Variable Neighborhood Search Heuristics Research Articles

IBA-VNS: A Logic-Based Machine Learning Algorithm and Its Application in Surgery

The interpretability and explainability of machine learning (ML) approaches play a key role in the trustworthiness of ML models in various applications. The objective of this paper is to incorporate a logic-based reasoning in the ML model that is not only accurate but also interpretable and easily applied. More precisely, we propose a hybrid IBA-VNS approach based on interpolative Boolean algebra (IBA) and variable neighborhood search (VNS). IBA is chosen over traditional multi-valued and/or fuzzy logic techniques due to its consistency in preserving all Boolean axioms. The VNS heuristic is used for model training, i.e., determining the optimal logical aggregation function within the IBA framework for solving observed prediction problems. Obtained logic aggregation functions are easy to understand and may provide additional insight to the decision-maker. The proposed approach does not require any domain knowledge and is applicable in various domains. IBA-VNS is evaluated on several standard datasets. Further, IBA-VNS is applied to the real-world problem of predicting hospital length of stay (LOS), showing exceptional results in terms of interpretability and accuracy. In fact, the dataset is collected from the LabSerb program regarding colorectal surgeries in the period 2015–2023. The proposed approach extracted knowledge regarding the problem, i.e., the causal relations between the patient’s health condition and LOS, along with achieving an MAE of 1.144 days.

Novel variable neighborhood search heuristics for truck management in distribution warehouses problem.

Logistics and sourcing management are core in any supply chain operation and are among the critical challenges facing any economy. The specialists classify transport operations and warehouse management as two of the biggest and costliest challenges in logistics and supply chain operations. Therefore, an effective warehouse management system is a legend to the success of timely delivery of products and the reduction of operational costs. The proposed scheme aims to discuss truck unloading operations problems. It focuses on cases where the number of warehouses is limited, and the number of trucks and the truck unloading time need to be manageable or unknown. The contribution of this article is to present a solution that: (i) enhances the efficiency of the supply chain process by reducing the overall time for the truck unloading problem; (ii) presents an intelligent metaheuristic warehouse management solution that uses dispatching rules, randomization, permutation, and iteration methods; (iii) proposes four heuristics to deal with the proposed problem; and (iv) measures the performance of the proposed solution using two uniform distribution classes with 480 trucks' unloading times instances. Our result shows that the best algorithm is , as it has a percentage of 78.7% of the used cases, an average gap of 0.001, and an average running time of 0.0053 s.

A Variable Neighborhood Search Approach for the Dynamic Single Row Facility Layout Problem

The dynamic single row facility layout problem (DSRFLP) is defined as the problem of arranging facilities along a straight line during a multi-period planning horizon with the objective of minimizing the sum of the material handling and rearrangement costs. The material handling cost is the sum of the products of the flow costs and center-to-center distances between facilities. In this paper, we focus on metaheuristic algorithms for this problem. The main contributions of the paper are three-fold. First, a variable neighborhood search (VNS) algorithm for the DSRFLP is proposed. The main version of VNS uses an innovative strategy to start the search from a solution obtained by constructing an instance of the single row facility layout problem (SRFLP) from a given instance of the DSRFLP and applying a heuristic algorithm for the former problem. Second, a fast local search (LS) procedure is developed. The innovations of this procedure are two-fold: (i) the fast insertion and swap neighborhood exploration techniques are adapted for the case of the dynamic version of the SRFLP; and (ii) to reduce the computational time, the swap operation is restricted on pairs of facilities of equal lengths. Provided the number of planning periods is a constant, the neighborhood exploration procedures for n facilities have only O(n2) time complexity. The superiority of these procedures over traditional LS techniques is also shown by performing numerical tests. Third, computational experiments on DSRFLP instances with up to 200 facilities and three or five planning periods are carried out to validate the effectiveness of the VNS approach. The proposed VNS heuristic is compared with the simulated annealing (SA) method which is the state of the art algorithm for the DSRFLP. Experiments show that VNS outperforms SA by a significant margin.

