Decomposition Techniques for Hybrid MILP/CP Models applied to Scheduling and Routing Problems

Castro, Pedro M.; Grossmann, Ignacio E.; Rousseau, Louis-Martin

doi:10.1007/978-1-4419-1644-0_4

Cited by 4 publications

(3 citation statements)

References 66 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Interested readers can consult the survey by Gualandi and Malucelli (2013) or the book chapter by Castro, Grossmann and Rousseau (2011) for further details.…”

Section: Constraint-based Column Generationmentioning

confidence: 99%

Hybrid optimization of vehicle routing problems

Lam

2023

Constraints

View full text Add to dashboard Cite

Vehicle routing problems are combinatorial optimization problems that aspire to design vehicle routes that minimize some measure of cost, such as the total distance traveled or the time at which the last vehicle returns to a depot, while adhering to various restrictions. Vehicle routing problems are of profound interest in both academia and industry because they are opportunities to study graph structures and algorithms, and because they underpin practical applications in a multitude of industries, but notably, the transportation and logistics industries. This dissertation presents two applications relevant to industry and develops a fully hybrid method for solving a classical vehicle routing problem.The first application combines vehicle routing with crew scheduling. In industry, vehicle routing and crew scheduling are usually performed in stages due to the large search space of integrated models. The first stage finds minimal-cost vehicle routes with little consideration to crew constraints and objectives. The second stage schedules crews on the routes from the first stage. Disregarding crew constraints in the first stage can lead to suboptimality or even infeasibility of the overall problem in the second stage. To quantify the suboptimality of staged optimization models, two formulations of the integrated problem are developed. The first is an ordinary mixed integer programming model, and the second is a constraint programming model containing a linear relaxation global constraint that performs cost-based filtering. The two integrated models are solved using a branch-and-bound search and a highly specialized large neighborhood search. The large neighborhood search exploits the substructures linking the vehicle routing and crew scheduling elements of the problem, and when executed on the constraint programming model, is shown to perform significantly better than the other approaches.The second application introduces a number of scheduling constraints to the Vehicle Routing Problem with Pickup and Delivery and Time Windows. The scheduling constraints arise from a lack of loading bays or equipment that unloads and loads incoming vehicles. These constraints limit the number of vehicles present or in service at any particular site by requiring the arrival of vehicles to be scheduled around the availabilities of a scarce resource. A mixed integer programming model, a constraint programming model and a sequential model are implemented for the problem but are shown to be inferior to a branch-and-price-and-check model, which hybridizes column generation and constraint programming with nogood learning. This thesis concludes with a hybrid method, named Branch-and-Check with Explanations, that unifies linear programming, constraint programming and Boolean satisfiability. The method iii begins with a linear programming model that omits several critical constraints. The solver uses the linear programming model to find objective bounds and candidate solutions, which are checked by a constraint programming model for feasibili...

show abstract

“…Interested readers can consult the survey by Gualandi and Malucelli (2013) or the book chapter by Castro, Grossmann and Rousseau (2011) for further details.…”

Section: Constraint-based Column Generationmentioning

confidence: 99%

Hybrid optimization of vehicle routing problems

Lam

2023

Constraints

View full text Add to dashboard Cite

show abstract

“…Branch-and-cut, decomposition, constraint programming, metaheuristic, hybrid approaches, and satisfiability modulo theories are also explored (Castro et al, 2011;Kopanos et al, 2009;Maravelias and Grossmann, 2004;Mistry et al, 2018;Till et al, 2007;Velez and Maravelias, 2013a;Wu and Ierapetritou, 2003). Recently, generalized-disjunctive programming has emerged as a novel framework for effectively solving process scheduling problems using big-M and convex hull reformulations (Castro and Grossmann, 2012).…”

Section: Brief Literature Overviewmentioning

confidence: 99%

Approximation algorithms for process systems engineering

Letsios

Baltean-Lugojan

Ceccon

et al. 2020

Computers & Chemical Engineering

View full text Add to dashboard Cite

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.

show abstract

“…Column generation and their extensions, such as branch-and-price, branch-andcut-and-price, and hybrid and metaheuristics column generation-based methods, have been widely and successfully used for solving large-scale vehicle routing problems, airline crew scheduling problems, machine scheduling, cutting and packing problems, generalized assignment problems, employee timetabling, and many others, see Desaulniers et al (2005), Silva and Wood (2006), Castro et al (2010), Archetti and Speranza (2014), Raidl (2015), and Costa et al (2019). In agricultural planning, Sigurd et al (2004) and Oppen et al (2010) solved a rich vehicle routing problem for the transportation of live animals that must be visited in a given sequence through column generation.…”

Section: Column Generationmentioning

confidence: 99%

Decomposition-based heuristic for the zoning and crop planning problem with adjacency constraints

Albornoz

Zamora

2020

TOP

View full text Add to dashboard Cite

This paper tackles management zone delineation and crop planning problems in an integrated precision agriculture framework. The zoning problem defines relatively homogeneous management zones regarding their soil properties, and for which specific rates of agricultural inputs are necessary. From a sustainable point of view, the crop planning problem considers cropping of species from different botanic families in adjacent zones at the same time. With this in mind, we propose a novel linear binary integer program for an integrated zoning and crop planning problem with adjacency constraints. In this model, we maximize the incomes of the crop plan subject to zoning constraints and adjacency constraints on crop families. The proposed model has a column-based formulation, and as such, we develop a decompositionbased heuristic which make use of the column generation method with columndependent rows. The decomposition strategy involves a master problem that deals with ensuring homogeneity of the selected management zones within the field partition and ensuring that the crop plan meets adjacency policies. On the other hand, the pricing problem generates rectangular management zones whose incorporation improves the objective value of the master problem. The algorithm is implemented in JuMP, a modeling language for mathematical optimization embedded in Julia. Results from a set of instances show the relevance of the decomposition-based heuristic.

show abstract

Decomposition Techniques for Hybrid MILP/CP Models applied to Scheduling and Routing Problems

Cited by 4 publications

References 66 publications

Hybrid optimization of vehicle routing problems

Hybrid optimization of vehicle routing problems

Approximation algorithms for process systems engineering

Decomposition-based heuristic for the zoning and crop planning problem with adjacency constraints

Contact Info

Product

Resources

About