An Analogy between Bin Packing Problem and Permutation Problem: A New Encoding Scheme

Part 2: Knowledge Discovery and SharingInternational audienceThe bin packing problem aims to pack a set of items in a minimum number of bins, with respect to the size of the items and capacity of the bins. This is an NP-hard problem. Several approach methods have been developed to solve this problem. In this paper, we propose a new encoding scheme which is used in a hybrid resolution: a metaheuristic is matched with a list algorithm (Next Fit, First Fit, Best Fit) to solve the bin packing problem. Any metaheuristic can be used but in this paper, our proposition is implemented on a single solution based metaheuristic (stochastic descent, simulated annealing, kangaroo algorithm). This hybrid method is tested on literature instances to ensure its good results

Machine Learning for Variable Cost and Size Bin Packing Problem

Nowadays, third-party logistics is an essential component of efficient delivery, enabling companies to purchase carrier services instead of keeping an expensive fleet of vehicles. However, the contracts with the carriers usually have to be booked beforehand when the delivery demand is unknown. This led to the managerial task of choosing an appropriate set of bins (fleet contracts) under uncertainty. Such a decision problem is defined as the Variable Cost and Size Bin Packing Problem with Stochastic Items [1]. It consists of packing the set of items (goods) with uncertain volumes and quantity into containers (bins) of different fixed costs and capacities. Since this problem cannot be solved for large realistic instances by means of exact solvers, this paper introduces a Machine Learning heuristic to approximate the first stage decision variables. Several numerical experiments are outlined to show the effectiveness of the proposed approach to deal with realistic instances of up to 3000 items. Moreover, different classification approaches are compared to gain insight into heuristic performance to deal with the outlined problem. [1] Crainic, T. G., Gobbato, L., Perboli, G., Rei, W., Watson, J. P., & Woodruff, D. L. (2014). Bin packing problems with uncertainty on item characteristics: An application to capacity planning in logistics. Procedia-Social and Behavioral Sciences, 111, 654-66

Machine Learning heuristic for Variable Cost and Size Bin Packing Problem with Stochastic Items

Third-party logistics becomes an essential component of efficient delivery, enabling companies to rent transportation services instead of keeping an expensive fleet of vehicles. However, the contracts with the carriers usually have to be booked beforehand when the delivery demand is unknown. This decision process is strongly affected by uncertainty, provided with a long (tactical) planning horizon, and can be expressed as choosing an appropriate set of bins (fleet contracts). Formally, it can be modeled as the Variable Cost and Size Bin Packing Problem with Stochastic Items [1]. It consists of packing the set of items (goods) with uncertain volumes and quantities into containers (bins) of different fixed costs and capacities. This problem is described via a two-stage stochastic programming approach, where the cost of the bins of the second stage is significantly higher. Since it cannot be solved for large realistic instances by means of exact solvers for a reasonable time and memory consumption, this paper introduces a Machine Learning heuristic to approximate the first stage decision variables. Several numerical experiments are outlined to show the effectiveness of the proposed approach to deal with realistic instances of up to 3000 items. Further, the proposed heuristic is compared to the recent Progressive Hedging-based heuristic and showed a significant computational time reduction. Finally, different classification approaches are compared, and the feature selection process is explained to gain insight into heuristic performance to deal with the outlined problem. [1] Crainic, T. G., Gobbato, L., Perboli, G., Rei, W., Watson, J. P., & Woodruff, D. L. (2014). Bin packing problems with uncertainty on item characteristics: An application to capacity planning in logistics. ProcediaSocial and Behavioral Sciences, 111, 654-662

Diffusion Limits in the Online Subsequence Selection Problems

In the stochastic sequential optimisation problems it is of interest to study features of strategies more delicate than just their performance measure. In this talk we focus on variations of the online monotone subsequence and bin packing problems, where it is possible to give a fairly explicit asymptotic description of the selection processes under strategies that are sufficiently close to optimality. We show that the transversal fluctuations of the shape and the length of selected subsequence approach Gaussian functional limits that are very different from their counterparts in the offline problem, where the full set of data can be used in selection algorithms

SLO-aware Colocation of Data Center Tasks Based on Instantaneous Processor Requirements

In a cloud data center, a single physical machine simultaneously executes dozens of highly heterogeneous tasks. Such colocation results in more efficient utilization of machines, but, when tasks' requirements exceed available resources, some of the tasks might be throttled down or preempted. We analyze version 2.1 of the Google cluster trace that shows short-term (1 second) task CPU usage. Contrary to the assumptions taken by many theoretical studies, we demonstrate that the empirical distributions do not follow any single distribution. However, high percentiles of the total processor usage (summed over at least 10 tasks) can be reasonably estimated by the Gaussian distribution. We use this result for a probabilistic fit test, called the Gaussian Percentile Approximation (GPA), for standard bin-packing algorithms. To check whether a new task will fit into a machine, GPA checks whether the resulting distribution's percentile corresponding to the requested service level objective, SLO is still below the machine's capacity. In our simulation experiments, GPA resulted in colocations exceeding the machines' capacity with a frequency similar to the requested SLO.Comment: Author's version of a paper published in ACM SoCC'1

Overcommitment in Cloud Services -- Bin packing with Chance Constraints

This paper considers a traditional problem of resource allocation, scheduling jobs on machines. One such recent application is cloud computing, where jobs arrive in an online fashion with capacity requirements and need to be immediately scheduled on physical machines in data centers. It is often observed that the requested capacities are not fully utilized, hence offering an opportunity to employ an overcommitment policy, i.e., selling resources beyond capacity. Setting the right overcommitment level can induce a significant cost reduction for the cloud provider, while only inducing a very low risk of violating capacity constraints. We introduce and study a model that quantifies the value of overcommitment by modeling the problem as a bin packing with chance constraints. We then propose an alternative formulation that transforms each chance constraint into a submodular function. We show that our model captures the risk pooling effect and can guide scheduling and overcommitment decisions. We also develop a family of online algorithms that are intuitive, easy to implement and provide a constant factor guarantee from optimal. Finally, we calibrate our model using realistic workload data, and test our approach in a practical setting. Our analysis and experiments illustrate the benefit of overcommitment in cloud services, and suggest a cost reduction of 1.5% to 17% depending on the provider's risk tolerance