A survey of recent developments in multiobjective optimization

Chinchuluun, Altannar; Pardalos, Pãnos M.

doi:10.1007/s10479-007-0186-0

Cited by 278 publications

(104 citation statements)

References 73 publications

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“…It conveys trade-off information to a decision maker who prefers less to more in each objective. For an introduction to multi-objective optimization and surveys of recent developments we refer the reader to [6,8] and [5].…”

Section: Introductionmentioning

confidence: 99%

An approximation algorithm for convex multi-objective programming problems

Shao

Ehrgott

2010

J Glob Optim

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In multi-objective convex optimization it is necessary to compute an infinite set of nondominated points. We propose a method for approximating the nondominated set of a multi-objective nonlinear programming problem, where the objective functions and the feasible set are convex. This method is an extension of Benson's outer approximation algorithm for multi-objective linear programming problems. We prove that this method provides a set of weakly ε-nondominated points. For the case that the objectives and constraints are differentiable, we describe an efficient way to carry out the main step of the algorithm, the construction of a hyperplane separating an exterior point from the feasible set in objective space. We provide examples that show that this cannot always be done in the same way in the case of non-differentiable objectives or constraints.

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Section: Introductionmentioning

confidence: 99%

An approximation algorithm for convex multi-objective programming problems

Shao

Ehrgott

2010

J Glob Optim

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“…Typically, competing objectives like these arise in practice. In the presence of two competing objectives, problem (4.22) becomes a multi-objective problem of the form [8] min…”

Section: Handling Competing Objectivesmentioning

confidence: 99%

Real-Time Optimization Strategies for Building Systems

Zavala

2012

Ind. Eng. Chem. Res.

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We analyze different optimization strategies for real-time energy management in building systems. We have found that exploiting building-wide multivariable interactions between CO 2 , humidity, pressure, occupancy, and temperature leads to significant reductions of energy intensity. Our analysis indicates that it is possible to obtain energy savings of more than 50% compared with traditional control strategies. The exploitation of the thermal comfort zone has been found to be the most relevant factor driving energy savings. We discuss strategies to handle multiple competing objectives as well as economic functions and we analyze financial incentives provided by real-time prices and existing market designs. Numerical experiments are provided to support the claims.

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“…Multiobjective optimization, also known as multiobjective programming, vector optimization, multi-criteria optimization, multiattribute optimization or Pareto optimization, has a rich history, dating back to the emergence of rigorous mathematical programming [21]. Several books have been written on the topic [11,28,14], and many in-depth surveys [34,37,12,13,15].…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Optimization by Decision Diagrams

Bergman

Ciré

2016

Lecture Notes in Computer Science

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Always cite the published version, so the author(s) will receive recognition through services that track citation counts, e.g. Scopus. If you need to cite the page number of the author manuscript from TSpace because you cannot access the published version, then cite the TSpace version in addition to the published version using the permanent URI (handle) found on the record page.This article was made openly accessible by U of T Faculty. Please tell us how this access benefits you. Your story matters. Abstract. In this paper we present a technique for solving multiobjective discrete optimization problems using decision diagrams. The proposed methodology is related to an algorithm designed for multiobjective optimization for dynamic programming, except utilizing decision diagram theory to reduce the state space, which can lead to orders of magnitude performance gains over existing algorithms. The decision diagrambased technique is applied to knapsack, set covering, and set partitioning problems, exhibiting improvements over state-of-the-art general-purpose multiobjective optimization algorithms. Multiobjective Optimization by Decision Diagrams

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A survey of recent developments in multiobjective optimization

Cited by 278 publications

References 73 publications

An approximation algorithm for convex multi-objective programming problems

An approximation algorithm for convex multi-objective programming problems

Real-Time Optimization Strategies for Building Systems

Multiobjective Optimization by Decision Diagrams

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