Introduction of an underground waste container system–model and solution approaches

In Germany, household waste is collected via a door-to-door collection system. This form of waste collection is already reaching its limits due to the increasing volume of household waste and lack of space for even more dustbins, especially in densely populated cities. In this paper we investigate an alternative collection system: an underground waste collection system in which waste would be collected at central locations in so-called underground containers with a much larger capacity. If an underground container system is to be introduced to replace the present door-to-door waste collection system, a number of decisions of varying scope have to be made: Where should the underground containers be placed? How much capacity should be provided at which collection site? Which household should dispose of its waste where? How often, when and in what order should the waste collection vehicles empty the containers? In this paper we develop a model to illustrate the combination of the underlying problems by extending a problem known from literature. We present both hierarchical and integrated approaches to solve it. The proposed solution approaches combine in different ways two variable neighborhood search heuristics and a mixed integer programming-based exact method. We show that great benefits can be achieved through the use of integrated solution approaches. But we show too that integrated solution approaches do not necessarily dominate hierarchical ones.

Virtual Machine Placement with Disk Anti-colocation Constraints Using Variable Neighborhood Search Heuristic

In a cloud computing environment, virtual machine placement (VMP) represents an important challenge to select the most suitable set of physical machines (PMs) to host a set of virtual machines (VMs). The challenge is how to find optimal or near-optimal solution effectively and efficiently especially when VMP is considered as a NP-hard problem. However, the existing algorithms have focused mostly on compute resources when provisioning VMs and ignore storage resources. Therefore, they often generate non-optimal compute and storage resources for executing users applications. To address this problem, we outline more in details the binary linear programming (BLP) model previously proposed to solve the consolidated VMP with disk anti-colocation constraint (denoted VMcP-DAC) and we solve it using a heuristic algorithm. Our approach considers a special type of disk anti-colocation requirements to prevent Input/Output (IO) performance bottleneck. We implement a variable neighborhood search based optimization heuristic (denoted VNS-H) to solve the VMcP-DAC by minimizing both the resource wastage and the operational expenditure. To the best of our knowledge, only three studies in the literature that are devoted to VMcP-DAC problem. In two of these three works, authors proposed exact algorithms that are unable to solve large scale VMcP-DAC problem instances. For this reason, in a previous work, we proposed a decomposition based method to overcome the convergence issues for only large scale problems. In the present paper, our goal is to solve VMcP-DAC problem instances suitable for both regular and large data centers. We investigate the effectiveness of the proposed VNS-H, showing that it has a better convergence characteristics and it is more computationally efficient than compared methods from the literature.

Introduction of an Underground Waste Container System–Model and Solution Approaches

In Germany, household waste is collected via a door-to-door collection system. This form of waste collection is already reaching its limits due to the increasing volume of household waste and lack of space for even more dustbins, especially in densely populated cities. In this paper we investigate an alternative collection system: an underground waste collection system in which waste would be collected at central locations in so-called underground containers with a much larger capacity. If an underground container system is to be introduced to replace the present door-to-door waste collection system, a number of decisions of varying scope have to be made: Where should the underground containers be placed? How much capacity should be provided at which collection site? Which household should dispose of its waste where? How often, when and in what order should the waste collection vehicles empty the containers? In this paper we develop a model to illustrate the combination of the underlying problems by extending a problem known from literature. We present both hierarchical and integrated approaches to solving it. The proposed solution approaches combine in different ways two variable neighborhood search heuristics and a mixed integer programming-based exact method. We show that great benefits can be achieved through the use of integrated solution approaches. But we show too that integrated solution approaches do not necessarily dominate hierarchical ones.

