Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated cri-terion vectors (P...
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Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated cri-terion vectors (Pareto front) and a clear overview of the different trade-offs of the problem. However, providing many solutions to the decision-maker may also be overwhelming. As an alternative approach, showing a representative set of the Pareto front may be advantageous. Choosing such a representative set is by itself also a multi-objective problem that must consider the number of alternatives to present, the uniformity, and/or the coverage of the representation, to guarantee its quality. This paper proposes three algorithms for the representation problem for multi-objective integer linear programming problems with two or more objective functions, each one of them dealing with each dimension of the problem (cardi-nality, coverage, and uniformity). Such algorithms are all based on the epsilon-constraint approach. In addition, the paper also presents strategies to overcome poor estimations of the Pareto front bounds. The algo-rithms were tested on the ability to efficiently generate the whole Pareto front or a representation of it. The uniformity and cardinality algorithms proved to be very efficient both on binary and on integer problems, being amongst the best in the literature. Both coverage and uniformity algorithms provide good quality representations on their targeted objective, while the cardinality algorithm appears to be the most flexible, privileging uniformity for lower cardinality representations and coverage on higher cardinality.(c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://***/licenses/by-nc-nd/4.0/ )
A general method to solve multi-objective de novo programming problem having both maximizing and minimizing types of objectives has been proposed. The method in one hand provides a platform to get a maximum number of ...
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A general method to solve multi-objective de novo programming problem having both maximizing and minimizing types of objectives has been proposed. The method in one hand provides a platform to get a maximum number of objectives to their targeted ideal (maximum/minimum) values and on the other hand gives the decision-maker flexibility to choose the objectives according to his/her priority towards the attainment of their ideal values. The proposed method has been illustrated with a numerical problem and a real-life example. A comparison with two other existing methods for such problems has also been provided.
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be ...
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In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a complete set of efficient extreme solutions, and the corresponding set of extreme non-dominated points, for a bi-objective linear programme. Using a Benders-like reformulation, the decomposition approach decouples the problem into a bi-objective master problem and a bi-objective subproblem, each of which is solved using the bi-objective parametric simplex algorithm. The master problem provides candidate efficient solutions that the subproblem assesses for feasibility and optimality. As in standard Benders decomposition, optimality and feasibility cuts are generated by the subproblem and guide the master problem solve. This paper discusses bi-objective Benders decomposition from a theoretical perspective, proves the correctness of the proposed reformulation and addresses the need for so-called weighted optimality cuts. Furthermore, we present an algorithm to solve the reformulation and discuss its performance for three types of bi-objective optimisation problems.
The Multiobjective Minimum Spanning Tree (MO-MST) problem generalizes the Minimum Spanning Tree problem by weighting the edges of the input graph using vectors instead of scalars. In this paper, we design a new Dynami...
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The Multiobjective Minimum Spanning Tree (MO-MST) problem generalizes the Minimum Spanning Tree problem by weighting the edges of the input graph using vectors instead of scalars. In this paper, we design a new Dynamic programming MO-MST algorithm. Dynamic programming for a MO-MST instance requests solving a One-to-One Multiobjective Shortest Path (MOSP) instance and both instances have equivalent solution sets. The MOSP instance is defined on a so called transition graph. We study the original size of this graph in detail and reduce its size using cost-dependent arc pruning criteria. To solve the MOSP instance on the reduced transition graph, , we design the Implicit Graph Multiobjective Dijkstra Algorithm (IG-MDA), exploiting recent improvements on MOSP algorithms from the literature. All in all, the new IG-MDA outperforms the current state of the art on a big set of instances from the literature. Our code and results are publicly available.
Renewable liquid fuels produced from biomass, hydrogen, and carbon dioxide play an important role in reaching climate neutrality in the transportation sector. For large-scale deployment, production facilities and corr...
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Renewable liquid fuels produced from biomass, hydrogen, and carbon dioxide play an important role in reaching climate neutrality in the transportation sector. For large-scale deployment, production facilities and corresponding logistics have to be established. However, the implementation of such a large-scale renewable fuel production network requires acceptance by citizens. To gain insights into the structure of efficient and socially accepted renewable fuel production networks, we propose a bi-objective mixed -integer programming model. In addition to an economic objective function, we consider social acceptance as a second objective function. We use results from a conjoint analysis study on the acceptance and preference of renewable fuel production networks, considering the regional topography, facility size, production pathway, and raw material transportation to model social acceptance. We find significant trade-offs between the economic and social acceptance objective. The most favorable solution from a social acceptance perspective is almost twice as expensive as the most efficient economical solution. However, it is possible to strongly increase acceptance at a moderate expense by carefully selecting sites with preferred regional topography.
