An improved version of the augmented ε-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems

doi:10.1016/J.AMC.2013.03.002

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An improved version of the augmented ε-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems

Journal Article•DOI•

An improved version of the augmented ε-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems

George Mavrotas¹, Kostas Florios¹•Institutions (1)

National Technical University of Athens¹

01 May 2013-Applied Mathematics and Computation (Elsevier)-Vol. 219, Iss: 18, pp 9652-9669

TL;DR: It is demonstrated that AUGMECON2 is especially suitable for Multi-Objective Integer Programming (MOIP) problems and capable of producing the exact Pareto set in MOIP problems by appropriately tuning its running parameters.

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About: This article is published in Applied Mathematics and Computation.The article was published on 2013-05-01. It has received 378 citations till now. The article focuses on the topics: Integer programming & Combinatorial optimization.

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Journal Article•DOI•

Resilient and sustainable supply chain design: sustainability analysis under disruption risks

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Armin Jabbarzadeh¹, Behnam Fahimnia², Fatemeh Sabouhi¹•Institutions (2)

Iran University of Science and Technology¹, University of Sydney²

04 May 2018-International Journal of Production Research

TL;DR: A stochastic bi-objective optimisation model is developed that utilises a fuzzy c-means clustering method to quantify and assess the sustainability performance of the suppliers and determines outsourcing decisions and resilience strategies that minimise the expected total cost and maximise the overall sustainability performance in disruptions.

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Abstract: Resilience to disruptions and sustainability are both of paramount importance to supply chains. However, the interactions between the two have not been thoroughly explored in the academic literatur...

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215 citations

Cites background or methods from "An improved version of the augmente..."

...Meena and Sarmah (2013) formulate a mixed integer non-linear programming model for determining order allocation considering different capacities, failure probabilities and quantity discounts for each supplier. Kamalahmadi and MellatParast (2016) examine an optimal allocation of demand across a set of suppliers in a supply chain that is exposed to supply risk and environmental risk....
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...Meena and Sarmah (2013) formulate a mixed integer non-linear programming model for determining order allocation considering different capacities, failure probabilities and quantity discounts for each supplier. Kamalahmadi and MellatParast (2016) examine an optimal allocation of demand across a set of suppliers in a supply chain that is exposed to supply risk and environmental risk. Their model integrates supplier selection and demand allocation with transportation channel selection and provides contingency plans to mitigate the negative impacts of disruptions and minimise total network costs. A scenario-based bi-objective possibilistic mixed integer linear model is presented by Torabi, Baghersad, and Mansouri (2015) to build resilient supply bases for global supply chains in response to disruption risks....
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...Meena and Sarmah (2013) formulate a mixed integer non-linear programming model for determining order allocation considering different capacities, failure probabilities and quantity discounts for each supplier....
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...The augmented ε-constraint method is amongst the most efficient and powerful multi-objective approaches (Mavrotas 2009; Mavrotas and Florios 2013; Fahimnia et al. 2015; Torabi, Baghersad, and Mansouri 2015)....
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...Meena and Sarmah (2013) formulate a mixed integer non-linear programming model for determining order allocation considering different capacities, failure probabilities and quantity discounts for each supplier. Kamalahmadi and MellatParast (2016) examine an optimal allocation of demand across a set of suppliers in a supply chain that is exposed to supply risk and environmental risk. Their model integrates supplier selection and demand allocation with transportation channel selection and provides contingency plans to mitigate the negative impacts of disruptions and minimise total network costs. A scenario-based bi-objective possibilistic mixed integer linear model is presented by Torabi, Baghersad, and Mansouri (2015) to build resilient supply bases for global supply chains in response to disruption risks. The model applies several proactive strategies such as suppliers’ business continuity plans and fortification of suppliers to enhance the resilience of the selected supply base. Based on the two popular measures of value-at-risk (VaR) and conditional value-at-risk (CVaR), Sawik (2011a, 2011b, 2013c, 2017) and Namdar et al. (2017) present portfolio methodologies for managing supply disruption risks....
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Journal Article•DOI•

Toward an integrated sustainable-resilient supply chain: A pharmaceutical case study

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Behzad Zahiri¹, Jun Zhuang¹, Mehrdad Mohammadi²•Institutions (2)

University at Buffalo¹, Mines ParisTech²

01 Jul 2017-Transportation Research Part E-logistics and Transportation Review

TL;DR: In this article, a multi-objective integrated sustainable-resilient mixed integer linear programming model for designing a pharmaceutical supply chain network under uncertainty is presented, and a new fuzzy possibilistic-stochastic programming approach is developed.