Discrete Fireworks Algorithm for Single Machine Scheduling Problems

Over the recent years, Fireworks Algorithm has recorded an increasing success on solving continuous optimization problems, due to its efficiency, simplicity and more importantly its rapid convergence to good optimums. Thus, the Fireworks Algorithm performance is now widely comparable with the most popular methods in the optimization field such as evolutionary computation and swarm intelligence techniques. This paper introduces a discrete Fireworks Algorithm for combinatorial single machine scheduling problems. Taking advantage of the robust design of the original Fireworks Algorithm, a new adaptation of sparks generation is proposed with a novel use of the control parameters. To verify the explorative performance of the algorithm, a hybridization with Variable Neighborhood Search heuristic is implemented. To validate it, the proposed method is tested with several benchmarks instances of the single machine total weighted tardiness. A comparison with other optimization algorithms is also included. The obtained results exhibit the high performance of the proposed method.

A general variable neighborhood search for the swap-body vehicle routing problem

The Swap-Body Vehicle Routing Problem, a generalization of the well known Vehicle Routing Problem, can be stated as follows: the vehicle fleet consisting of trucks, semi-trailers, and swap bodies, is available at a single depot to serve a given set of customers. To serve a subset of customers, one may use either a truck carrying one swap body or a train (a truck with a semi-trailer attached to it) carrying two swap bodies. In both cases, a vehicle (a truck or a train) must perform a route starting and ending at the depot, so to satisfy demands of visited customers, maximal allowed route duration, allowed load on the used vehicle, and accessibility constraint of each customer. The accessibility constraint indicates whether a customer is allowed to be visited by a train or not. In addition, a set of swap locations is given where semi-trailers and swap bodies may be parked or swapped. The goal of the Swap-Body Vehicle Routing Problem is to minimize the total costs consisting of the fixed costs for using vehicles and costs for performing routes. In this paper, we propose two general variable neighborhood search heuristics to solve this problem. The quality of the proposed methods is evaluated on the instances provided by the organizers of VeRolog Solver Challenge 2014.

Adaptive general variable neighborhood search heuristics for solving the unit commitment problem

Abstract The unit commitment problem (UCP) for thermal units consists of finding an optimal electricity production plan for a given time horizon. In this paper we propose hybrid approaches which combine Variable Neighborhood Search (VNS) metaheuristic and mathematical programming to solve this NP-hard problem. Four new VNS based methods, including one with adaptive choice of neighborhood order used within deterministic exploration of neighborhoods, are proposed. A convex economic dispatch subproblem is solved by Lambda iteration method in each time period. Extensive computational experiments are performed on well-known test instances from the literature as well as on new large instances generated by us. It appears that the proposed heuristics successfully solve both small and large scale problems. Moreover, they outperform other well-known heuristics that can be considered as the state-of-the-art approaches.

An Adaptable Variable Neighborhood Search for the Vehicle Routing Problem with Order Outsourcing

In practice, many package transportation companies lower their costs by hiring outside carriers to serve orders that cannot be served efficiently by their own trucks. The problem which takes the order outsource option into account is the Vehicle Routing Problem with Private Fleet and Common Carrier. In this variant of the Vehicle Routing Problem, orders are either delivered by an outside carrier, the common carrier, which receives an order specific price for this or by the own fleet, the private fleet, such that the total costs, which is the sum of the outside carrier costs and the delivery costs of the own fleet, is minimized. This paper presents two Adaptable Variable Neighborhood Search heuristics which are highly competitive and several new test instances which are based upon efficiency instead of necessity.

