A large neighborhood search algorithm and lower bounds for the variable-Sized bin packing problem with conflicts

In this paper we consider a one-dimensional bin packing problem where the bins do not have identical sizes, or a variable-sized bin packing problem, to minimize the bin consumption, i.e., the total size of the opened bins. The identical size problem has been extensively studied in the literature both for static and dynamic settings. The worst-case or average-case performance has been analyzed. Our problem setting particularly arises in metal cutting industries. Therefore, it presents a great practical relevance. Four greedy approximation algorithms based on a construction approach called largest object first with least absolute waste (LFLAW), largest object first with least relative waste (LFLRW), least absolute waste (LAW), and least relative waste (LRW) are examined. Their absolute worst-case performances are analyzed. The worst case bounds are 2 for LFLAW and LFLRW, 3 for LAW, and 2+ln 2 for LRW. We also show that these worst-case bounds are tight.

In this paper, a greedy heuristic and two local search algorithms, 1-opt local search and k-opt local search, are proposed for the unconstrained binary quadratic programming problem (BQP). These heuristics are well suited for the incorporation into meta-heuristics such as evolutionary algorithms. Their performance is compared for 115 problem instances. All methods are capable of producing high quality solutions in short time. In particular, the greedy heuristic is able to find near optimum solutions a few percent below the best-known solutions, and the local search procedures are sufficient to find the best-known solutions of all problem instances with n ≤ 100. The k-opt local searches even find the best-known solutions for all problems of size n ≤ 250 and for 11 out of 15 instances of size n e 500 in all runs. For larger problems (n e 500, 1000, 2500), the heuristics appear to be capable of finding near optimum solutions quickly. Therefore, the proposed heuristics—especially the k-opt local search—offer a great potential for the incorporation in more sophisticated meta-heuristics.

Energy takes about half the operational expenses of data centers making energy conservation a critical goal. Fine-grained control over frequency of processors aids in reducing power at the cost of performance degradation. Placing tasks on servers is formulated as a bin packing and tight packing is considered to be energy conserving as idle servers can be shut down. However, we reveal that due to neglecting task deadline and operating at higher frequency leads to higher energy consumption compared to distributing of tasks over larger number of machines at lower frequencies.In this paper, we explore how to provision tasks in an energy-optimal manner. We show that task-based provisioning is a variable-sized bin packing problem and analyze energy efficiency of 14 classical and proposed heuristics for different distributions of task deadline requirements. We establish that tight packing leads to higher energy usage and we need to consider the task deadline while provisioning. Our heuristics saves as much as 65% energy compared to existing greedy heuristics for an instance of provisioning.

A new MILP model and fast heuristics for the variable-sized bin packing problem with time windows

The problem of BLASTing a genome against a database of DNA sequences to identify potential relationships with other genomes can be divided into subproblems quite naturally. We consider a setting where the problem is distributed to PCs having idle time. This results in a new variant of bin packing, where a rectangle is divided into smaller rectangles that are to be packed in variable-sized bins which arrive on-line. A rectangle fits in a bin, if the sum of its height and width is no more than the size of the bin. The goal is to minimize the total size of the bins used for packing the entire rectangle. Simple algorithms exist that work well on small instances of the problem and in the special case where all processors (bins) have the same capacity. We propose an algorithm Slices that works well for more realistic instances in a scenario where the processors vary significantly and arrive on-line.

A hybrid heuristic algorithm for the 2D variable-sized bin packing problem

Variable Sized Bin Packing With Color Constraints

Performing a local search around solutions found by an evolutionary algorithm is a common practice. Local search is well known to significantly improve the solutions, in particular in the case of combinatorial problems. In this paper a new local search procedure is proposed that uses a locally established utopia point. In the tests in which several instances of the Travelling Salesman Problem (TSP) were solved using an evolutionary algorithm the proposed local search procedure outperformed a local search procedure based on Pareto dominance. Because the local search is focused on improving individual solutions and the multiobjective evolutionary algorithm can improve diversity, various strategies of sharing computational resources between the evolutionary algorithm and the local search are used in this paper. The results attained by the tested methods are compared with respect to computation time, which allows a fair comparison between strategies that distribute computational resources between the evolutionary optimization and the local search in various proportions.