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Abstract: In this paper, a novel multi-objective integrated sustainable-resilient mixed integer linear programming model for designing a pharmaceutical supply chain network under uncertainty is presented. To cope with the uncertainty aspect of the model, a new fuzzy possibilistic-stochastic programming approach is developed. Additionally, due to NP-hard nature of the problem, we propose a novel Pareto-based lower bound method as well as a new meta-heuristic algorithm. Several numerical examples, as well as a case study targeting Truvada© supply chain for the LGBTQ community, as they account for majority of the market for such product, in France is proposed.

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187 citations

Journal Article•DOI•

Stochastic multi-objective energy management in residential microgrids with combined cooling, heating, and power units considering battery energy storage systems and plug-in hybrid electric vehicles

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Mostafa Sedighizadeh¹, Masoud Esmaili², Nahid Mohammadkhani¹•Institutions (2)

Shahid Beheshti University¹, Islamic Azad University²

10 Sep 2018-Journal of Cleaner Production

TL;DR: A residential microgrid consisting of combined cooling, heating and power, plug-in hybrid electric vehicles, photovoltaic unit, and battery energy storage systems is modeled to obtain the optimal scheduling state of these units by taking into account the uncertainty of distributed energy resources.

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130 citations

Journal Article•DOI•

A hybrid robust possibilistic approach for a sustainable supply chain location-allocation network design

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Masoud Rabbani¹, Seyed Ali Akbar Hosseini-Mokhallesun¹, Amir Hossein Ordibazar¹, Hamed Farrokhi-Asl²•Institutions (2)

University of Tehran¹, Iran University of Science and Technology²

02 Jan 2020-International Journal of Systems Science: Operations & Logistics

TL;DR: A multi-objective multi-period sustainable location-allocation supply chain network model that addresses the challenge of different levels of technology for vehicle fleet and its implications for sustainability.

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Abstract: In this paper, a multi-objective multi-period sustainable location-allocation supply chain network model will be presented. Different levels of technology for vehicle fleet, which leads to differen...

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118 citations

Journal Article•DOI•

Building organizational resilience in the face of multiple disruptions

[...]

Navid Sahebjamnia, S. Ali Torabi¹, S. Afshin Mansouri²•Institutions (2)

University of Tehran¹, Brunel University London²

01 Mar 2018-International Journal of Production Economics

TL;DR: The proposed model demonstrates the interaction between the organizational resilience and required resources, particularly in respect to the total budget and external resources, which is necessary for developing continuity and recovery strategies.

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107 citations

Cites background from "An improved version of the augmente..."

...…been proposed in the literature, trying to improve its presentation or to tune it for particular problems (Behnamian et al., 2009; Fazlollahi et al., 2012; Khalili-Damghani et al., 2013; Liu and Papageorgiou, 2013; Mavrotas and Florios, 2013; Olivares-Benitez et al., 2013; Soysal et al., 2014)....
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References

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Book•

Multi-Objective Optimization Using Evolutionary Algorithms

[...]

Kalyanmoy Deb, Deb Kalyanmoy

01 Jan 2001

TL;DR: This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study.

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Abstract: From the Publisher: Evolutionary algorithms are relatively new, but very powerful techniques used to find solutions to many real-world search and optimization problems. Many of these problems have multiple objectives, which leads to the need to obtain a set of optimal solutions, known as effective solutions. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run. · Comprehensive coverage of this growing area of research · Carefully introduces each algorithm with examples and in-depth discussion · Includes many applications to real-world problems, including engineering design and scheduling · Includes discussion of advanced topics and future research · Features exercises and solutions, enabling use as a course text or for self-study · Accessible to those with limited knowledge of classical multi-objective optimization and evolutionary algorithms The integrated presentation of theory, algorithms and examples will benefit those working and researching in the areas of optimization, optimal design and evolutionary computing. This text provides an excellent introduction to the use of evolutionary algorithms in multi-objective optimization, allowing use as a graduate course text or for self-study.

