Mixed Integer Linear Programming Models to Solve a Real-Life Vehicle Routing Problem with Pickup and Delivery

Remarkable advancements have been achieved in machine learning and computer vision through the utilization of deep neural networks. Among the most advantageous of these networks is the convolutional neural network (CNN). It has been used in pattern recognition, medical diagnosis, and signal processing, among other things. Actually, for these networks, the challenge of choosing hyperparameters is of utmost importance. The reason behind this is that as the number of layers rises, the search space grows exponentially. In addition, all known classical and evolutionary pruning algorithms require a trained or built architecture as input. During the design phase, none of them consider the process of pruning. In order to assess the effectiveness and efficiency of any architecture created, pruning of channels must be carried out before transmitting the dataset and computing classification errors. For instance, following pruning, an architecture of medium quality in terms of classification may transform into an architecture that is both highly light and accurate, and vice versa. There exist countless potential scenarios that could occur, which prompted us to develop a bi-level optimization approach for the entire process. The upper level involves generating the architecture while the lower level optimizes channel pruning. Evolutionary algorithms (EAs) have proven effective in bi-level optimization, leading us to adopt the co-evolutionary migration-based algorithm as a search engine for our bi-level architectural optimization problem in this research. Our proposed method, CNN-D-P (bi-level CNN design and pruning), was tested on the widely used image classification benchmark datasets, CIFAR-10, CIFAR-100 and ImageNet. Our suggested technique is validated by means of a set of comparison tests with regard to relevant state-of-the-art architectures.

show abstract

“…Fig. 3 An example of a BLOP with two levels is illustrated [43] variables x u act as parameters (as shown in Fig. 3).…”

Section: Definitionmentioning

confidence: 99%

Embedding channel pruning within the CNN architecture design using a bi-level evolutionary approach

Louati

Bechikh

et al. 2023

J Supercomput

Self Cite

View full text Add to dashboard Cite

show abstract

“…The formal definition of BLOP is provided below: Single-level problems are intrinsically more complex to solve than BLOPs. It is not unexpected that the majority of previous research has focused on the more straightforward situations of BLOP, such as problems with good features like linear objectives, constraint functions, convexity or quadraticity [ 77 ]. Despite the fact that it was the first study on bi-level optimization originates from the 1970s, the utility of these mathematical programs in representing hierarchical decision-making engineering and processes challenges were not realized until the early 1980s.…”

Section: Appendix a Manually Designed Cnn Architectures Used For Comp...mentioning

confidence: 99%

Joint design and compression of convolutional neural networks as a Bi-level optimization problem

Louati

Bechikh

Louati

et al. 2022

Neural Comput & Applic

Self Cite

View full text Add to dashboard Cite

Over the last decade, deep neural networks have shown great success in the fields of machine learning and computer vision. Currently, the CNN (convolutional neural network) is one of the most successful networks, having been applied in a wide variety of application domains, including pattern recognition, medical diagnosis and signal processing. Despite CNNs’ impressive performance, their architectural design remains a significant challenge for researchers and practitioners. The problem of selecting hyperparameters is extremely important for these networks. The reason for this is that the search space grows exponentially in size as the number of layers increases. In fact, all existing classical and evolutionary pruning methods take as input an already pre-trained or designed architecture. None of them take pruning into account during the design process. However, to evaluate the quality and possible compactness of any generated architecture, filter pruning should be applied before the communication with the data set to compute the classification error. For instance, a medium-quality architecture in terms of classification could become a very light and accurate architecture after pruning, and vice versa. Many cases are possible, and the number of possibilities is huge. This motivated us to frame the whole process as a bi-level optimization problem where: (1) architecture generation is done at the upper level (with minimum NB and NNB) while (2) its filter pruning optimization is done at the lower level. Motivated by evolutionary algorithms’ (EAs) success in bi-level optimization, we use the newly suggested co-evolutionary migration-based algorithm (CEMBA) as a search engine in this research to address our bi-level architectural optimization problem. The performance of our suggested technique, called Bi-CNN-D-C (Bi-level convolution neural network design and compression), is evaluated using the widely used benchmark data sets for image classification, called CIFAR-10, CIFAR-100 and ImageNet. Our proposed approach is validated by means of a set of comparative experiments with respect to relevant state-of-the-art architectures.

show abstract

“…This formulation has applications in numerous fields, such as transportation, retail, manufacturing and management [2,3]. For example, last-mile delivery companies repeatedly solve the vehicle routing problem as daily delivery tasks (stops and routes) change, with the goal of minimizing total delivery costs [4]. Similarly, crew scheduling problems have to be solved daily or weekly in the aviation industry, where the MILP formulation is the most practical notation for expressing such problems [5].…”

Section: Introductionmentioning

confidence: 99%

Automatic MILP solver configuration by learning problem similarities

Hosny

Reda

2023

Ann Oper Res

View full text Add to dashboard Cite

A large number of real-world optimization problems can be formulated as Mixed Integer Linear Programs (MILP). MILP solvers expose numerous configuration parameters to control their internal algorithms. Solutions, and their associated costs or runtimes, are significantly affected by the choice of the configuration parameters, even when problem instances have the same number of decision variables and constraints. On one hand, using the default solver configuration leads to suboptimal solutions. On the other hand, searching and evaluating a large number of configurations for every problem instance is time-consuming and, in some cases, infeasible. In this study, we aim to predict configuration parameters for unseen problem instances that yield lower-cost solutions without the time overhead of searching-and-evaluating configurations at the solving time. Toward that goal, we first investigate the cost correlation of MILP problem instances that come from the same distribution when solved using different configurations. We show that instances that have similar costs using one solver configuration also have similar costs using another solver configuration in the same runtime environment. After that, we present a methodology based on Deep Metric Learning to learn MILP similarities that correlate with their final solutions' costs. At inference time, given a new problem instance, it is first projected into the learned metric space using the trained model, and configuration parameters are instantly predicted using previously-explored configurations from the nearest neighbor instance in the learned embedding space. Empirical results on real-world problem

show abstract

Mixed Integer Linear Programming Models to Solve a Real-Life Vehicle Routing Problem with Pickup and Delivery

Cited by 18 publications

References 29 publications

Embedding channel pruning within the CNN architecture design using a bi-level evolutionary approach

Embedding channel pruning within the CNN architecture design using a bi-level evolutionary approach

Joint design and compression of convolutional neural networks as a Bi-level optimization problem

Automatic MILP solver configuration by learning problem similarities

Contact Info

Product

Resources

About