The heterogeneity among objectives in multi-objective optimization can be viewed from several perspectives. In this paper, we are interested in the heterogeneity arising in the underlying landscape of the objective fu...
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The heterogeneity among objectives in multi-objective optimization can be viewed from several perspectives. In this paper, we are interested in the heterogeneity arising in the underlying landscape of the objective functions, in terms of multi-modality and search difficulty. Building on recent efforts leveraging the so-called single- objective NK-landscapes to model such a setting, we conduct a three-fold empirical analysis on the impact of objective heterogeneity on the landscape properties and search difficulty of bi-objective optimization problems. Firstly, for small problems, we propose two techniques based on studying the distribution of the solutions in the objective space. Secondly, for large problems, we investigate the ability of existing landscape features to capture the degree of heterogeneity among the two objectives. Thirdly, we study the behavior of two state-of-the-art multi-objective evolutionary algorithms, namely MOEA/D and NSGA-II, when faced with a range of problems with different degrees of heterogeneity. Although one algorithm is found to consistently outperform the other, the dynamics of both algorithms vary similarly with respect to objective heterogeneity. Our analysis suggests that novel approaches are needed to understand the fundamental properties of heterogeneous bi-objective optimization problems and to tackle them more effectively.
This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algo...
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This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where the search for a feasible point is prioritized if not available before improving the current solution set, or in a progressive barrier approach, where any trial point whose constraint violation function values are above a threshold are rejected. This threshold is progressively decreased along the iterations. As in the single-objective case, it is proved that these two variants generate feasible and/or infeasible sequences which converge either in the feasible case to a set of local Pareto optimal points or in the infeasible case to Clarke stationary points according to the constraint violation function. Computational experiments show that these two approaches are competitive with other state-of-the-art algorithms.
Multi-objective optimization is challenging for computationally expensive objectives because most optimization methods rely on a large number of function evaluations to approach the Pareto-optimal front. To this end, ...
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Multi-objective optimization is challenging for computationally expensive objectives because most optimization methods rely on a large number of function evaluations to approach the Pareto-optimal front. To this end, this article develops a novel multi-objective optimization algorithm, the Multi-objective Parallel Local Surrogate-assisted search (MOPLS) algorithm, which combines surrogate approximation and parallel computing. In each iteration, MOPLS incorporates a tabu mechanism to determine new points for expensive evaluations via a series of independent surrogate-assisted local searches. A master-worker architecture in MOPLS allows the algorithm to conduct either synchronous or asynchronous parallel processing. On a number of benchmark problems, MOPLS outperforms recent surrogate-assisted algorithms within a limited computational budget. Empirical results from parallel experiments indicate that MOPLS can significantly improve its efficiency through parallelism, and the asynchronous MOPLS shows advantages in handling objectives with non-constant evaluation times. Finally, the better performance of MOPLS over alternatives in calibrating a complex watershed simulation model demonstrates its competitiveness in solving real-world engineering applications.
In this paper, we study a method for finding robust solutions to multiobjective optimization problems under uncertainty. We follow the set-based minmax approach for handling the uncertainties which leads to a certain ...
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In this paper, we study a method for finding robust solutions to multiobjective optimization problems under uncertainty. We follow the set-based minmax approach for handling the uncertainties which leads to a certain set optimization problem with the strict upper type set relation. We introduce, under some assumptions, a reformulation using instead the strict lower type set relation without sacrificing the compactness property of the image sets. This allows to apply vectorization results to characterize the optimal solutions of these set optimization problems as optimal solutions of a multiobjective optimization problem. We end up with multiobjective semi-infinite problems which can then be studied with classical techniques from the literature.
Transitioning to a carbon-neutral supply chain poses challenges in visualizing and reducing carbon emissions throughout logistics networks. This study presents a comprehensive framework that integrates blockchain tech...
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Transitioning to a carbon-neutral supply chain poses challenges in visualizing and reducing carbon emissions throughout logistics networks. This study presents a comprehensive framework that integrates blockchain technology (BCT) and carbon capture, utilization, and storage (CCUS) into the two-echelon production routing problem (PRP). A multi-objective mixed-integer linear programming model is developed for the problem, considering economic, environmental, and social objectives. To approximate a Pareto optimal solution for the complex model, a Lagrangian matheuristic algorithm (AugMathLagr) is employed. Computational results demonstrate that the integration of BCT and CCUS may not always be the optimal approach for reducing carbon emissions and creating social value, as it can also lead to higher costs. Sensitivity analyses indicate that the adoption of BCT and CCUS is influenced by parameters such as carbon caps, carbon accounting errors, and carbon capture rates. These findings offer valuable insights for policymakers aiming to achieve a carbon-neutral supply chain through the integration of BCT and CCUS.
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