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Methodology
Published in Tolga Bektaş, Freight Transport and Distribution, 2017
Matheuristics are hybrid methods that combine mathematical programming, or in general optimisation methods, with heuristic algorithms. The aim is to take advantage of the power and capabilities of both classes of methods. Hybridisation can be done in at least two ways, as described here: Embed mathematical programming within a heuristic or a metaheuristic algorithm, in which one or several optimisation problems are solved optimally. This might be the case, for example, when integrated problems are solved by using a heuristic, but where each individual and smaller problem forming the integrated problem is solved optimally.Use heuristics within the framework of an exact algorithm, in which smaller or subproblems can be solved using a heuristic algorithm. One example to this approach would be to solve the subproblems arising in Benders decomposition or Lagrangean relaxation by using a heuristic or metaheuristic algorithm. A benefit of this approach would be a speed-up in the running time of the algorithm, but this would be at the expense of loss of optimality, or a guarantee thereof. In other words, the bounds provided by such an algorithm would not necessarily be valid.
A multi-start route improving matheuristic for the production routeing problem
Published in International Journal of Production Research, 2023
Simen T. Vadseth, Henrik Andersson, Magnus Stålhane, Masoud Chitsaz
As a result, the complexity of the problem has motivated the study of heuristic solution methods for the PRP. Several heuristics have been developed and they include a memetic algorithm by Boudia and Prins (2009), tabu search heuristics by Bard and Nananukul (2009) and Armentano, Shiguemoto, and Løkketangen (2011), an adaptive large neighbourhood search heuristic by Adulyasak, Cordeau, and Jans (2014b) and a variable neighbourhood search heuristic by Qiu et al. (2018). However, the advancement of CPUs and mixed integer linear programming (MILP) solvers in the last few decades have led to the success of heuristics that integrate mathematical programming techniques into a heuristic framework. These heuristics are often referred to as matheuristics (Boschetti et al. 2009). The survey of Archetti and Speranza (2014) highlights the contributions of matheuristics to routeing problems and their success in solving problems that combine routeing with other activities, such as production and/or inventory control.
Integrated approaches for logistics network planning: a systematic literature review
Published in International Journal of Production Research, 2022
Aura Maria Jalal, Eli Angela Vitor Toso, Reinaldo Morabito
The methods used to solve the integrated LNP optimisation models can be classified into exact and non-exact methods. Exact solution methods include techniques able to find optimal solutions: Benders decomposition (BD) (Benders 1962), column generation (Savelsbergh 2008), branch-and-cut (B&C), branch-and-price (B&P), and decomposition methods with exact solutions. Non-exact solution methods include heuristics and meta-heuristics. Taking into account that the integration of decisions suggests addressing problems simultaneously, an idea for solving the models is the decomposition of the integrated problem into subproblems that are easier to solve with exact or heuristic methods, for instance, Benders decomposition based heuristics. Some heuristic methods explore features of mathematical programming with exact, heuristics, and meta-heuristics methods, called matheuristics. Table 8 presents the solution methods used in the articles of the sample.
Robust single allocation p-hub median problem under hose and hybrid demand uncertainties: models and algorithms
Published in International Journal of Management Science and Engineering Management, 2020
Nader Ghaffarinasab, Abdullah Zare Andaryan, Ali Ebadi Torkayesh
Matheuristics are hybrid algorithms combining mathematical programming techniques with metaheuristic solution approaches (Maniezzo, Stützle, & Voß, 2009) In the context of the combinatorial optimization problems, matheuristic algorithms are getting more attention with respect to the frequency of their usage in the literature due to their successful implementation and appropriateness to many combinatorial optimization problems. Within the field of facility location, some papers have been published on the successful application of matheuristics (Ghaffarinasab, 2018; Lüer-Villagra et al., 2019; Sender, Siwczyk, Mutzel, & Clausen, 2017; Stefanello, de Araujo, & Müller, 2015). Overviews on combinations of metaheuristics with mathematical programming techniques are given by Maniezzo et al. (2009) and Archetti and Speranza (2014).