One of the most important solutions for dimensionality reduction in data preprocessing, and improving classification performance is gene selection in microarray data since they usually have several thousand genes with very few samples. Because of these characteristics, the complexity of classification models increases and their efficiency decreases. The gene selection problem inherently pursues two goals: reducing the number of genes and increasing the classification efficiency. Therefore, this paper presents a novel hybrid filter-wrapper solution based on the Fisher-score method and Multi-Objective Forest Optimization Algorithm (MOFOA). In the proposed method, as a preprocessing step, the Fisher-score method selects 500 discriminative genes by removing redundant/irrelevant genes. Then, MOFOA searches to find the subset of optimal genes using concepts such as repository, crowding-distance, and binary tournament selection. Moreover, the proposed method solves the gene selection problem and, at the same time, optimizes the kernel parameters in the SVM classification model. Six microarray datasets were used to evaluate the performance of the proposed method. Afterward, a comparison was made between its results and those of the four multi-objective hybrid methods presented in the literature in terms of classification performance, the number of selected genes, running time, and hypervolume criteria. According to the results, in addition to selecting fewer genes, the proposed solution has achieved greater classification accuracy in most cases and has been able to obtain a performance similar to or better than that of other multi-objective gene selection approaches.

The multi-objective problem of multi-depot vehicle routing (MOMDVRP) is proposed by considering the minimization of the traveled arc costs and the balance of routes. Seven mathematical models were reviewed to determine the route balance equation and the best-performing model is selected for this purpose. The solution methodology consists of three stages; in the first one, beginning solutions are built up by means of a constructive heuristic. In the second stage, fronts are constructed from each starting solution using the iterated local search multi-objective metaheuristics (ILSMO). In the third stage, we obtain a single front by using concepts of dominance, taking as a base the fronts of the previous stage. Thus, the first two fronts are taken and a single front is formed that corresponds to the current solution of the problem; next the third front is added to the current Pareto front of the problem, the procedure is repeated until exhaustion of the list of the fronts initially obtained. The resulting front is the solution to the problem. To validate the methodology we use instances from the specialized literature, which have been used for the multi-depot routing problem (MDVRP). The results obtained provide very good quality. Finally, decision criteria are used to select the most appropriate solution for the front, both from the point of view of the balance and the route cost.

This paper aims a novel and a useful multi-objective optimization approach named Non-Dominated Sorting Ions Motion Algorithm (NSIMO) built on the search procedure of Ions Motion Algorithm (IMO). NSIMO uses selective crowding distance and non-dominated sorting method to obtain various non-domination levels and preserve diversity amongst the best set of solutions. The suggested technique is employed to various multi-objective benchmark functions having different characteristics like convex, concave, multimodal, and discontinuous Pareto fronts. The recommended method is analyzed on different engineering problems having distinct features. The results of the proposed approach are compared with other well-regarded and novel algorithms. Furthermore, we present that the projected method is easy to implement, capable of producing a nearly true Pareto front and algorithmically inexpensive.

There are huge amounts of emissions associated with construction industry during its different stages from cradle till building demolition. This study presents a methodology that integrates multi-objective optimization and multi-criteria decision making (MCDM) in order to enable construction decision-makers to select the most sustainable construction alternatives. Four objectives functions are investigated, which are: construction time, lifecycle cost, environmental impact and primary energy in order to construct the Pareto front. A novel hybrid MCDM is designed based on seven multi-criteria decision making techniques to select the best solution among the set of the Pareto optimal solutions. Sensitivity analysis is performed in order to determine the most sensitive attribute and construction stages that influence environmental emissions. The analysis illustrates that WSM, COPRAS and TOPSIS provided the best rankings of the alternatives, primary energy is the most sensitive attribute for different MCDM methods. Moreover, PROMETHEE II is the most robust MCDM method.

A note published by Chinta et al. (2016) [Chinta, S., Kommadath, R. & Kotecha, P. (2016) A note on multi-objective improved teaching–learning based optimization algorithm (MO-ITLBO). Information Science, 373, 337-350.] reported some impediments in implementation of MO-ITLBO algorithm. However, it is observed that their comments are based on incorrect understanding of TLBO, ITLBO and MO-ITLBO algorithms. Their raised issues are thoroughly addressed in this paper and it is proved that MO-ITLBO algorithm has no lacunae.

