Local Search Heuristics Research Articles

Adaptive large variable neighborhood search for a multiperiod vehicle and technician routing problem

AbstractThe VeRoLog Solver Challenge 2018–2019 of the EURO working group vehicle routing and logistics (VeRoLog) considers a multiperiod vehicle and technician routing and scheduling problem. This paper proposes a combination of large neighborhood and local search heuristics and a decomposition approach to efficiently generate competitive solutions under restricted computational resources. The interplay of the heuristics, the decomposition, and the way the search space is explored are orchestrated by an adaptive layer that explicitly considers the instance to be solved, a time limit and the performance of the computing environment. In a computational study it is shown that the method is efficient and effective, especially under tight time restrictions.

A decomposition-based heuristic procedure for the Medical Student Scheduling problem

In this paper, we consider a real-life medical student scheduling problem in order to ensure students are able to complete the relevant training program to acquire the postulated medical proficiency. A training program includes mandatory and elective disciplines that students are able to select based on their interests and availability. These internship positions are offered by local hospitals that specify minimum and maximum staffing requirements. The curriculum manager tries to assign students to particular disciplines and hospitals while considering the objectives and the large number of requirements of different stakeholders, i.e. the educational requirements set by the medical school, the staffing requirements set by the involved hospitals and the student characteristics. We propose a heuristic solution methodology composed of a constructive heuristic and two local search heuristics to improve the initial solution. These heuristics embody different complementary neighbourhood structures derived based on the decomposition of the problem in order to find high-quality solutions very efficiently. In order to show the stable performance of the proposed solution methodology, we conducted computational experiments on a comprehensive synthetic dataset of smaller-sized instances and large-scale real-life instances. Results demonstrate that our approach can produce (near-)optimal solutions in a very short timespan. A comparison is made with the real-life approach, demonstrating significant improvements and the contribution to real-life decision-making.

Efficient hybrid local search heuristics for solving the travelling thief problem

Real-world problems often consist of several interdependent subproblems. The degree of interaction of the subproblems is associated with the complexity of the problem and solving each subproblem optimally not ensure the optimal solution of the overall problem. The Travelling Thief Problem (TTP) integrates two well-known combinatorial optimization problems namely the classical Travelling Salesman Problem (TSP) and the 0–1 Knapsack Problem (KP). TTP was introduced to represent the complication of a real-world combinatorial optimization problem. The goal of this problem is to provide a tour to a thief over all the cities and a picking plan that determines which item should be taken from which city to achieve the maximum benefits. The KP component of the TTP is more efficient as compared to the TSP component for optimization. Our proposed method mainly focuses on constructing a picking plan for a near-optimal tour generated by Chained Lin–Kernighan Heuristic (CLKH). In this picking plan, items are picked up according to their scoring value which is calculated by our proposed formulation. Additionally, bit-flip is used for a better solution that can give a more profitable picking plan. The experimental results suggest that our proposed approach can meet or beat current state-of-the-art methods for a large number of TTP instances.

Two-machine chain-reentrant ow shop with the no-wait constraint

This paper addresses the chain-reentrant flow shop scheduling problem with two machines and n non-preemptive jobs in the presence of the no-wait constraint; we assume that each job passes from the first machine to the second and returns back to the first machine. The objective is to minimise the makespan. The general problem is NP-hard in the strong sense. Based on a dynamic programming algorithm, we prove that the problem is polynomially solvable when the execution order of the jobs through the machines is a fixed permutation. For the resolution of the general problem, we propose a linear mathematical model, local search heuristics, a simulated annealing metaheuristic and lower bounds with numerical experiments. [Received: 8 February 2019; Revised: 19 June 2019; Revised: 26 August 2019; Revised: 8 October 2019; Revised: 9 November 2019; Accepted: 11 November 2019]

Cell-Based Local Search Heuristics for Guide Path Design of Automated Guided Vehicle Systems With Dynamic Multicommodity Flow

