A one direction search method to find the exact nondominated frontier of biobjective mixed-binary linear programming problems

Fattahi, Ali; Türkay, Metin

doi:10.1016/j.ejor.2017.09.026

Cited by 22 publications

(11 citation statements)

References 12 publications

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“…The augmented epsilon-constraint (AUGMECON) method by Mavrotas [18], its improved version (AUGMECON2) by Mavrotas and Florios [19] proposes solution methods to find a set of exact solutions in multi-objective problems by adding slack variables into the objective functions that are taken as constraints and penalty term into the main objective function. Fattahi and Turkay [20] presents a novel one-direction search (ODS) method to find an exact non-dominated frontier of bi-objective MILPs. Moreover, multi-objective evolutionary algorithms (MOEAs) are widely used in getting solutions for large-scale real-life problems.…”

Section: Literature Reviewmentioning

confidence: 99%

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Design and Analysis of Novel Hybrid Multi-Objective Optimization Approach for Data-Driven Sustainable Delivery Systems

Resat

2020

IEEE Access

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This study presents a novel two-stage solution method designed for sustainable last-mile delivery systems in urban areas. A proposed hybrid solution methodology includes multi-criteria decision-making system to select the most efficient logistics providers by considering different performance indicators, and a mixed-integer linear optimization model for last-mile cargo distributions by drones within metropolitan areas. We present a multi-objective modeling approach by considering time windows for customer services and charging operations of drones and outline important characteristics of the mathematical programming problem to minimize transportation cost (in the meantime carbon dioxide emissions) and total sustainability score of the system by using epsilon constraint method to find out the Pareto frontiers. The main novelty of the proposed solution methodology is the inclusion of many performance indicators of last-mile delivery systems into multi-objective models for design of a sustainable city logistics. Additionally, the proposed model is applied to an illustrative case by using real-life data of one of the metropolitan in Turkey. The approach is shown as comparative analysis of proposed method with other two state-of-art solution methodologies for multi-objective problems, after defining some pre-processing, symmetry breaking steps, valid inequalities, and logic cuts. INDEX TERMS Discrete optimization, mixed-integer linear programming, vehicle routing problem.

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Section: Literature Reviewmentioning

confidence: 99%

“…Constraints (16) specify that the customer can be assigned to transfer point only if there is an arc connecting the transfer point and customer. Constraints 17- (20) are the variables domain.…”

Section: B Model Formulationmentioning

confidence: 99%

Design and Analysis of Novel Hybrid Multi-Objective Optimization Approach for Data-Driven Sustainable Delivery Systems

Resat

2020

IEEE Access

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“…There are a few papers for finding all ND points of MOILPs; for instance, Ehrgott (2006), Ozlen and Azizoglu (2009), Jorge (2009), Przybylski et al (2010), Lokman and Köksalan (2013), Mavrotas and Florios (2013), and Ozlen et al (2014) propose algorithms for solving MOILPs. A small number of studies exist in the literature with exact solution approach for finding the ND points of MOMILPs when the number of objective functions is greater than two (see Vincent et al (2013), Belotti et al (2013), Stidsen et al (2014), Boland et al (2015), Soylu and Yıldız (2016), and Fattahi and Turkay (2018) for solving bi-objective MILPs). We use the Generator of ND and Efficient Frontier (GoNDEF) method that ensures finding all or a large proportion of ND points for MOMILPs (Rasmi and Türkay, 2019).…”

Section: Finding Non-dominated Pointsmentioning

confidence: 99%

A multi-criteria decision analysis to include environmental, social, and cultural issues in the sustainable aggregate production plans

Rasmi

Kazan

Türkay

2019

Computers & Industrial Engineering

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Aggregate production planning (APP) that is an important concept of supply chain management (SCM), is one of the tools to determine production rates, inventory levels, and workforce requirements for fulfilling customer demands in a multi-period setting. Traditional APP models employ a single objective function to optimize monetary issues only. In this paper, we present a multiobjective APP model to analyze economic, social, environmental, and cultural pillars inclusively; moreover, each pillar includes several sub-pillars in the model. The resulting model includes an accurate representation of the problem with binary and continuous variables under sustainability considerations. We illustrate the effectiveness of the model in an appliance manufacturer and solve the problem using an exact solution method for multi-objective mixed-integer linear programs (MOMILP). We find a large number of the non-dominated (ND) points in the objective function space and analyze their trade-offs systematically. We show how this framework supports multiple criteria decision making process in the APP problems in the presence of sustainability considerations. Our approach provides a comprehensive analysis of the ND points of sustainable APP (SAPP) problems, and hence, the trade-offs of objective functions are insightful to the decision makers.

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“…However, fortunately, since a few algorithms have been recently developed for finding a full representation of the nondominated frontier of bi-objective mixed integer linear programs (see for instance Boland et al (2015b), Fattahi and Turkay (2018), Soylu and Yıldız (2016), and Vincent et al (2013)), generating an exact algorithm for optimizing a linear function over the efficient set of bi-objective mixed integer linear programs should now be possible.…”

Section: Introductionmentioning

confidence: 99%

A New Exact Algorithm to Optimize a Linear Function over the Set of Efficient Solutions for Biobjective Mixed Integer Linear Programs

Altamiranda

Charkhgard

2019

INFORMS Journal on Computing

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We present the first (criterion space search) algorithm for optimizing a linear function over the set of efficient solutions of bi-objective mixed integer linear programs. The proposed algorithm is developed based on the Triangle Splitting Method (Boland et al. 2015b) which can find a full representation of the nondominated frontier of any bi-objective mixed integer linear program. The proposed algorithm is easy to implement and converges quickly to an optimal solution. An extensive computational study shows the efficacy of the algorithm. We numerically show that the proposed algorithm can be used to quickly generate a provably high-quality approximate solution because it maintains a lower bound and an upper bound on the optimal value of the linear function at any point in time.

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A one direction search method to find the exact nondominated frontier of biobjective mixed-binary linear programming problems

Cited by 22 publications

References 12 publications

Design and Analysis of Novel Hybrid Multi-Objective Optimization Approach for Data-Driven Sustainable Delivery Systems

Design and Analysis of Novel Hybrid Multi-Objective Optimization Approach for Data-Driven Sustainable Delivery Systems

A multi-criteria decision analysis to include environmental, social, and cultural issues in the sustainable aggregate production plans

A New Exact Algorithm to Optimize a Linear Function over the Set of Efficient Solutions for Biobjective Mixed Integer Linear Programs

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