A New Scalarization Technique and New Algorithms to Generate Pareto Fronts

Burachik, Regina S.; Kaya, C. Yalçın; Rizvi, M. M.

doi:10.1137/16m1083967

Cited by 42 publications

(43 citation statements)

References 20 publications

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“…Note that several points in L NDS correspond to the same network design: L NDS represents the union of 6 fronts, corresponding to 6 different network designs, i.e. sets of CNPs candidate valve locations candidate pipe locations Bragalli et al (2008). The original network model is available at http://www.or.deis.unibo.it/research_pages/ORinstances/ORinstances.htm selected for addition.…”

Section: Net25mentioning

confidence: 99%

“…The pescara model is a reduced version of the WDN of an Italian medium-size city, studied by Bragalli et al (2008). The original network model counts 71 junctions, 3 reservoirs, 99 pipes and is defined on a single time step.…”

Section: Pescaramentioning

confidence: 99%

“…Scalarization methods, including the method of -constraints, are known to be sensitive to the order of the objective functions (Logist and Van Impe 2012) and the choice of scalarization parameters (Kim and De Weck 2005;Burachik et al 2017). In the method we propose in Sect.…”

Section: Scalarization Approachmentioning

confidence: 99%

“…knees), while the normalized boundary intersection (NBI) method (Das and Dennis 1998) requires the non-dominated set to be simply connected (i.e. not composed of disconnected branches) to guarantee finding a Pareto optimal solution for all parametrized problems (Burachik et al 2017). Previous works have shown that these limitations could be successfully addressed by using adaptive choices of scalarization parameters (Kim and De Weck 2005) or grid generation techniques (Burachik et al 2017(Burachik et al , 2019, to focus on unexplored regions of the Pareto front and obtain representative approximations of non-dominated sets with irregular geometries.…”

Section: Note On the Choice Of Scalarization Parameters Jmentioning

confidence: 99%

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Bi-objective design-for-control of water distribution networks with global bounds

2021

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This manuscript investigates the design-for-control (DfC) problem of minimizing pressure induced leakage and maximizing resilience in existing water distribution networks. The problem consists in simultaneously selecting locations for the installation of new valves and/or pipes, and optimizing valve control settings. This results in a challenging optimization problem belonging to the class of non-convex bi-objective mixed-integer non-linear programs (BOMINLP). In this manuscript, we propose and investigate a method to approximate the non-dominated set of the DfC problem with guarantees of global non-dominance. The BOMINLP is first scalarized using the method of $$\epsilon $$ ϵ -constraints. Feasible solutions with global optimality bounds are then computed for the resulting sequence of single-objective mixed-integer non-linear programs, using a tailored spatial branch-and-bound (sBB) method. In particular, we propose an equivalent reformulation of the non-linear resilience objective function to enable the computation of global optimality bounds. We show that our approach returns a set of potentially non-dominated solutions along with guarantees of their non-dominance in the form of a superset of the true non-dominated set of the BOMINLP. Finally, we evaluate the method on two case study networks and show that the tailored sBB method outperforms state-of-the-art global optimization solvers.

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Section: Net25mentioning

confidence: 99%

Section: Pescaramentioning

confidence: 99%

Section: Scalarization Approachmentioning

confidence: 99%

Section: Note On the Choice Of Scalarization Parameters Jmentioning

confidence: 99%

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Bi-objective design-for-control of water distribution networks with global bounds

2021

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“…A classical technique to solve a multiobjective optimization problem is to convert the problem into a parameter-dependent single-objective one, known as scalarization. This approach was recently followed by Burachik et al [8] (see also the comment in the conclusions of [9]). The scalarized problems are then parameter-dependent single-objective mixed integer convex optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Solving Multiobjective Mixed Integer Convex Optimization Problems

Santis¹,

Eichfelder²,

Niebling³

et al. 2020

SIAM J. Optim.

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Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, but we built linear outer approximations of the image set in an adaptive way. We are able to guarantee correctness in terms of detecting both the efficient and the nondominated set of multiobjective mixed integer convex problems according to a prescribed precision. As far as we know, the procedure we present is the first deterministic algorithm devised to handle this class of problems. Our numerical experiments show results on biobjective and triobjective mixed integer convex instances.

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Multi-objective branch-and-bound for the design-for-control of water distribution networks with global bounds

Ulusoy,

Stoianov

2024

Struct Multidisc Optim

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This study investigates a design-for-control (DfC) problem formulation for the joint minimization of pressure-induced leakage, maximization of resilience, and minimization of cost in water distribution networks (WDN). The DfC problem, which consists in simultaneously installing new valves and/or pipes and optimizing valve control settings, results in a challenging optimization problem belonging to the class of non-convex multi-objective mixed-integer non-linear programs (MOMINLP). Due to their complex mathematical structure, multi-objective WDN design-for-control problems have previously been solved using general-purpose evolutionary algorithms or local deterministic methods, which do not provide guarantees on the quality of the returned solutions. While branch-and-bound (BB) frameworks have been proposed to approximate the Pareto fronts of MOMINLPs with global bounds, they rely on the availability of attainable solutions which, for WDN design-for-control problems, can be hard to identify. Moreover, in the absence of general-purpose solvers, the performance of multi-objective BB implementations depends, for a given application, on the choice of adequate branching and lower bounding strategies. In this study, we investigate a multi-objective BB algorithm based on tailored branching, lower bounding and additional upper bounding strategies to efficiently approximate the Pareto front of WDN design-for-control problems with bounds of $$\epsilon$$ ϵ -non-dominance. The proposed algorithm is applied to the optimal DfC of two case study networks and is shown to outperform alternative solution methods.

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A New Scalarization Technique and New Algorithms to Generate Pareto Fronts

Cited by 42 publications

References 20 publications

Bi-objective design-for-control of water distribution networks with global bounds

Bi-objective design-for-control of water distribution networks with global bounds

Solving Multiobjective Mixed Integer Convex Optimization Problems

Multi-objective branch-and-bound for the design-for-control of water distribution networks with global bounds

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