This article discusses the guide path design of automated guided vehicle (AGV) systems for which we propose a model that incorporates a dynamic multicommodity flow with capacity constraints from a pickup to a delivery point. The problem is formulated as the selection of a guide path connecting a given set of pickup/delivery points. A cell-based local search that is based on an original neighborhood technique is developed. In the proposed method, the guide path is effectively optimized based on a local search of cell-based neighborhood search preserving connectivity constraints and the subsequent solution of a dynamic multicommodity flow problem. The performance of the proposed method is strengthened by the redundant elimination of arcs and intensification of search according to the concept of the flow-concentrated cell. The effectiveness of the proposed method is demonstrated by comparing it with a general-purpose solver and recent algorithms for fixed-charge capacitated multicommodity network design problems. A real case study is presented to demonstrate the applicability of the proposed method by using simulation software. Note to Practitioners —Due to the recent growth of online shipping, the design of automated warehousing systems is receiving much attention. Most automated warehousing systems introduce multiple automated guided vehicles (AGVs) for transportation. This article presents an efficient optimization of guide path design considering congestions and dynamic multicommodity flow routing. We develop cell-based local search heuristics for the guide path design problem for AGV systems that can be applied to a large-scale transportation model to solve the problem efficiently. Our major finding is that the guide path design with the dynamic multicommodity flow can significantly reduce the delays caused by congestions and improve the efficiency of the warehousing systems. The effectiveness of the derived guide path design is evaluated by simulation software. The feasibility of the guide path is confirmed in several case studies.

Memetic improved cuckoo search algorithm for automatic B-spline border approximation of cutaneous melanoma from macroscopic medical images

This work follows up a previous paper at conference Cyberworlds 2018 for automatic border approximation of cutaneous melanoma and other skin lesions from macroscopic medical images. Given a set of feature points on the boundary of the skin lesion obtained by a dermatologist, we introduce a new method for automatic least-squares B-spline curve fitting of such feature points. The method is based on the original cuckoo search algorithm used in the conference paper but with three major modifications: (1) we use an enhanced version of the algorithm in which the parameters change dynamically with the generations; (2) this improved method is coupled with the Luus-Jaakola local search heuristics for better performance; (3) the original Bézier curves are now replaced by the more powerful and more general B-spline curves, providing extra flexibility and lower polynomial degree. The new method (called memetic improved cuckoo search algorithm) has been applied to a benchmark comprised of ten medical images of skin lesions. The computer results show that it performs very well and yields a border curve enclosing the lesion and fitting the feature points with good accuracy. Furthermore, a comparison with ten alternative methods in the literature (six standard mathematical methods for B-spline fitting, two state-of-the art methods in medical imaging, the method in our conference paper and the non-memetic version of our new method) shows that it outperforms all these methods in terms of numerical accuracy for the instances in our reference benchmark.

Preemptive multi-skilled resource constrained project scheduling problem with hard/soft interval due dates

This paper considers a preemptive multi-skilled resource constrained project scheduling problem in a just-in-time environment where each activity has an interval due date to be completed. In this problem setting, resuming a preempted activity requires an extra setup cost, while each time unit violation from the given due date incurs earliness or tardiness penalty. Also, processing cost of each skill to execute any activity depends on the assigned staff member to accomplish the skill. The objective function of the model aims to minimize the total cost of allocating staff to skills, earliness–tardiness penalties and preemption costs. Two integer formulations are proposed for the model which are compared in terms of number of variables, constraints and elapsed run-time to optimality. Furthermore, an ant colony based metaheuristic is developed to tackle real life scales of the proposed model. This algorithm relies on two intelligent local search heuristics. Parameters of the algorithm are calibrated using Taguchi method. The results of the experiments for the proposed algorithm confirm that the proposed algorithm has satisfying performance.

On the Time Complexity of Algorithm Selection Hyper-Heuristics for Multimodal Optimisation

Selection hyper-heuristics are automated algorithm selection methodologies that choose between different heuristics during the optimisation process. Recently selection hyperheuristics choosing between a collection of elitist randomised local search heuristics with different neighbourhood sizes have been shown to optimise a standard unimodal benchmark function from evolutionary computation in the optimal expected runtime achievable with the available low-level heuristics. In this paper we extend our understanding to the domain of multimodal optimisation by considering a hyper-heuristic from the literature that can switch between elitist and nonelitist heuristics during the run. We first identify the range of parameters that allow the hyper-heuristic to hillclimb efficiently and prove that it can optimise a standard hillclimbing benchmark function in the best expected asymptotic time achievable by unbiased mutation-based randomised search heuristics. Afterwards, we use standard multimodal benchmark functions to highlight function characteristics where the hyper-heuristic is efficient by swiftly escaping local optima and ones where it is not. For a function class called CLIFFd where a new gradient of increasing fitness can be identified after escaping local optima, the hyper-heuristic is extremely efficient while a wide range of established elitist and non-elitist algorithms are not, including the well-studied Metropolis algorithm. We complete the picture with an analysis of another standard benchmark function called JUMPd as an example to highlight problem characteristics where the hyper-heuristic is inefficient. Yet, it still outperforms the wellestablished non-elitist Metropolis algorithm.