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12,134 citations

Journal Article•DOI•

Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach

[...]

Eckart Zitzler¹, Lothar Thiele¹•Institutions (1)

ETH Zurich¹

01 Nov 1999-IEEE Transactions on Evolutionary Computation

TL;DR: The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface.

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Abstract: Evolutionary algorithms (EAs) are often well-suited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EAs are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the strength Pareto EA (SPEA), that combines several features of previous multiobjective EAs in a unique manner. It is characterized by (a) storing nondominated solutions externally in a second, continuously updated population, (b) evaluating an individual's fitness dependent on the number of external nondominated points that dominate it, (c) preserving population diversity using the Pareto dominance relationship, and (d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EAs on the 0/1 knapsack problem.

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7,512 citations

Journal Article•DOI•

Combinatorial optimization: algorithms and complexity

[...]

Christos H. Papadimitriou¹, Kenneth Steiglitz²•Institutions (2)

National Technical University of Athens¹, Princeton University²

01 Jun 1982-American Mathematical Monthly

TL;DR: This clearly written, mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more.

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Abstract: This clearly written , mathematically rigorous text includes a novel algorithmic exposition of the simplex method and also discusses the Soviet ellipsoid algorithm for linear programming; efficient algorithms for network flow, matching, spanning trees, and matroids; the theory of NP-complete problems; approximation algorithms, local search heuristics for NPcomplete problems, more All chapters are supplemented by thoughtprovoking problems A useful work for graduate-level students with backgrounds in computer science, operations research, and electrical engineering Mathematicians wishing a self-contained introduction need look no further—American Mathematical Monthly 1982 ed

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7,221 citations

Book•

Integer and Combinatorial Optimization

[...]

George L. Nemhauser¹, Laurence A. Wolsey²•Institutions (2)

Georgia Institute of Technology¹, Université catholique de Louvain²

01 Jan 1988

TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.

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Abstract: FOUNDATIONS. The Scope of Integer and Combinatorial Optimization. Linear Programming. Graphs and Networks. Polyhedral Theory. Computational Complexity. Polynomial-Time Algorithms for Linear Programming. Integer Lattices. GENERAL INTEGER PROGRAMMING. The Theory of Valid Inequalities. Strong Valid Inequalities and Facets for Structured Integer Programs. Duality and Relaxation. General Algorithms. Special-Purpose Algorithms. Applications of Special- Purpose Algorithms. COMBINATORIAL OPTIMIZATION. Integral Polyhedra. Matching. Matroid and Submodular Function Optimization. References. Indexes.

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6,287 citations

Book•

Evolutionary algorithms for solving multi-objective problems

[...]

Gary B. Lamont, David A. Van Veldhuizen

30 Jun 2002

TL;DR: This paper presents a meta-anatomy of the multi-Criteria Decision Making process, which aims to provide a scaffolding for the future development of multi-criteria decision-making systems.

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Abstract: List of Figures. List of Tables. Preface. Foreword. 1. Basic Concepts. 2. Evolutionary Algorithm MOP Approaches. 3. MOEA Test Suites. 4. MOEA Testing and Analysis. 5. MOEA Theory and Issues. 3. MOEA Theoretical Issues. 6. Applications. 7. MOEA Parallelization. 8. Multi-Criteria Decision Making. 9. Special Topics. 10. Epilog. Appendix A: MOEA Classification and Technique Analysis. Appendix B: MOPs in the Literature. Appendix C: Ptrue & PFtrue for Selected Numeric MOPs. Appendix D: Ptrue & PFtrue for Side-Constrained MOPs. Appendix E: MOEA Software Availability. Appendix F: MOEA-Related Information. Index. References.

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5,994 citations