Variable neighborhood search heuristics for a test assembly design problem

Test assembly design problems appear in the areas of psychology and education, among others. The goal of these problems is to construct one or multiple tests to evaluate the test subject. This paper studies a recent formulation of the problem known as the one-dimensional minimax bin-packing problem with bin size constraints (MINIMAX_BSC). In the MINIMAX_BSC, items are initially divided into groups and multiple tests need to be constructed using a single item from each group, while minimizing differences among the tests. We first show that the problem is NP-Hard, which remained an open question. Second, we propose three different local search neighborhoods derived from the exact resolution of special cases of the problem, and combine them into a variable neighborhood search (VNS) metaheuristic. Finally, we test the proposed algorithm using real-life-based instances. The results show that the algorithm is able to obtain optimal or near-optimal solutions for instances with up to 60000-item pools. Consequently, the algorithm is a viable option to design large-scale tests, as well as to provide tests for online small-sized situations such as those found in e-learning platforms.

0 – 1 Quadratic Knapsack Problem solved with VNS algorithm

In this paper we propose two variants of the variable neighborhood search heuristics to solve the (0 – 1) Quadratic Knapsack Problem. The mixed variable neighborhood descent (Mixed-VND) and the Skewed general variable neighborhood search (SGVNS). The proposed algorithms were tested over a set of large-sized instances with 1000 and 2000 binary variables and the results were compared to those reported from the literature. Encouraging results are obtained.

Variable neighborhood search for the pharmacy duty scheduling problem

In this paper, we study on the Pharmacy Duty Scheduling (PDS) problem, where a subset of pharmacies should be on duty on national holidays, at weekends and at nights in order to be able to satisfy the emergency drug needs of the society. PDS problem is a multi-period p-median problem with special side constraints and it is an NP-Hard problem. We propose four Variable Neighborhood Search (VNS) heuristics. The first one is the basic version, BVNS. The latter two, Variable Neighborhood Decomposition Search (VNDS) and Variable Neighborhood Restricted Search (VNRS), aim to obtain better results in less computing time by decomposing or restricting the search space. The last one, Reduced VNS (RVNS), is for obtaining good initial solutions rapidly for BVNS, VNDS and VNRS. We test BVNS, VNRS and VNDS heuristics on randomly generated instances and report the computational test results. We also use VNS heuristics on real data for the pharmacies in central İzmir and obtain significant improvements.

Heuristics for Routing Heterogeneous Unmanned Vehicles with Fuel Constraints

This paper addresses a multiple depot, multiple unmanned vehicle routing problem with fuel constraints. The objective of the problem is to find a tour for each vehicle such that all the specified targets are visited at least once by some vehicle, the tours satisfy the fuel constraints, and the total travel cost of the vehicles is a minimum. We consider a scenario where the vehicles are allowed to refuel by visiting any of the depots or fuel stations. This is a difficult optimization problem that involves partitioning the targets among the vehicles and finding a feasible tour for each vehicle. The focus of this paper is on developing fast variable neighborhood descent (VND) and variable neighborhood search (VNS) heuristics for finding good feasible solutions for large instances of the vehicle routing problem. Simulation results are presented to corroborate the performance of the proposed heuristics on a set of 23 large instances obtained from a standard library. These results show that the proposed VND heuristic, on an average, performed better than the proposed VNS heuristic for the tested instances.

A variable neighborhood search method for a two-mode blockmodeling problem in social network analysis

AbstractThis paper presents a variable neighborhood search (VNS) algorithm that is specially designed for the blockmodeling of two-mode binary network matrices in accordance with structural equivalence. Computational results for 768 synthetic test networks revealed that the VNS heuristic outperformed a relocation heuristic (RH) and a tabu search (TS) method for the same problem. Next, the three heuristics were applied to two-mode network data pertaining to the votes of member countries on resolutions in the United Nations General Assembly. A comparative analysis revealed that the VNS heuristic often provided slightly better criterion function values than RH and TS, and that these small differences in criterion function values could sometimes be associated with substantial differences in the actual partitions obtained. Overall, the results suggest that the VNS heuristic is a promising approach for blockmodeling of two-mode binary networks. Recommendations for extensions to stochastic blockmodeling applications are provided.

