Budget allocation problems in portfolio management are inherently multi-objective as they entail different types of assets of which performance metrics are not directly comparable. Existing asset management methods th...
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Budget allocation problems in portfolio management are inherently multi-objective as they entail different types of assets of which performance metrics are not directly comparable. Existing asset management methods that either consolidate multiple goals to form a single objective ( a priori ) or populate a Pareto optimal set ( a posteriori ) may not be sufficient because a decision maker (DM) may not possess comprehensive knowledge of the problem domain. Moreover, current techniques often present a Pareto optimal set with too many options, making it counter-productive. In order to provide the DM with a diverse yet compact solution set, this paper proposes a three-step approach. In the first step, we employ different approximation functions to capture investment-performance relationships at the asset-type level. These simplified relationships are then used as inputs for the multi-objective optimisation model in the second step. In the final step, Pareto optimal solutions generated by a selected evolutionary algorithm are pruned by a clustering method. To measure the spread of representative solutions over the Pareto front, we present two novel indicators based on average Euclidean distance and cosine similarity between original Pareto solutions and representative solutions. Through numerical examples, we demonstrate that this approach can provide a set of representative solutions that maintain high integrity of the original Pareto front. We also put forward suggestions on choosing appropriate approximation functions, pruning methods, and indicators. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )
Optimizing a linear function over the efficient set of a multiobjective integer linear programming (MOILP) problem is a topic of unquestionable practical as well as mathematical interest within the field of multiple c...
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Optimizing a linear function over the efficient set of a multiobjective integer linear programming (MOILP) problem is a topic of unquestionable practical as well as mathematical interest within the field of multiple criteria decision making. As known, those problems are particularly difficult to deal with due to the discrete nature of the efficient set, which is not explicitly known, nor a suitable implicit description is available. In this work an exact algorithm is presented to optimize a linear function over the efficient set of a MOILP. The approach here proposed defines a sequence of progressively more constrained single-objective integer problems that successively eliminates undesirable points from further consideration. The algorithm has been coded in C Sharp, using CPLEX solver, and computational experiments have been undertaken in order to analyze performance properties of the algorithm over different problem instances randomly generated. (c) 2008 Elsevier B.V. All rights reserved.
This paper presents a multiple reference point approach for multi-objective optimization problems of discrete and combinatorial nature. When approximating the Pareto Frontier, multiple reference points can be used ins...
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This paper presents a multiple reference point approach for multi-objective optimization problems of discrete and combinatorial nature. When approximating the Pareto Frontier, multiple reference points can be used instead of traditional techniques. These multiple reference points can easily be implemented in a parallel algorithmic framework. The reference points can be uniformly distributed within a region that covers the Pareto Frontier. An evolutionary algorithm is based on an achievement scalarizing function that does not impose any restrictions with respect to the location of the reference points in the objective space. Computational experiments are performed on a bi-objective flow-shop scheduling problem. Results, quality measures as well as a statistical analysis are reported in the paper. (C) 2010 Elsevier B.V. All rights reserved.
Preference functions have been widely used to scalarize multipleobjectives. Various forms such as linear, quasiconcave, or general monotone have been assumed. In this article, we consider a general family of function...
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Preference functions have been widely used to scalarize multipleobjectives. Various forms such as linear, quasiconcave, or general monotone have been assumed. In this article, we consider a general family of functions that can take a variety of forms and has properties that allow for estimating the form efficiently. We exploit these properties to estimate the form of the function and converge towards a preferred solution(s). We develop the theory and algorithms to efficiently estimate the parameters of the function that best represent a decision maker's preferences. This in turn facilitates fast convergence to preferred solutions. We demonstrate on a variety of experiments that the algorithms work well both in estimating the form of the preference function and converging to preferred solutions.
Branch and bound is a well-known generic method for computing an optimal solution of a single objective optimization problem. Based on the idea "divide to conquer", it consists in an implicit enumeration pri...
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Branch and bound is a well-known generic method for computing an optimal solution of a single objective optimization problem. Based on the idea "divide to conquer", it consists in an implicit enumeration principle viewed as a tree search. Although the branch and bound was first suggested by Land and Doig (1960), the first complete algorithm introduced as a multi-objective branch and bound that we identified was proposed by Kiziltan and Yucaoglu (1983). Rather few multi-objective branch and bound algorithms have been proposed. This situation is not surprising as the contributions on the extensions of the components of branch and bound for multi-objective optimization are recent. For example, the concept of bound sets, which extends the classic notion of bounds, has been mentioned by Villarreal and Karwan (1981). But it was only developed for the first time in 2001 by Ehrgott and Gandibleux, and fully defined in 2007. This paper describes a state-of-the-art of multi-objective branch and bound, which reviews concepts, components and published algorithms. It mainly focuses on the contributions belonging to the class of optimization problems who has received the most of attention in this context from 1983 until 2015: the linear optimization problems with zero-one variables and mixed 0-1/continuous variables. Only papers aiming to compute a complete set of efficient solutions are discussed. (C) 2017 Elsevier B.V. All rights reserved.