Multi-objective multi-unit process plan generation in a reconfigurable manufacturing environment: a comparative study of three hybrid metaheuristics

Low costs, high reactivity and high quality products are necessary criteria for industries to achieve competitiveness in nowadays market. In this context, reconfigurable manufacturing systems (RMSs) have emerged to fulfil these requirements. RMS is one of the latest manufacturing paradigms, where machines components, software or material handling units can be added, removed, modified or interchanged as needed and when imposed by the necessity to react and respond rapidly and cost-effectively to changing. This research work addresses the multi-objective single-product multi-unit process plan generation problem in a reconfigurable manufacturing environment where three hybrid heuristics are proposed and compared namely: repetitive single-unit process plan heuristic (RSUPP), iterated local search on single-unit process plans heuristic (LSSUPP) and archive-based iterated local search heuristic (ABILS). Single-unit process plans are generated using the adapted non-dominated sorting genetic algorithm (NSGA-II). Moreover, in addition to the minimisation of the classical total production cost and the total completion time, the minimisation of the maximum machines exploitation time is considered as a novel optimisation criterion, in order to have high quality products. To illustrate the applicability of the three approaches, examples are presented and the obtained numerical results are analysed.

A decomposition-based coevolutionary multiobjective local search for combinatorial multiobjective optimization

Abstract Multiobjective evolutionary algorithm based on decomposition (MOEA/D) divides a multiobjective optimization problem into a number of single-objective subproblems and solves them in a collaborative way. MOEA/D can be naturally extended by the common, intensification oriented method of local search for solving combinatorial multiobjective optimization problems (CMOPs). However, the performance of MOEA/D strongly depends on the distribution of direction vectors and the decomposition method it adopts. In this paper, an efficient coevolutionary multiobjective local search based on decomposition (CoMOLS/D) is proposed. In CoMOLS/D, two sets of direction vectors and two populations with different decomposition methods are adopted to coevolve with each other. Among them, one population aims to achieve fast convergence while the other one puts more effort for maintaining the complementarily diverse solutions based on the convergence population. In the experimental studies, CoMOLS/D is compared with four decomposition-based local search heuristics, i.e., MOEA/D-LS (WS, TCH, PBI and iPBI); a dominance-based local search, i.e., e-MOEA-LS; an indicator-based local search, i.e., IBEA-LS; and a state-of-the-art local search with dual populations, i.e., ND/DPP-LS; on two well-known CMOPs. The experimental results show that CoMOLS/D significantly outperforms the compared algorithms on most of the test instances.

Simple Hyper-Heuristics Control the Neighbourhood Size of Randomised Local Search Optimally for LeadingOnes.

Selection hyper-heuristics (HHs) are randomised search methodologies which choose and execute heuristics during the optimisation process from a set of low-level heuristics. A machine learning mechanism is generally used to decide which low-level heuristic should be applied in each decision step. In this article, we analyse whether sophisticated learning mechanisms are always necessary for HHs to perform well. To this end we consider the most simple HHs from the literature and rigorously analyse their performance for the LeadingOnes benchmark function. Our analysis shows that the standard Simple Random, Permutation, Greedy, and Random Gradient HHs show no signs of learning. While the former HHs do not attempt to learn from the past performance of low-level heuristics, the idea behind the Random Gradient HH is to continue to exploit the currently selected heuristic as long as it is successful. Hence, it is embedded with a reinforcement learning mechanism with the shortest possible memory. However, the probability that a promising heuristic is successful in the next step is relatively low when perturbing a reasonable solution to a combinatorial optimisation problem. We generalise the "simple" Random Gradient HH so success can be measured over a fixed period of time , instead of a single iteration. For LeadingOnes we prove that the Generalised Random Gradient (GRG) HH can learn to adapt the neighbourhood size of Randomised Local Search to optimality during the run. As a result, we prove it has the best possible performance achievable with the low-level heuristics (Randomised Local Search with different neighbourhood sizes), up to lower-order terms. We also prove that the performance of the HH improves as the number of low-level local search heuristics to choose from increases. In particular, with access to low-level local search heuristics, it outperforms the best-possible algorithm using any subset of the heuristics. Finally, we show that the advantages of GRG over Randomised Local Search and Evolutionary Algorithms using standard bit mutation increase if the anytime performance is considered (i.e., the performance gap is larger if approximate solutions are sought rather than exact ones). Experimental analyses confirm these results for different problem sizes (up to ) and shed some light on the best choices for the parameter in various situations.

