In this paper, we provide novel generalizations of the D-type-I functions by relaxing the D-Preinvexity functions using the mean-valued theorem. Under these new generalizations of the DPreinvexity type-I functions, we...
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In this paper, we provide novel generalizations of the D-type-I functions by relaxing the D-Preinvexity functions using the mean-valued theorem. Under these new generalizations of the DPreinvexity type-I functions, we also study the optimality solutions for multipleobjective nonlinear programming problems. We also establish and illustrate the duality theorems (weak, strong, and converse) for the Wolf-type and Mond-Weir-type for multipleobjective nonlinear programming problems using these new generalizations of the D-Preinvexity type-I functions.
The literature on portfolio selection mostly concentrates on computational analysis rather than on modelling efforts. In response, this paper provides a comprehensive literature review of multipleobjective determinis...
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The literature on portfolio selection mostly concentrates on computational analysis rather than on modelling efforts. In response, this paper provides a comprehensive literature review of multipleobjective deterministic and stochastic programming models for the portfolio selection problem. First, we summarize different concepts related to portfolio selection theory, including pricing models and portfolio risk measures. Second, we report the mathematical models that are generally used to solve deterministic and stochastic multiple objective programming problems. Finally, we present how these models can be used to solve the portfolio selection problem.
Compromise solutions, as feasible points as close as possible to the ideal (utopia) point, are important solutions in multiple objective programming. It is known in the literature that each compromise solution is a pr...
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Compromise solutions, as feasible points as close as possible to the ideal (utopia) point, are important solutions in multiple objective programming. It is known in the literature that each compromise solution is a properly efficient solution if the sum of the image set and conical ordering cone is closed. In this paper, we prove the same result in a general setting without any assumption.
This paper describes an approach for markedly reducing the time required to obtain all efficient extreme points of a multipleobjective linear program (MOLP) with three objectives. The approach is particularly useful ...
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This paper describes an approach for markedly reducing the time required to obtain all efficient extreme points of a multipleobjective linear program (MOLP) with three objectives. The approach is particularly useful when working with such MOLPs possessing large numbers of efficient extreme points. By subdividing the criterion cone into sub-cones, the paper shows how the task of computing all efficient extreme points can be broken down into parts so that the parts can be solved concurrently, thus allowing all efficient extreme points to be computed in much reduced elapsed time. The paper investigates several schemes for conducting this task and reports on a volume of computational experience. (C) 2019 Published by Elsevier B.V.
In this paper, we focused on characterizing and solving the multiple objective programming problems which have some imprecision of a vague nature in their formulation. The Rough Set Theory is only used in modeling the...
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In this paper, we focused on characterizing and solving the multiple objective programming problems which have some imprecision of a vague nature in their formulation. The Rough Set Theory is only used in modeling the vague data in such problems, and our contribution in data mining process is confined only in the "post-processing stage". These new problems are called rough multiple objective programming (RMOP) problems and classified into three classes according to the place of the roughness in the problem. Also, new concepts and theorems are introduced on the lines of their crisp counterparts;e.g. rough complete solution, rough efficient set, rough weak efficient set, rough Pareto front, weighted sum problem, etc. To avoid the prolongation of this paper, only the 1st-class, where the decision set is a rough set and all the objectives are crisp functions, is investigated and discussed in details. Furthermore, a flowchart for solving the 1st-class RMOP problems is presented. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
Most of the known methods for finding the efficient set of a multipleobjective linear programming (MOLP) problem are bottom-up search methods. Main difficulties of the known bottom-up search methods are to find all e...
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Most of the known methods for finding the efficient set of a multipleobjective linear programming (MOLP) problem are bottom-up search methods. Main difficulties of the known bottom-up search methods are to find all efficient extreme points adjacent to and to enumerate all efficient faces incident to an efficient degenerate extreme point. Main drawbacks of these methods are that the computational cost is still large and an implementation of them is still difficult. In this paper we propose a new local bottom-up search method for finding all maximal efficient faces for an MOLP problem. Our method is based on the maximal descriptor index sets for efficient edges and extreme rays for the MOLP problem in which the maximal descriptor index sets for edges and extreme rays incident to an efficient degenerate extreme point are easily found on the basis of solving some special linear programming problems. In addition, all efficient extreme points adjacent to and all efficient faces incident to an efficient extreme point can be easily found without using the simplex tables corresponding to bases of this point. Our method can overcome difficulties caused by the degeneracy of faces and is easy to implement. Some comparisons of our method with the known bottom-up search methods are presented. A numerical example is given to illustrate the method.
