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.
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.
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.
Multi-objective optimization is an optimization problem with some conflicting objectives to be attained, simultanously. This paper reviewed literature about multi-objective optimization problems for supply chain management. The review aimed to provide the lastest research views and recomendations for further studies. We discussed the lastest ten years publications about multi-objective optimization for supply chain management. The scope of this review was classified into five categories i.e. problem statements, multi-objective frameworks, mathematical formulation modeling, optimization techniques, and representation of supply chain. Multi-objective optimization approaches, both classical and metaheuristic approaches, were discussed, accordingly. In this review, we conducted conclusion and recomendations about likelihood research directions in future.
The present work proposes a multi-objective improved teaching-learning based optimization (MO-ITLBO) algorithm for unconstrained and constrained multi-objective function optimization. The MO-ITLBO algorithm is the improved version of basic teaching-learning based optimization (TLBO) algorithm adapted for multi-objective problems. The basic TLBO algorithm is improved to enhance its exploration and exploitation capacities by introducing the concept of number of teachers, adaptive teaching factor, tutorial training and self-motivated learning. The MO-ITLBO algorithm uses a grid-based approach to adaptively assess the non-dominated solutions (i.e. Pareto front) maintained in an external archive. The performance of the MO-ITLBO algorithm is assessed by implementing it on unconstrained and constrained test problems proposed for the Congress on Evolutionary Computation 2009 (CEC 2009) competition. The performance assessment is done by using the inverted generational distance (IGD) measure. The IGD measures obtained by using the MO-ITLBO algorithm are compared with the IGD measures of the other state-of-the-art algorithms available in the literature. Finally, Lexicographic ordering is used to assess the overall performance of competitive algorithms. Results have shown that the proposed MO-ITLBO algorithm has obtained the 1st rank in the optimization of unconstrained test functions and the 3rd rank in the optimization of constrained test functions.
This paper considers a multi-objective version of the Multiple Traveling Salesman Problem (MOmTSP). In particular, two objectives are considered: the minimization of the total traveled distance and the balance of the working times of the traveling salesmen. The problem is formulated as an integer multi-objective optimization model. A non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve the MOmTSP. The solution scheme allows one to find a set of ordered solutions in Pareto fronts by considering the concept of dominance. Tests on real world instances and instances adapted from the literature show the effectiveness of the proposed algorithm.
Reliability is one of the most important characteristics of the electrical and mechanical systems with applications in the space communication industries, internet networks, telecommunication systems, power generation systems, and productive facilities. What adds to the importance of reliability in these systems are system complications, nature of competitive markets, and increasing production costs due to failures. This paper investigates availability optimization of a system using both repairable and non-repairable components, simultaneously. The availability-redundancy allocation problems involve the determination of component availability (i.e., life time and repair time of the components) and the redundancy levels that produce maximum system availability. These problems are often subject to some constraints on their components such as cost, weight, and volume. To maximize the availability and to minimize the total cost of the system, a new Mixed Integer Nonlinear Programming (MINLP) model is presented. To solve the proposed model, an improved version of the genetic algorithm is designed as an efficient meta-heuristic algorithm. Finally, in order to verify the efficiency of the proposed algorithm, a numerical example of a system is presented that consists of both repairable and non-repairable components.
In hierarchical production planning system, Aggregate Production Planning (APP) falls between the broad decisions of long-range planning and the highly specific and detailed short-range planning decisions. This study develops an interactive Multi-Objective Genetic Algorithm (MOGA) approach for solving the multi-product, multi-period aggregate production planning (APP) with forecasted demand, related operating costs, and capacity. The proposed approach attempts to minimize total costs with reference to inventory levels, labor levels, overtime, subcontracting and backordering levels, and labor, machine and warehouse capacity. Here several genetic algorithm parameters are considered for solving NP-hard problem (APP problem) and their relative comparisons are focused to choose the most auspicious combination for solving multiple objective problems. An industrial case demonstrates the feasibility of applying the proposed approach to real APP decision problems. Consequently, the proposed MOGA approach yields an efficient APP compromise solution for large-scale problems.
This paper presents a multi-objective location problem in a three level supply chain network under uncertain environment considering inventory decisions. The proposed model of this paper considers uncertainty for different parameters including procurement, transportation costs, supply, demand and the capacity of various facilities. The proposed model presents a robust optimization model, which specifies locations of distribution centers to be opened, inventory control parameters (r, Q), and allocation of supply chain components, concurrently. The resulted mixed-integer nonlinear programming minimizes the expected total cost of such a supply chain network comprising location, procurement, transportation, holding, ordering, and shortage costs. The model also minimizes the variability of the total cost of relief chain and minimizes the financial risk or the probability of not meeting a certain budget. We use the ?-constraint method, which is a multi-objective technique with implicit trade-off information given, to solve the problem and using a couple of numerical instances, we examine the performance of the proposed approach.