Variable Neighborhood Search heuristic for the Inventory Routing Problem in fuel delivery

In this paper we observe the extension of the vehicle routing problem (VRP) in fuel delivery that includes petrol stations inventory management and which can be classified as the Inventory Routing Problem (IRP) in fuel delivery. The objective of the IRP is to minimize the total cost of vehicle routing and inventory management. We developed a Variable Neighborhood Search (VNS) heuristic for solving a multi-product multi-period IRP in fuel delivery with multi-compartment homogeneous vehicles, and deterministic consumption that varies with each petrol station and each fuel type. The stochastic VNS heuristic is compared to a Mixed Integer Linear Programming (MILP) model and the deterministic “compartment transfer” (CT) heuristic. For three different scale problems, with different vehicle types, the developed VNS heuristic outperforms the deterministic CT heuristic. Also, for the smallest scale problem instances, the developed VNS was capable of obtaining the near optimal and optimal solutions (the MILP model was able to solve only the smallest scale problem instances).

The tree representation for the pickup and delivery traveling salesman problem with LIFO loading

The feasible solutions of the traveling salesman problem with pickup and delivery (TSPPD) are commonly represented by vertex lists. However, when the TSPPD is required to follow a policy that loading and unloading operations must be performed in a last-in-first-out (LIFO) manner, we show that its feasible solutions can be represented by trees. Consequently, we develop a novel variable neighborhood search (VNS) heuristic for the TSPPD with last-in-first-out loading (TSPPDL) involving several search operators based on the tree data structure. Extensive experiments suggest that our VNS heuristic is superior to the current best heuristics for the TSPPDL in terms of solution quality, while requiring no more computing time as the size of the problem increases.

Neighborhood search heuristics for selecting hierarchically well-formulated subsets in polynomial regression

The importance of subset selection in multiple regression has been recognized for more than 40 years and, not surprisingly, a variety of exact and heuristic procedures have been proposed for choosing subsets of variables. In the case of polynomial regression, the subset selection problem is complicated by two issues: (1) the substantial growth in the number of candidate predictors, and (2) the desire to obtain hierarchically well-formulated subsets that facilitate proper interpretation of the regression parameter estimates. The first of these issues creates the need for heuristic methods that can provide solutions in reasonable computation time; whereas the second requires innovative neighborhood search approaches that accommodate the hierarchical constraints. We developed tabu search and variable neighborhood search heuristics for subset selection in polynomial regression. These heuristics are applied to a classic data set from the literature and, subsequently, evaluated in a simulation study using synthetic data sets. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis

The selection of a subset of variables from a pool of candidates is an important problem in several areas of multivariate statistics. Within the context of principal component analysis (PCA), a number of authors have argued that subset selection is crucial for identifying those variables that are required for correct interpretation of the components. In this paper, we adapt the variable neighborhood search (VNS) paradigm to develop two heuristics for variable selection in PCA. The performances of these heuristics were compared to those obtained by a branch-and-bound algorithm, as well as forward stepwise, backward stepwise, and tabu search heuristics. In the first experiment, which considered candidate pools of 18 to 30 variables, the VNS heuristics matched the optimal subset obtained by the branch-and-bound algorithm more frequently than their competitors. In the second experiment, which considered candidate pools of 54 to 90 variables, the VNS heuristics provided better solutions than their competitors for a large percentage of the test problems. An application to a real-world data set is provided to demonstrate the importance of variable selection in the context of PCA.

Algorithms for ℓ1-Embeddability and Related Problems

Assouad has shown that a real-valued distance d = (dij)1 ? i < j ? n is isometrically embeddable in ?1space if and only if it belongs to the cut cone on n points. Determining if this condition holds is NP-complete. We use Assouad's result in a constructive column generation algorithm for ?1-embeddability. The subproblem is an unconstrained 0-1 quadratic program, solved by Tabu Search and Variable Neighborhood Search heuristics as well as by an exact enumerative algorithm. Computational results are reported. Several ways to approximate a distance which is not ?1-embeddable by another one which is are also studied.