Hybrid large neighbourhood search algorithm for capacitated vehicle routing problem

The use of video data for a variety of applications has gained immense popularity. These applications include traffic monitoring, surveillance, retail store management, etc. Thousands of publicly accessible network cameras distributed around the world are potential sources of video data. The applications analyzing data from network cameras have different resource requirements (CPU, memory, etc.) and performance requirements (video frame rate). A preferred way to meet these requirements is to use a cloud infrastructure and a pay-per-use model of the cloud. Cloud computing offers resources, referred to as cloud instances, with different capacities and at different locations. The cost of these instances are dependent on their capacities and locations. The frame rate of the video data obtained from a network camera impacts the accuracy of the analysis and is dependent on the location of the cloud instance. Hence it is important to select the locations of the instances to meet the application performance requirements. This paper presents a resource management approach to select the locations, types, and number of cloud instances to analyze real-time video data from the network cameras while meeting the performance requirements and reducing the analysis cost. We model the resource management problem as a variable size bin packing problem and describe a heuristic algorithm to find a solution. This paper uses Amazon EC2 to evaluate our new resource manager, and observes that our method can reduce the analysis cost up to 56% compared with two other strategies for selecting instance locations.

MEMPSODE: A global optimization software based on hybridization of population-based algorithms and local searches

A modified quasisecant method for global optimization

An efficient aerodynamic topology optimization method was constructed based on the parameterized level set method (PLSM) and large neighborhood search algorithm. The traditional aerodynamic optimization design process is to optimize the shape of a basic shape, and the aerodynamic configuration is determined. The determination of the basic shape relies on the experience of human designers, making it difficult to obtain innovative aerodynamic configurations. To this end, the PLSM is used to obtain aerodynamic configurations of supersonic Busemann biplane with different topological structures. In response to the characteristics of large sample size and low computational efficiency in aerodynamic topology optimization design, a large neighborhood search algorithm is adopted as the optimization algorithm. Aerodynamic topology optimization design was carried out to achieve good drag reduction effect for the Busemann biplane. Compared with shape optimization design, aerodynamic topology design can generate airfoils with different topological structures, greatly improving the design freedom and making it possible to find different aerodynamic configurations in a wide design space.

The runway system is more likely to be a bottleneck area for airport operations because it serves as a link between the air routes and airport ground traffic. As a key problem of air traffic flow management, the aircraft runway scheduling problem (ARSP) is of great significance to improve the utilization of runways and reduce aircraft delays. This paper proposes a large neighborhood search algorithm combined with simulated annealing and the receding horizon control strategy (RHC-SALNS) which is used to solve the ARSP. In the framework of simulated annealing, the large neighborhood search process is embedded, including the breaking, reorganization and local search processes. The large neighborhood search process could expand the range of the neighborhood building in the solution space. A receding horizon control strategy is used to divide the original problem into several subproblems to further improve the solving efficiency. The proposed RHC-SALNS algorithm solves the ARSP instances taken from the actual operation data of Wuhan Tianhe Airport. The key parameters of the algorithm were determined by parametric sensitivity analysis. Moreover, the proposed RHC-SALNS is compared with existing algorithms with excellent performance in solving large-scale ARSP, showing that the proposed model and algorithm are correct and efficient. The algorithm achieves better optimization results in solving large-scale problems.

This tutorial presents a novel search system—the Attractor-Based Search System (ABSS)—that can solve the Traveling Salesman Problem very efficiently with optimality guarantee. From the perspective of dynamical systems, a heuristic local search algorithm for an NP-complete combinatorial problem is a discrete dynamical system. In a local search system, an attractor drives the search trajectories into the vicinity of a globally optimal point in the solution space, and the convergence of local search trajectories makes the search system become a global and deterministic system. The attractor contains a small set of the most promising solutions to the problem. The attractor can reduce the problem size exponentially, and thus make the exhaustive search feasible. Therefore, this new search paradigm is called optimizing with attractor. The ABSS consists of two search phases: local search phase and exhaustive search phase. The local search process is used to quickly construct the attractor in the solution space, and the exhaustive search process is used to completely search the attractor to identify the optimal solution. Therefore, the exact optimal solution can be found quickly by combining local search and exhaustive search. This tutorial introduces the concept of an attractor in a local search system, and describes the process of optimizing with the attractor, using the Traveling Salesman Problem as the study platform.