Heuristics in Mixed Integer Programming

Fischetti, Matteo; Lodi, Andrea

doi:10.1002/9780470400531.eorms0376

Cited by 44 publications

(18 citation statements)

References 22 publications

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“…Being based on mixed-integer linear programming renders the simultaneous epitope selection and assembly problem of string-of-beads vaccines NP-hard. In most cases, this does not prevent the solver to find a solution in a reasonable time, in part because of the many heuristics (Fischetti and Lodi, 2011;Bixby et al, 2000;Berthold, 2006) that can be employed. Though, certain constraint configurations can make the solving process slower.…”

Section: Discussionmentioning

confidence: 99%

Joint epitope selection and spacer design for string-of-beads vaccines

Dorigatti

Schubert

2020

Preprint

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Motivation: Conceptually, epitope-based vaccine design poses two distinct problems: (1) selecting the best epitopes eliciting the strongest possible immune response, and (2) arranging and linking the selected epitopes through short spacer sequences to string-of-beads vaccines so as to increase the recovery likelihood of each epitope during antigen processing. Current state-of-the-art approaches solve this design problem sequentially. Consequently, such approaches are unable to capture the inter-dependencies between the two design steps, usually emphasizing theoretical immunogenicity over correct vaccine processing and resulting in vaccines with less effective immunogencity. Results: In this work, we present a computational approach based on linear programming that solves both design steps simultaneously, allowing to weigh the selection of a set of epitopes that have great immunogenic potential against their assembly into a string-of-beads construct that provides a high chance of recovery. We conducted Monte-Carlo cleavage simulations to show that, indeed, a fixed set of epitopes often cannot be assembled adequately, whereas selecting epitopes to accommodate proper cleavage requirements substantially improves their recovery probability and thus the effective immunogenicity, pathogen, and population coverage of the resulting vaccines by at least two fold. Availability: The software and the data analyzed are available at https://github.com/SchubertLab/JessEV

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Section: Discussionmentioning

confidence: 99%

Joint epitope selection and spacer design for string-of-beads vaccines

Dorigatti

Schubert

2020

Preprint

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“…Large neighborhood search (LNS) heuristics are an important component of modern MIP solvers, see, e.g., [6,8,18,26]. The main idea of LNS is to restrict the search for "good" solutions to a neighborhood centered at a particular reference point-typically the incumbent or another feasible solution.…”

Section: Large Neighborhood Search For Mipmentioning

confidence: 99%

“…There are different common approaches applied by many heuristics, e.g., rounding of the LP solution or diving, which iteratively changes the current subproblem temporarily and solves the corresponding LP relaxation until an integral solution is obtained. For more details on primal heuristics, we refer to [6,8,18]. In this paper, we introduce two novel heuristics based on the large neighborhood search (LNS) paradigm.…”

Section: Introductionmentioning

confidence: 99%

Structure-Based Primal Heuristics for Mixed Integer Programming

Gamrath

Berthold

Stefan

et al. 2015

Optimization in the Real World

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Primal heuristics play an important role in the solving of mixed integer programs (MIPs). They help to reach optimality faster and provide good feasible solutions early in the solving process. In this paper, we present two new primal heuristics which take into account global structures available within MIP solvers to construct feasible solutions at the beginning of the solving process. These heuristics follow a large neighborhood search (LNS) approach and use global structures to define a neighborhood that is with high probability significantly easier to process while (hopefully) still containing good feasible solutions. The definition of the neighborhood is done by iteratively fixing variables and propagating these fixings. Thereby, fixings are determined based on the predicted impact they have on the subsequent domain propagation. The neighborhood is solved as a sub-MIP and solutions are transferred back to the original problem. Our computational experiments on standard MIP test sets show that the proposed heuristics find solutions for about every third instance and therewith help to improve the average solving time.

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“…A major goal is developing general purpose solvers selecting the most appropriate solution method for each concrete MILP instance. Heuristics are an essential tool in MILP solving (Berthold, 2014;Fischetti and Lodi, 2010;Schulz et al, 1997;Williamson and Shmoys, 2011). Performance guarantees, which arise from the theory of approximation algorithms, evaluate and classify the computational performance of heuristics.…”

Section: Problem Classificationmentioning

confidence: 99%

Approximation algorithms for process systems engineering

Letsios

Baltean-Lugojan

Ceccon

et al. 2020

Computers & Chemical Engineering

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Designing and analyzing algorithms with provable performance guarantees enables efficient optimization problem solving in different application domains, e.g. communication networks, transportation, economics, and manufacturing. Despite the significant contributions of approximation algorithms in engineering, only limited and isolated works contribute from this perspective in process systems engineering. The current paper discusses three representative, N P-hard problems in process systems engineering: (i) pooling, (ii) process scheduling, and (iii) heat exchanger network synthesis. We survey relevant results and raise major open questions. Further, we present approximation algorithms applications which are relevant to process systems engineering: (i) better mathematical modeling, (ii) problem classification, (iii) designing solution methods, and (iv) dealing with uncertainty. This paper aims to motivate further research at the intersection of approximation algorithms and process systems engineering.

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Heuristics in Mixed Integer Programming

Cited by 44 publications

References 22 publications

Joint epitope selection and spacer design for string-of-beads vaccines

Joint epitope selection and spacer design for string-of-beads vaccines

Structure-Based Primal Heuristics for Mixed Integer Programming

Approximation algorithms for process systems engineering

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