Finding the efficient set of a multipleobjective linear programming (MOLP) problem is difficult and finding the efficient sets of many MOLP problems is still more difficult. In this paper, a common formula to compute...
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Finding the efficient set of a multipleobjective linear programming (MOLP) problem is difficult and finding the efficient sets of many MOLP problems is still more difficult. In this paper, a common formula to compute the efficient sets of an arbitrary number of the MOLP problems corresponding to different right-hand side vectors is dealt with. We show that all the previously discovered methods and future methods for determining the efficient set of a MOLP problem which are not based on the efficient basic set of this MOLP problem cannot find such a common formula. In addition, our common formula is the union of the least number of descriptor sets for faces of the constraint polyhedrons among all possible common formulae for computing the efficient sets of the above MOLP problems. In order to increase the usefulness of the common formula, we give an efficient method for determining the efficient basic set of a MOLP problem. Some comparisons between our method and the methods for finding all extreme points of a convex polyhedral set in determining the efficient basic set of a MOLP problem are presented. A numerical example is given to illustrate the method.
In this paper, we address the thesis defence scheduling problem, a critical academic scheduling management process, which has been overshadowed in the literature by its counterparts, course timetabling and exam schedu...
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In this paper, we address the thesis defence scheduling problem, a critical academic scheduling management process, which has been overshadowed in the literature by its counterparts, course timetabling and exam scheduling. Specifically, we address the single defence assignment type of thesis defence schedul-ing problems, where each committee is assigned to a single defence, scheduled for a specific day, hour and room. We formulate a multi-objective mixed-integer linear programming model, which aims to be applicable to a broader set of cases than other single defence assignment models present in the literature, which have a focus on the characteristics of their universities. For such a purpose, we introduce a dif-ferent decision variable, propose constraint formulations that are not regulation and policy specific, and cover and offer new takes on the more common objectives seen in the literature. We also include new objective functions based on our experience with the problem at our university and by applying knowl-edge from other academic scheduling problems. We also propose a two-stage solution approach. The first stage is employed to find the number of schedulable defences, enabling the optimisation of instances with unschedulable defences. The second stage is an implementation of the augmented & epsilon;-constraint method, which allows for the search of a set of different and non-dominated solutions while skipping redundant iterations. The methodology is tested for case-studies from our university, significantly outperforming the solutions found by human schedulers. A novel instance generator for thesis scheduling problems is presented. Its main benefit is the generation of the availability of committee members and rooms in availability and unavailability blocks, resembling their real-world counterparts. A set of 96 randomly generated instances of varying sizes is solved and analysed regarding their relative computational performance, the number of schedulable de
In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear...
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In this paper, we investigate the possibility of improving the performance of multi-objective optimization solution approaches using machine learning techniques. Specifically, we focus on multi-objective binary linear programs and employ one of the most effective and recently developed criterion space search algorithms, the so-called KSA, during our study. This algorithm computes all nondominated points of a problem with p objectives by searching on a projected criterion space, i.e., a (p-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(p-1)$$\end{document}-dimensional criterion apace. We present an effective and fast learning approach to identify on which projected space the KSA should work. We also present several generic features/variables that can be used in machine learning techniques for identifying the best projected space. Finally, we present an effective bi-objective optimization-based heuristic for selecting the subset of the features to overcome the issue of overfitting in learning. Through an extensive computational study over 2000 instances of tri-objective knapsack and assignment problems, we demonstrate that an improvement of up to 18% in time can be achieved by the proposed learning method compared to a random selection of the projected space. To show that the performance of our algorithm is not limited to instances of knapsack and assignment problems with three objective functions, we also report similar performance results when the proposed learning approach is used for solving random binary integer program instances with four objective functions.
Although goal programming is one of the most used techniques for modeling and solving multi-objective optimization problems due to modeling elegance and mathematical simplicity. However, the existing goal programming ...
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Although goal programming is one of the most used techniques for modeling and solving multi-objective optimization problems due to modeling elegance and mathematical simplicity. However, the existing goal programming methods have some deficiencies in assigning the weights and then finding the solution per the objectives' priority to tackle the incommensurabilty in heterogeneous objectives. Therefore, this article proposes an efficient scalarization technique to solve the multi-objective optimization problem by introducing a modified goal function. The performance of the proposed method is evaluated using some closeness measure to the ideal solution for several test problems. A real application of the proposed method is illustrated in finding the best locations to establish municipal solid waste (MSW) management intermediate facilities in Nashik city (India). The model selects the three best locations out of the given eight potential locations to establish facilities by considering environmental and economic objectives. Overall, this study provides a theoretical advancement supported by a real-life MSW management application.
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