The growing environmental and economic concerns oblige logistics operations managers to look for simple solutions to optimize their processes and to corporate sustainability in logistics networks. Logistics collaboration is one of the management practices to foster the sustainability of freight transport. This paper presents an ‘ex ante’ decision support tool to evaluate the economic and ecologic impacts of shippers’ horizontal collaboration in urban freight delivery. Optimization model as a two-echelon location routing problem (2E-LRP) is exploited to demonstrate the benefits of joining facility location and vehicle routing decisions under multi-objective optimization approach. Numerical instances reproducing the real urban network are regenerated to test the proposed mechanism. Scenario analysis is conducted to analyze and discuss the effect of parameters’ changes in generated gains.

In this paper, a novel multi-objective robust possibilistic programming model is proposed, which simultaneously considers maximizing the distributive justice in relief distribution, minimizing the risk of relief distribution, and minimizing the total logistics costs. To effectively cope with the uncertainties of the after-disaster environment, the uncertain parameters of the proposed model are considered in the form of fuzzy trapezoidal numbers. The proposed model not only considers relief commodities priority and demand points priority in relief distribution, but also considers the difference between the pre-disaster and post-disaster supply abilities of the suppliers. In order to solve the proposed model, the LP-metric and the improved augmented ε-constraint methods are used. Second, a set of test problems are designed to evaluate the effectiveness of the proposed robust model against its equivalent deterministic form, which reveales the capabilities of the robust model. Finally, to illustrate the performance of the proposed robust model, a seismic region of northwestern Iran (East Azerbaijan) is selected as a case study to model its relief logistics in the face of future earthquakes. This investigation indicates the usefulness of the proposed model in the field of crisis.

The main aim of this paper is to present a novel multi-objective gray wolf optimization (MOGWO) by utilizing the Kriging meta-model. To this end, surrogate models are used in Multi-Objective Gray Wolf Optimizer as the fitness function. The meta-model is obtained based on exact analysis and numerical simulations. Inheritable Latin Hypercube Design (ILHD) is used as the design of experiments for generation and testing the Kriging model. Then, sensitivity analysis is done to evaluate the effect of design parameter on system responses. The sensitivity analysis leads to appropriate selection of optimization design variables. Hence, the MOGWO algorithm is applied to the problem, the set of non-dominated optimal points are obtained as Pareto Front and one optimal point is selected based on the minimum distance approach. The most important purpose of the methodology is to improve the time consuming in multi-objective optimization problems. In conclusion, for the design of hydrazine catalyst bed was utilized from the proposed methodology. In case, design variables are catalyst bed pellet diameter, loading factor, thrust chamber pressure and Reaction efficiency and objective functions are increasing performance and reducing mass and pressure drop. The results of optimal catalyst bed parameters and also corresponding value of objective functions are shown the performance of methodology in the space propulsion system applications.

Reliability issues are most important types of optimization problems and they are used in communication, transportation and electrical systems. This paper presents two mathematical models to solve the k-out-of-n redundancy problem where there are two objectives: maximization of reliability and minimization of cost subject to two constraints. Constraints are associated with weight and volume. In addition, strategy of redundancy is intended and ready to go cold and the components of the systems are also identical, because the model is to solve the complex models of the genetic algorithm (GA) and simulated annealing (SA). The proposed study uses NSGAII and MOPSO to solve the proposed studies and compare them using TOPSIS method.

The identification of optimal tire design parameters for satisfying different requirements, i.e. tire performance characteristics, plays an essential role in tire design. In order to improve tire performance characteristics, formulation and solving of multi-objective optimization problem must be performed. This paper presents a multi-objective optimization procedure for determination of optimal tire design parameters for simultaneous minimization of strain energy density at two distinctive zones inside the tire. It consists of four main stages: pre-analysis, design of experiment, mathematical modeling and multi-objective optimization. Advantage of the proposed procedure is reflected in the fact that multi-objective optimization is based on the Pareto concept, which enables design engineers to obtain a complete set of optimization solutions and choose a suitable tire design. Furthermore, modeling of the relationships between tire design parameters and objective functions based on multiple regression analysis minimizes computational and modeling effort. The adequacy of the proposed tire design multi-objective optimization procedure has been validated by performing experimental trials based on finite element method.