Search results

Although the multi-criteria technique analytic hierarchy process (AHP) has successfully been applied in many areas, either selecting or ranking alternatives or to derive priority vector (weights) for a set of criteria, there is a significant drawback in using this technique if the pairwise comparison matrix (PCM) has inconsistent comparisons, in other words, a consistency ratio (CR) above the value of 0.1, the final solution cannot be validated. Many studies have been developed to treat the inconsistency problem, but few of them tried to satisfy different quality measures, which are minimum inconsistency (fMI), the total number of adjusted pairwise comparisons (fNC), original rank preservation (fKT), minimum average weights adjustment (fWA) and finally, minimum L1 matrix norm between the original PCM and the adjusted PCM (fLM).

The approach is defined in four steps: first, the decision-maker should choose which quality measures she/he wishes to use, ranging from one to all quality measures. In the second step, the authors encode the PCM to be used in a many-objective optimization algorithm (MOOA), and each pairwise comparison can be adjusted individually. The authors generate consistent solutions from the obtained Pareto optimal front that carry the desired quality measures in the third step. Lastly, the decision-maker selects the most suitable solution for her/his problem. Remarkably, as the decision-maker can choose one (mono-objective), two (multi-objective), three or more (many-objectives) quality measures, not all MOOAs can handle or perform well in mono- or multi-objective problems. The unified non-sorting algorithm III (U-NSGA III) is the most appropriate MOOA for this type of scenario because it was specially designed to handle mono-, multi- and many-objective problems.

The use of two quality measures should not guarantee that the adjusted PCM is similar to the original PCM; hence, the decision-maker should consider using more quality measures if the objective is to preserve the original PCM characteristics.

For the first time, a many-objective approach reduces the CR to consistent levels with the ability to consider one or more quality measures and allows the decision-maker to adjust each pairwise comparison individually.

The paper aims to propose an innovative two-stage decision model to address the sustainable-resilient supplier selection and order allocation (SSOA) problem in the single-valued neutrosophic (SVN) environment.

First, the sustainable and resilient performances of suppliers are evaluated by the proposed integrated SVN-base-criterion method (BCM)-an acronym in Portuguese of interactive and multi-criteria decision-making (TODIM) method, with consideration of the uncertainty in the decision-making process. Then, a novel multi-objective optimization model is formulated, and the best sustainable-resilient order allocation solution is found using the U-NSGA-III algorithm and TOPSIS method. Finally, based on a real-life case in the automotive manufacturing industry, experiments are conducted to demonstrate the application of the proposed two-stage decision model.

The paper provides an effective decision tool for the SSOA process in an uncertain environment. The proposed SVN-BCM-TODIM approach can effectively handle the uncertainties from the decision-maker’s confidence degree and incomplete decision information and evaluate suppliers’ performance in different dimensions while avoiding the compensatory effect between criteria. Moreover, the proposed order allocation model proposes an original way to improve sustainable-resilient procurement values.

The paper provides a supplier selection process that can effectively integrate sustainability and resilience evaluation in an uncertain environment and develops a sustainable-resilient procurement optimization model.

Recently, many-objective optimization evolutionary algorithms have been the main issue for researchers in the multi-objective optimization community. To deal with many-objective problems (typically for four or more objectives) some modern frameworks are proposed which have the potential of achieving the finest non-dominated solutions in many-objective spaces. The effectiveness of these algorithms deteriorates greatly as the problem’s dimension increases. Diversity reduction in the objective space is the main reason of this phenomenon.

To properly deal with this undesirable situation, this work introduces an indicator-based evolutionary framework that can preserve the population diversity by producing a set of discriminated solutions in high-dimensional objective space. This work attempts to diversify the objective space by proposing a fitness function capable of discriminating the chromosomes in high-dimensional space. The numerical results prove the potential of the proposed method, which had superior performance in most of test problems in comparison with state-of-the-art algorithms.

The achieved numerical results empirically prove the superiority of the proposed method to state-of-the-art counterparts in the most test problems of a known artificial benchmark.

This paper provides a new interpretation and important insights into the many-objective optimization realm by emphasizing on preserving the population diversity.

The purpose of this paper is to design an improved multi-objective algorithm with better spread and convergence than some current algorithms. The proposed application is for engineering design problems.

This study proposes two novel approaches which focus on faster convergence to the Pareto front (PF) while adopting the advantages of Strength Pareto Evolutionary Algorithm-2 (SPEA2) for better spread. In first method, decision variables corresponding to the optima of individual objective functions (Utopia Point) are strategically used to guide the search toward PF. In second method, boundary points of the PF are calculated and their decision variables are seeded to the initial population.

The proposed methods are tested with a wide range of constrained and unconstrained multi-objective test functions using standard performance metrics. Performance evaluation demonstrates the superiority of proposed algorithms over well-known existing algorithms (such as NSGA-II and SPEA2) and recent ones such as NSLS and E-NSGA-II in most of the benchmark functions. It is also tested on an engineering design problem and compared with a currently used algorithm.

The algorithms are intended to be used for practical engineering design problems which have many variables and conflicting objectives. A complex example of Welded Beam has been shown at the end of the paper.

The algorithm would be useful for many design problems and social/industrial problems with conflicting objectives.

This paper presents two novel hybrid algorithms involving SPEA2 based on: local search; and Utopia point directed search principles. This concept has not been investigated before.