We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible so-luti...
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We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible so-lutions. We review different optimality concepts for ordinal optimization problems and discuss their sim-ilarities and differences. We then focus on two prevalent optimality concepts that are shown to be equiv-alent. Our main focus lies on the investigation of a bijective linear transformation that transforms ordinal optimization problems to associated standard multi-objective optimization problems with binary cost co-efficients. Since this transformation preserves all properties of the underlying problem, problem-specific solution methods remain applicable. A prominent example is dynamic programming and Bellman's prin-ciple of optimality, that can be applied, e.g., to ordinal shortest path and ordinal knapsack problems. We investigate the interrelation between scalarization techniques and methods based on the hypervolume indicator when applied to the ordinal and the transformed problem, respectively. Furthermore, we ex-tend our results to multi-objective optimization problems that combine ordinal and real-valued objective functions.& COPY;2023 Elsevier B.V. All rights reserved.
Due to the increased demand for efficient recycling systems for end-of-life (EOL) products, the role of disassembly lines in reverse supply chains has become crucial. Parallel disassembly lines can handle multi-type E...
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Due to the increased demand for efficient recycling systems for end-of-life (EOL) products, the role of disassembly lines in reverse supply chains has become crucial. Parallel disassembly lines can handle multi-type EOL products and consist of two or more lines. However, previous research has primarily focused on two-line disassembly systems and has not fully addressed the optionality of common stations. To address this gap, this study proposes three exact methods for optimizing multi-line parallel disassembly systems with optional common stations, partial disassembly mode, and AND/OR precedence relations. Firstly, a mixed-integer linear programming (MILP) model is formulated that optimizes three objectives: weighted line length, additional profits, and hazard evaluation. Secondly, two constraint programming (CP) models are developed with different solution methodologies to provide more extensive applications and efficient solutions. An illustrative example shows that production mode can significantly reduce line length and workstations, and computational results demonstrate that both CP methods outperform the MILP model in terms of solution quality and computational efficiency. Specifically, the CP-I method demonstrates a higher level of stability and efficiency in most instances, while the CP-II method excels in optimizing line length and station utilization. These results illustrate the potential for optimizing multi-line disassembly systems with optional common stations to enhance production flexibility in remanufacturing processes.& COPY;2023 Elsevier Inc. All rights reserved.
A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. On...
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A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. For that computation one often makes use of so-called local upper bounds. In this paper we present a generalization of this concept. For the first time, this allows to apply a warm start strategy to the computation of an enclosure. We also show how this generalized concept allows to remove empty areas of an enclosure by deleting certain parts of the lower and upper bound sets which has not been possible in the past. We demonstrate how to apply our ideas to the box approximation algorithm, a general framework to compute an enclosure, as recently used in the solver called BAMOP. We show how that framework can be simplified and improved significantly, especially concerning its practical numerical use. In fact, we show for selected numerical instances that our new approach is up to eight times faster than the original one. Hence, our new framework is not only of theoretical but also of practical use, for instance for continuous convex or mixed-integer quadratic optimization problems.(c) 2023 Elsevier B.V. All rights reserved.
The paper focuses on investors whose strength of interest in sustainability issues (such as environmental, social, and governance) causes ESG to become a third criterion alongside risk and return in portfolio selectio...
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The paper focuses on investors whose strength of interest in sustainability issues (such as environmental, social, and governance) causes ESG to become a third criterion alongside risk and return in portfolio selection. This causes the efficient frontier to become an efficient surface. This means that an investor's optimal portfolio is no longer the point of most preferred risk/return tradeoff on the mean-variance (M-V) efficient frontier, but is the point of most preferred risk/return/ESG tradeoff on the investor's M-V-ESG efficient surface. However, to find such a point requires non-trivial ESG integration which is the name given to the process of integrating ESG into the portfolio construction process after screening. With the third objective transporting the problem into 3D-space, it is difficult to search the efficient surface in any kind of comprehensive fashion using M-V based or other bi-criterion techniques as this is akin to a 2 -dimensional being trying to view a 3-dimensional object. To remedy the situation, the paper proposes a tri-criterion approach that computes efficient surfaces and special non-contour curves (called NC-efficient fronts in the paper) that are stretched across the efficient surface so as to dragnet it for the points of best ESG integration within it. Using the methodology and data from the S&P500, the paper conducts computational tests on problems with up to 500 securities and under different constraint conditions so as to know what to expect from the new approach over a range of situations.(c) 2022 Elsevier B.V. All rights reserved.
This paper investigates two approaches for solving bi-objective constrained minimum spanning tree problems. The first seeks to minimize the tree weight, keeping the problem's additional objective as a constraint, ...
