Multi-objective sequence dependent setup times permutation flowshop: A new algorithm and a comprehensive study

The permutation flowshop scheduling problem has been thoroughly studied in recent decades, both from single objective as well as from multi-objective perspectives. To the best of our knowledge, little has been done regarding the multi-objective flowshop with Pareto approach when sequence dependent setup times are considered. As setup times and multi-criteria problems are important in industry, we must focus on this area. We propose a simple, yet powerful algorithm for the sequence dependent setup times flowshop problem with several criteria. The presented method is referred to as Restarted Iterated Pareto Greedy or RIPG and is compared against the best performing approaches from the relevant literature. Comprehensive computational and statistical analyses are carried out in order to demonstrate that the proposed RIPG method clearly outperforms all other algorithms and, as a consequence, it is a state-of-art method for this important and practical scheduling problem.     

TOPSIS for bi-level MODM problems

TOPSIS (technique for order preference by similarity to ideal solution) is a multiple criteria method to identify solutions from a finite set of alternatives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. This paper proposes a fuzzy TOPSIS algorithm to solve bi-level multi-objective decision-making (BL-MODM) problems, and in which the objective function at each level are non-linear functions which are to be maximized. The proposed model for getting the satisfactory solution of the BL-MODM problems includes the membership functions for the upper level decision variables vector with possible tolerances, the membership function of the distance function from the positive ideal solution (PIS) and the membership function of the distance function from the negative ideal solution (NIS). A numerical illustrative example is given to clarify the proposed TOPSIS approach of this paper.     

Isolated efficiency in nonsmooth semi-infinite multi-objective programming

ABSTRACT

In this paper, isolated efficient solutions of a given nonsmooth Multi-Objective Semi-Infinite Programming problem (MOSIP) are studied. Two new Data Qualifications (DQs) are introduced and it is shown that these DQs are, to a large extent, weaker than already known Constraint Qualifications (CQs). The relationships between isolated efficiency and some relevant notions existing in the literature, including robustness, are established. Various necessary and sufficient conditions for characterizing isolated efficient solutions of a general problem are derived. It is done invoking the tangent cones, the normal cones, the generalized directional derivatives, and some gap functions. Using these characterizations, the (strongly) perturbed Karush-Kuhn-Tucker (KKT) optimality conditions for MOSIP are analyzed. Furthermore, it is shown that each isolated efficient solution is a Geoffrion properly efficient solution under appropriate assumptions. Moreover, Kuhn-Tucker (KT) and Klinger properly efficient solutions for a nonsmooth MOSIP are defined and it is proved that each isolated efficient solution is a KT properly efficient solution in general, and a Klinger properly efficient solution under a DQ. Finally, in the last section, the largest isolated efficiency constant for a given isolated efficient solution is determined.     

Multi-choice goal programming formulation based on the conic scalarizing function

The multi-choice goal programming allows the decision maker to set multi-choice aspiration levels for each goal to avoid underestimation of the decision. In this paper, we propose an alternative multi-choice goal programming formulation based on the conic scalarizing function with three contributions: (1) the alternative formulation allows the decision maker to set multi-choice aspiration levels for each goal to obtain an efficient solution in the global region, (2) the proposed formulation reduces auxiliary constraints and additional variables, and (3) the proposed model guarantees to obtain a properly efficient (in the sense of Benson) point. Finally, to demonstrate the usefulness of the proposed formulation, illustrative examples and test problems are included.     

A new multi-objective self-organizing optimization algorithm (MOSOA) for spatial optimization problems

Spatial planning is an important and complex activity. It includes land use planning and resource allocation as basic components. An abundance of papers can be found in the literature related to each one of these two aspects separately. On the contrary, a much smaller number of research reports deal with both aspects simultaneously. This paper presents an innovative evolutionary algorithm for treating combined land use planning and resource allocation problems. The new algorithm performs optimization on a cellular automaton domain, applying suitable transition rules on the individual neighbourhoods. The optimization process is multi-objective, based on non-domination criteria and self-organizing. It produces a Pareto front thus offering an advantage to the decision maker, in comparison to methods based on weighted-sum objective functions. Moreover, the present multi-objective self-organizing algorithm (MOSOA) can handle both local and global spatial constraints. A combined land use and water allocation problem is treated, in order to illustrate the cellular automaton optimization approach. Water is allocated after pumping from an aquifer, thus contributing a nonlinearity to the objective function. The problem is bi-objective aiming at (a) the minimization of soil and groundwater pollution and (b) the maximization of economic profit. An ecological and a socioeconomic constraint are imposed: (a) Groundwater levels at selected places are kept above prescribed thresholds. (b) Land use quota is predefined. MOSOA is compared to a standard multi-objective genetic algorithm and is shown to yield better results both with respect to the Pareto front and to the degree of compactness. The latter is a highly desirable feature of a land use pattern. In the land use literature, compactness is part of the objective function or of the constraints. In contrast, the present approach renders compactness as an emergent result.     

基于多目标遗传算法的增程式电动汽车动力系统参数匹配优化研究

在完成增程式电动汽车（E-REV）动力匹配与性能仿真基础上,针对E-REV动力系统参数匹配优化问题,以整车制造成本、汽车两种运行模式下等效百公里油耗以及百公里加速时间为目标,以驱动电机峰值功率、发动机额定功率以及电池能量为变量,设计了基于线性加权的多目标遗传算法。结果表明,适当牺牲汽车动力性可最大降低制造成本5.19%,并降低等效油耗9.61%以上。可以得出,通过改善匹配方案能进一步提高整车的动力经济性并降低制造成本,研究对E-REV市场推广及量产化具有重要意义。     

Approximate Pareto sets of minimal size for multi-objective optimization problems

We are interested in a problem introduced by Vassilvitskii and Yannakakis (2005), the computation of a minimum set of solutions that approximates within an accuracy ε$\epsilon$ the Pareto set of a multi-objective optimization problem. We mainly establish a new 3-approximation algorithm for the bi-objective case. We also propose a study of the greedy algorithm performance for the tri-objective case when the points are given explicitly, answering an open question raised by Koltun and Papadimitriou in (2007).     

Robustness analysis in Multi-Objective Mathematical Programming using Monte Carlo simulation

In most multi-objective optimization problems we aim at selecting the most preferred among the generated Pareto optimal solutions (a subjective selection among objectively determined solutions). In this paper we consider the robustness of the selected Pareto optimal solution in relation to perturbations within weights of the objective functions. For this task we design an integrated approach that can be used in multi-objective discrete and continuous problems using a combination of Monte Carlo simulation and optimization. In the proposed method we introduce measures of robustness for Pareto optimal solutions. In this way we can compare them according to their robustness, introducing one more characteristic for the Pareto optimal solution quality. In addition, especially in multi-objective discrete problems, we can detect the most robust Pareto optimal solution among neighboring ones. A computational experiment is designed in order to illustrate the method and its advantages. It is noteworthy that the Augmented Weighted Tchebycheff proved to be much more reliable than the conventional weighted sum method in discrete problems, due to the existence of unsupported Pareto optimal solutions.     

Designing a sustainable closed-loop supply chain network based on triple bottom line approach: A comparison of metaheuristics hybridization techniques

Recently, there is a growing concern about the environmental and social footprint of business operations. While most of the papers in the field of supply chain network design focus on economic performance, recently, some studies have considered environmental dimensions.