Continuous Multiobjective Programming

Wiecek, Margaret M.; Ehrgott, Matthias; Engau, Alexander

doi:10.1007/978-1-4939-3094-4_18

Cited by 28 publications

(18 citation statements)

References 345 publications

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“…In terms of exact solution methods, there are a number of algorithms for multi-objective linear programs (MOLP) that are basically designed based on multi-criteria simplex method (Wiecek et al, 2016;Yu and Zeleny, 1975). When we study multi-objective integer linear programs (MOILP), the feasible region is not convex as of MOLPs, and hence, these problems are highly complex.…”

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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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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“…Set-oriented methods attempt to capture the entire efficient set and iterate on sets instead of points. We refer the reader to Wiecek et al (2016) for more information on both scalarization and nonscalarization methods.…”

Section: Literature On Deterministic Multiobjectivementioning

confidence: 99%

“…Since the MOO literature is vast, we also refer the reader to Chankong and Haimes (1983), Ehrgott (2005), , Ehrgott and Wiecek (2005), Eichfelder (2008), Miettinen (1999), and Wiecek et al (2016) for theory and solution methods, and to Chinchuluun and Pardalos (2007), Marler and Arora (2004), and White (1990) for additional MOO overviews and applications.…”

Section: Literature On Deterministic Multiobjectivementioning

confidence: 99%

An Introduction to Multiobjective Simulation Optimization

Hunter

Applegate

Arora

et al. 2019

ACM Trans. Model. Comput. Simul.

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The multiobjective simulation optimization (MOSO) problem is a nonlinear multiobjective optimization problem in which multiple simultaneous and conflicting objective functions can only be observed with stochastic error. We provide an introduction to MOSO at the advanced tutorial level, aimed at researchers and practitioners who wish to begin working in this emerging area. Our focus is exclusively on MOSO methods that characterize the entire efficient or Pareto-optimal set as the solution to the MOSO problem; later, this set may be used as input to the broader multicriteria decision-making process. Our introduction to MOSO includes an overview of existing theory, methods, and provably convergent algorithms that explicitly control sampling error for (1) MOSO on finite sets, called multiobjective ranking and selection; (2) MOSO with integer-ordered decision variables; and (3) MOSO with continuous decision variables. In the context of integer-ordered and continuous decision variables, we focus on methods that provably converge to a local efficient set under the natural ordering. We also discuss key open questions that remain in this emerging field.

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“…The goal of MOLP is to find all (weakly) nondominated points of

scriptY

and for each

η \in Y_{false(w false) N}

one

𝛏 \in X_{false(w false) E}

such that C ξ = η . There are several methods in the MOLP literature that compute nondominated points and efficient solutions of an MOLP problem, see Wiecek, Ehrgott, and Engau () and references therein. Benson's outer approximation algorithm (Benson, ) is a procedure that finds all (weakly) nondominated points of the feasible set

scriptY

in the objective space of an MOLP.…”

Section: Preliminariesmentioning

confidence: 99%

A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis

Ehrgott

Hasannasab

Raith

2019

Multi Criteria Decision Anal

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Data envelopment analysis is a linear programming‐based operations research technique for performance measurement of decision‐making units. In this paper, we investigate data envelopment analysis from a multiobjective point of view to compute both the efficient extreme points and the efficient facets of the technology set simultaneously. We introduce a dual multiobjective linear programming formulation of data envelopment analysis in terms of input and output prices and propose a procedure based on objective space algorithms for multiobjective linear programmes to compute the efficient frontier. We show that using our algorithm, the efficient extreme points and facets of the technology set can be computed without solving any optimization problems. We conduct computational experiments to demonstrate that the algorithm can compute the efficient frontier within seconds to a few minutes of computation time for real‐world data envelopment analysis instances. For large‐scale artificial data sets, our algorithm is faster than computing the efficiency scores of all decision‐making units via linear programming.

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Continuous Multiobjective Programming

Cited by 28 publications

References 345 publications

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

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

An Introduction to Multiobjective Simulation Optimization

A multiobjective optimization approach to compute the efficient frontier in data envelopment analysis

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