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This paper investigates two approaches for solving bi-objective constrained minimum spanning tree problems. The first seeks to minimize the tree weight, keeping the problem's additional objective as a constraint, and the second aims at minimizing the other objective while constraining the tree weight. As case studies, we propose and solve bi-objective generalizations of the Hop-Constrained Minimum Spanning Tree Problem (HCMST) and the Delay-Constrained Minimum Spanning Tree Problem (DCMST). First, we present an Integer Linear programming (ILP) formulation for the HCMST. Then, we propose a new com-pact mathematical model for the DCMST based on the well-known Miller-Tucker-Zemlin subtour elimination constraints. Next, we extend these formulations as bi-objective models and solve them using an Augmented e-constraints method. Computational experiments per-formed on classical instances from the literature evaluated two different implementations of the Augmented e-constraints method for each problem. Results indicate that the algorithm performs better when minimizing the tree weight while constraining the other objective since this implementation finds shorter running times than the one that minimizes the additional objective and constrains the tree weight.
Many interactive approaches in multi-objective optimization assume the existence of an underlying pref-erence function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and...
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Many interactive approaches in multi-objective optimization assume the existence of an underlying pref-erence function that represents the preferences of a decision maker (DM). In this paper, we develop the theory and an exact algorithm that guarantees finding the most preferred solution of a DM whose pref-erences are consistent with a Tchebycheff function for multi-objective integer programs. The algorithm occasionally presents pairs of solutions to the DM and asks which one is preferred. It utilizes the prefer-ence information together with the properties of the Tchebycheff function to generate solutions that are candidates to be the most preferred solution. We test the performance of the algorithm on a set of three and four-objective combinatorial optimization problems.(c) 2022 Elsevier B.V. All rights reserved.
We propose a simple, flexible, efficient, and general framework for running large-scale highly-dynamic sponsored search auctions. Our framework aims at exploring optimal tradeoffs among various objectives of three par...
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We propose a simple, flexible, efficient, and general framework for running large-scale highly-dynamic sponsored search auctions. Our framework aims at exploring optimal tradeoffs among various objectives of three parties: platform, advertisers, and users. We model the optimal tradeoffs as an online linear program problem, which can be addressed by a simple approach based on semi-Lagrangian duality. Experimental results conducted on large-scale real-world traffic show that the proposed framework can significantly improve all objectives considered, as well as the platform's revenue.(c) 2023 Elsevier B.V. All rights reserved.
In this article, we present generalizations of the cone-preinvexity functions and study a pair of second-order symmetric solutions for multipleobjective nonlinear programming problems under these generalizations of t...
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In this article, we present generalizations of the cone-preinvexity functions and study a pair of second-order symmetric solutions for multipleobjective nonlinear programming problems under these generalizations of the cone-preinvexity functions. In addition, we establish and prove the theorems of weak duality, strong duality, strict converse duality, and self-duality by assuming the skew-symmetric functions under these generalizations of the cone-preinvexity functions. Finally, we provide four nontrivial numerical examples to demonstrate that the results of the weak and strong duality theorems are true.
Highway monitoring with traffic counting stations can provide data for the transporta-tion planning such as the origin-destination (O-D) trip tables. These O-D trip tables are important in the process of estimating tr...
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Highway monitoring with traffic counting stations can provide data for the transporta-tion planning such as the origin-destination (O-D) trip tables. These O-D trip tables are important in the process of estimating traffic flow on the highways, indicating where new investments are required. This paper presents a hybrid solution method for the Bi-objective Traffic Couting Location Problem (BTCLP) considering previous trip tables. The BTCLP minimizes the number of counting stations located and maxi-mizes the coverage of the O-D trips. The concept of coverage of trips between an O-D pair considers that a user can use different paths given a maximum deviation of the shortest path. The hybrid solution combines strategies from the e-Constraint method with an existing Partial Set Covering Framework and can be used as exact or heuris-tic approach. We explore scenarios considering different limits for deviations from shortest path for 26 real instances based on the Brazilian transportation road network. Our computational experiments show that the hybrid solution method provides good solutions for large-sized instances.
The literature review shows research gaps into the food supply chain design. In that context, this paper deals with the design of a sustainable supply chain. A multi-objective mixed-integer linear programming model in...
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The literature review shows research gaps into the food supply chain design. In that context, this paper deals with the design of a sustainable supply chain. A multi-objective mixed-integer linear programming model includes four decisions and three sustainable criteria (economic-total network costs-, environmental-carbon emissions-, and social-work conditions and societal development-). The model aims to determine the optimal location and capacity of processing and distribution facilities, to choose the suppliers from a set of potential candidates, to determine transportation modes between all the actors, and to define the quantity of product, in order to satisfy the demand of dairy products in a set of regions. The applicability of the model is tested in a realistic case in the dairy sector in the central region of Colombia. The results show the existent trade-offs between the three dimensions of sustainability. The unweighted balance results, giving more priority to the social dimension, which obtains the least deviation, affecting the environmental performance of the chain. The analysis carried out in this paper does help decision-makers that will have at hand a set of possible configurations to be chosen in order to comply with environmental and social regulations without neglecting economic performance.
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