Primal and dual algorithms for optimization over the efficient set

Liu, Zhengliang; Ehrgott, Matthias

doi:10.1080/02331934.2018.1484922

Cited by 15 publications

(6 citation statements)

References 26 publications

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“…Motivated by these drawbacks, minimization of an additional (single) objective function over the Pareto front has been of great interest to many researchers over the past decades-see, for example, [2,3,5,6,14,15,25,26,31,41,47]. Despite this rich collection of works, to the knowledge of the authors, it was not before the reference [7] that optimization over the Pareto front was studied and a numerical method proposed for convex multi-objective optimal control problems.…”

Section: Introductionmentioning

confidence: 99%

Optimization Over the Pareto Front of Nonconvex Multi-objective Optimal Control Problems

Kaya¹,

Maurer²

2023

Preprint

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Simultaneous optimization of multiple objective functions results in a set of trade-off, or Pareto, solutions. Choosing a, in some sense, best solution in this set is in general a challenging task: In the case of three or more objectives the Pareto front is usually difficult to view, if not impossible, and even in the case of just two objectives constructing the whole Pareto front so as to visually inspect it might be very costly. Therefore, optimization over the Pareto (or efficient) set has been an active area of research. Although there is a wealth of literature involving finite dimensional optimization problems in this area, there is a lack of problem formulation and numerical methods for optimal control problems, except for the convex case. In this paper, we formulate the problem of optimizing over the Pareto front of nonconvex constrained and time-delayed optimal control problems as a bi-level optimization problem. Motivated by existing solution differentiability results, we propose an algorithm incorporating (i) the Chebyshev scalarization, (ii) a concept of the essential interval of weights, and (iii) the simple but effective bisection method, for optimal control problems with two objectives. We illustrate the working of the algorithm on two example problems involving an electric circuit and treatment of tuberculosis and discuss future lines of research for new computational methods.

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Section: Introductionmentioning

confidence: 99%

Optimization Over the Pareto Front of Nonconvex Multi-objective Optimal Control Problems

Kaya¹,

Maurer²

2023

Preprint

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“…The methods described in these works are typically tailored to the structure of the underlying multi‐objective problem from which the Pareto set is generated. For instance, authors have considered optimization over the Pareto set of solutions arising from multi‐objective linear programs (Belkhiri et al, 2021; Yamamoto, 2002), multi‐objective integer linear programs (Boland et al, 2017; Cherfaoui & Moulaï, 2021; Jorge, 2009), multi‐objective integer linear fractional programs (Chaiblaine & Moulaı̈, 2022; Moulaï & Mekhilef, 2021), and multi‐objective nonlinear programs (An et al, 1996; Benson, 1984; Horst & Thoai, 1997; Liu & Ehrgott, 2018; Thoai, 2000). In contrast, the holistic fleet optimization problem requires the selection of a Pareto optimal system design that can best be incorporated into a complex fleet‐level modernization plan.…”

Section: Introductionmentioning

confidence: 99%

Holistic fleet optimization incorporating system design considerations

Henry

Hoffman

Waddell

et al. 2023

Naval Research Logistics

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The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real‐world system design optimization and fleet‐level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. This means that fleet‐level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio‐level considerations. In reality, these two problems are highly interconnected. To properly address this system‐fleet design interdependence, we present a general method for efficiently incorporating multi‐objective system design trade‐off information into a mixed‐integer linear programming (MILP) fleet‐level optimization. This work is motivated by the authors' experience with large‐scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet‐level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet‐level MILP.

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“…Later on, several algorithmic ideas were developed to solve multicriteria optimization problems with continuous decision variables. These techniques are grouped into three categories: adjacent vertex search methods (see, for instance, Ecker and Song, 1994;Fülöp, 1994;Liu and Ehrgott, 2018), nonadjacent methods (see Benson, 1992;Dauer and Fosnaugh, 1995;White, 1996;Sayin, 2000;Jorge, 2005) and dual approach (see Thach et al, 1996;Liu and Ehrgott, 2018). An overview of these methods can be found in Yamamoto (2002).…”

Section: Introductionmentioning

confidence: 99%

Parallel optimization over the integer efficient set

Younes

Sarah

Chaabane

2022

Int Trans Operational Res

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This paper introduces a modified sequential version method for optimizing a linear function over an integer efficient set, as well as a new exact parallel algorithm. The performance of parallel programming in this context is clear and shown through different instances with different sizes. Each procedure builds a finite monotonous sequence of values for the main criterion to be optimized, in a reasonable amount of CPU execution time. This latter remains much better. For the first time, the Algerian IBNBADIS cluster—CERIST—was used with this type of problem. Significant results are obtained by both proposed techniques, particularly with the parallel one.

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Primal and dual algorithms for optimization over the efficient set

Cited by 15 publications

References 26 publications

Optimization Over the Pareto Front of Nonconvex Multi-objective Optimal Control Problems

Optimization Over the Pareto Front of Nonconvex Multi-objective Optimal Control Problems

Holistic fleet optimization incorporating system design considerations

Parallel optimization over the integer efficient set

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