Decision making in the presence of uncertainty and multiple conflicting objectives is a real-life issue in many areas of human activity. To address this type of problem, we study highly robust (weakly) efficient solut...
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Decision making in the presence of uncertainty and multiple conflicting objectives is a real-life issue in many areas of human activity. To address this type of problem, we study highly robust (weakly) efficient solutions to uncertain multiobjective linear programs (UMOLPs) with objective-wise uncertainty in the objective function coefficients. We develop properties of the highly robust efficient set, characterize highly robust (weakly) efficient solutions using the cone of improving directions associated with the UMOLP, derive several upper and lower bound sets on the highly robust (weakly) efficient set, and present a robust counterpart for a class of UMOLPs. As various results rely on the acuteness of the cone of improving directions, we also propose methods to verify this property. (C) 2018 Elsevier B.V. All rights reserved.
This paper addresses the problem of scheduling medical residents that arises in different clinical settings of a hospital. The residents are grouped according to different seniority levels that are specified by the nu...
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This paper addresses the problem of scheduling medical residents that arises in different clinical settings of a hospital. The residents are grouped according to different seniority levels that are specified by the number of years spent in residency training. It is required from the residents to participate in the delivery of patient care services directly by working weekday and weekend day shifts in addition to their regular daytime work. A monthly shift schedule is prepared to determine the shift duties of each resident considering shift coverage requirements, seniority-based workload rules, and resident work preferences. Due to the large number of constraints often conflicting, a multi-objectiveprogramming model has been proposed to automate the schedule generation process. The model is implemented on a real case in the pulmonary unit of a local hospital for a 6-month period using sequential and weighted methods. The results indicate that high quality solutions can be obtained within a few seconds compared to the manually prepared schedules expending considerable effort and time. It is also shown that the employed weighting procedure based on seniority levels performs much better compared to the preemptive method in terms of computational burden. (C) 2008 Elsevier B.V. All rights reserved.
Bounds on efficient outcomes in interactive multiple criteria decision making problems are derived. Bounds are dynamic, i.e., they become stronger with the growing number of explicitly identified outcomes. They are al...
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Bounds on efficient outcomes in interactive multiple criteria decision making problems are derived. Bounds are dynamic, i.e., they become stronger with the growing number of explicitly identified outcomes. They are also parametric with respect to weighting coefficients. Computational cost to calculate bounds is negligible. Bounds of the sort offer a breakthrough for prohibitive size and/or solution time bottlenecks by allowing a decision maker to interact with an approximation of the underlying mathematical model rather the model itself. Possible applications of bounds to existing interactive decision making algorithms are discussed. Illustrative numerical examples are given. (C) 2002 Published by Elsevier Science B.V.
In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general form...
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In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the epsilon-constraint method, the Benson method, the hybrid method and the elastic epsilon-constraint method can be subsumed under these two problems. Then, considering approximate solutions, some relationships between epsilon-(weakly, properly) efficient points of a general (without any convexity assumption) multiobjective optimization problem and epsilon-optimal solutions of the introduced scalarized problem are achieved. (C) 2013 Elsevier B.V. All rights reserved.
To deal with the multi-objective optimization problems (MOPS), a meta-heuristic based on an improved shuffled frog leaping algorithm (ISFLA) which belongs to memetic evolution is presented. For the MOPs, both diversit...
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To deal with the multi-objective optimization problems (MOPS), a meta-heuristic based on an improved shuffled frog leaping algorithm (ISFLA) which belongs to memetic evolution is presented. For the MOPs, both diversity maintenance and searching effectiveness are crucial for algorithm evolution. In this work, modified calculation of crowding distance to evaluate the density of a solution, memeplex clustering analyses based on a grid to divide the population, and new selection measure of global best individual are proposed to ensure the diversity of the algorithm. A multi-objective extremal optimization procedure (MEOP) is also introduced and incorporated into ISFLA to enable the algorithm to evolve more effectively. Finally, the experimental tests on thirteen unconstrained MOPs and DTLZ many-objective problems show that the proposed algorithm is flexible to handle MOPs and many-objective problems. The effectiveness and robustness of the proposed algorithm are also analyzed in detail. (C) 2018 Elsevier Inc. All rights reserved.
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