding errors. One of the advantages of trust-region method is that it does not require the objective function of the model to be convex. The warehouses location problem involves the determination of the number and size of service center (warehouses) to supply a set of demand centers so as to minimize total distribution cost. The proposed approach is tested on two problems to confirm the effectiveness of the algorithm. Our results with the proposed approach have been compared to those reported in the literature

Relaxed I-SHOT trust-region algorithm for solving multi-objective economic emission load dispatch problem

In this paper, a new algorithm for tackling nonlinear constrained multi-objective optimization problems is introduced. This algorithm, which we call relaxed the interactive sequential hybrid optimization technique (relaxed I-SHOT), is based on a hybrid method between the I-SHOT method and step method (STEM) to transform a multi-objective problem into a single-objective one. An active set strategy is used together with a suggested penalty method to transform a single-objective constrained optimization problem into unconstrained one. A trust-region globalization strategy is added to the algorithm to solve the obtained unconstrained problem to ensure global convergence. The suggested approach is utilized to solve the multi-objective economic emission load dispatch (EELD) problems to assert the effectiveness of the proposed algorithm. The proposed algorithm is tested on the standard IEEE 30-bus 6-generator test system. The results of the proposed approach are compared against those reported in the literature. The comparison asserts the potential of the proposed algorithm to solve the EELD problem

A nonmonton active interior point trust region algorithm based on CHKS smoothing function for solving nonlinear bilevel programming problems

In this paper, an approach is suggested to solve nonlinear bilevel programming (NBLP) problems. In the suggested method, we convert the NBLP problem into a standard nonlinear programming problem with complementary constraints by applying the Karush-Kuhn-Tucker condition to the lower-level problem. By using the Chen-Harker-Kanzow-Smale (CHKS) smoothing function, the nonlinear programming problem is successively smoothed. A nonmonton active interior-point trust-region algorithm is introduced to solve the smoothed nonlinear programming problem to obtain an approximately optimal solution to the NBLP problem. Results from simulations on several benchmark problems and a real-world case about a watershed trading decision-making problem show how the effectiveness of the suggested approach in NBLP solution development