Approximation Schemes for Clustering with Outliers

Clustering problems are well studied in a variety of fields, such as data science, operations research, and computer science. Such problems include variants of center location problems, k -median and k -means to name a few. In some cases, not all data points need to be clustered; some may be discarded for various reasons. For instance, some points may arise from noise in a dataset or one might be willing to discard a certain fraction of the points to avoid incurring unnecessary overhead in the cost of a clustering solution. We study clustering problems with outliers. More specifically, we look at uncapacitated facility location (UFL), k - median , and k - means . In these problems, we are given a set X of data points in a metric space δ(., .), a set C of possible centers (each maybe with an opening cost), maybe an integer parameter k , plus an additional parameter z as the number of outliers. In uncapacitated facility location with outliers, we have to open some centers, discard up to z points of X , and assign every other point to the nearest open center, minimizing the total assignment cost plus center opening costs. In k - median and k - means , we have to open up to k centers, but there are no opening costs. In k - means , the cost of assigning j to i is δ 2 ( j , i ). We present several results. Our main focus is on cases where δ is a doubling metric (this includes fixed dimensional Euclidean metrics as a special case) or is the shortest path metrics of graphs from a minor-closed family of graphs. For uniform-cost UFL with outliers on such metrics, we show that a multiswap simple local search heuristic yields a PTAS. With a bit more work, we extend this to bicriteria approximations for the k - median and k - means problems in the same metrics where, for any constant ϵ > 0, we can find a solution using (1 + ϵ) k centers whose cost is at most a (1 + ϵ)-factor of the optimum and uses at most z outliers. Our algorithms are all based on natural multiswap local search heuristics. We also show that natural local search heuristics that do not violate the number of clusters and outliers for k - median (or k - means ) will have unbounded gap even in Euclidean metrics. Furthermore, we show how our analysis can be extended to general metrics for k - means with outliers to obtain a (25 + ϵ, 1 + ϵ)-approximation: an algorithm that uses at most (1 + ϵ) k clusters and whose cost is at most 25 + ϵ of optimum and uses no more than z outliers.

Efficient local search strategies for the Mixed Capacitated Arc Routing Problems under Time Restrictions with Intermediate Facilities

In this paper, we extend our previous work on greedy constructive heuristics for the Mixed Capacitated Arc Routing Problem under Time Restrictions with Intermediate Facilities (MCARPTIF) by developing efficient local search improvement heuristics for the problem. Five commonly used arc routing move operators were adapted for the problem, and basic local search implementations were tested on waste collection benchmark sets. Tests showed that despite the application of commonly used speed-up techniques, the local search implementations are very slow on large test instances with more than one-thousand required arcs and edges. In response, more advanced local search acceleration mechanisms from literature were adapted and combined for the MCARPTIF and tested on the same instances. On the large instances, the basic local search setups took between 15 min and 3 h to improve a single solution to local optima, whereas the accelerated implementations took at most 4 min while producing similar quality local optima. The best performing implementation made use of two existing acceleration mechanisms, namely Static-Move-Descriptors and Greedy-Compound-Independent-Moves. A third mechanism, Nearest-Neighbour-Lists was also tested and although it reduced execution times it resulted in local search terminating at worse quality local optima. Given the importance of local search within metaheuristics, the developed local search heuristics provide a significant contribution to arc routing. First, the implementations can be extended to and incorporated into metaheuristics for the MCARPTIF. Second, the acceleration mechanisms can be applied to existing local search metaheuristics for Capacitated Arc Routing Problems, thereby improving the efficiency of the metaheuristics and allowing them to better deal with large instances.

Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks

In this paper, we study the problem of learning a shallow artificial neural network that best fits a training data set. We study this problem in the over-parameterized regime where the numbers of observations are fewer than the number of parameters in the model. We show that with the quadratic activations, the optimization landscape of training, such shallow neural networks, has certain favorable characteristics that allow globally optimal models to be found efficiently using a variety of local search heuristics. This result holds for an arbitrary training data of input/output pairs. For differentiable activation functions, we also show that gradient descent, when suitably initialized, converges at a linear rate to a globally optimal model. This result focuses on a realizable model where the inputs are chosen i.i.d. from a Gaussian distribution and the labels are generated according to planted weight coefficients.

A Heuristic Local Search Algorithm for Improving Cluster and Routing Stability in Sensor Networks

Route selection using optimal nodes in Wireless Sensor Network (WSN) is a prominent task to improve network performance without deterioration. Intrinsic characteristics of the node, network traffic are some of the reason where routing algorithms fail to prove their consistency. In such cases, the conventional routing schemes must be equipped with additional network management features to retain network performance. This manuscript proposes a Heuristic Local Search (HLS) algorithm for improving routing efficiency of WSN. This search algorithm is backboned by clustering process; the cluster head is elected by satisfying balanced network metrics: energy and distance. Congestion preventive routing considers the same objective function in selecting an outside intermediate node that mitigates packet loss due to congestion. Implication of similar objective function under different constraints streamlines routing and prolongs the operation period of the cluster head. The process of the proposed HLS is evaluated using extensive simulation for the metrics: throughput, network lifetime, cluster head changes, energy utilization and packet loss ratio.

A Heuristic Local Search Algorithm for Improving Cluster and Routing Stability in Sensor Networks

Route selection using optimal nodes in Wireless Sensor Network (WSN) is a prominent task to improve network performance without deterioration. Intrinsic characteristics of the node, network traffic are some of the reason where routing algorithms fail to prove their consistency. In such cases, the conventional routing schemes must be equipped with additional network management features to retain network performance. This manuscript proposes a Heuristic Local Search (HLS) algorithm for improving routing efficiency of WSN. This search algorithm is backboned by clustering process; the cluster head is elected by satisfying balanced network metrics: energy and distance. Congestion preventive routing considers the same objective function in selecting an outside intermediate node that mitigates packet loss due to congestion. Implication of similar objective function under different constraints streamlines routing and prolongs the operation period of the cluster head. The process of the proposed HLS is evaluated using extensive simulation for the metrics: throughput, network lifetime, cluster head changes, energy utilization and packet loss ratio.

The impact of solution representations on heuristic net present value optimization in discrete time/cost trade-off project scheduling with multiple cash flow and payment models

The goal of this paper is to investigate the impact of different solution representations, as part of a metaheuristic approach, on net present value optimization in project scheduling. We specifically consider the discrete time/cost trade-off problem with net present value optimization and apply three payment models from literature. Each of these models determines the timing and size of cash flows from the contractor’s viewpoint. The contribution of this paper to literature is twofold.First, we include cash flow distribution variants in the payment models, to also distinguish between different manners in which value is created and costs are incurred, as part of a general model for the contractor’s cash flow management. This general model is developed in order to explicitly include the progress of activities in the determination of the timing and size of payments to the contractor, which is currently lacking in literature.Second, we employ an iterated local search framework to compare different solution representations and their corresponding local search and repair heuristics. The goal is to unambiguously show that the choice of a solution representation deserves a fair amount of attention, alongside the selection of appropriate diversification and intensification operators, even though this is not always the case in literature. Each part of the proposed algorithm is validated on a large dataset of test instances, generated to allow for a broad comparison of the solution representations. Our results clearly quantify the statistically significant differences between three types of representations for the project scheduling problem under study.

Ameliorated grey wolf optimization for economic load dispatch problem

Owing to no free lunch theorem, meta-heuristic search algorithms, behaviour and performance are different for solving specific class of optimization problems than another. Further, search algorithms are conceptualized of exploration and exploitation aspects. Ameliorated grey wolf optimization algorithm is proposed to solve economic power load dispatch problem that synergizes between exploration and exploitation aspects. Ameliorated grey wolf optimization procedure coordinates the behaviour of grey wolves, random exploratory search, local random search and opposition learning heuristics. Grey wolf optimization algorithm is considered to perform global search and random exploratory search applied to perform a search in the neighbourhood of already visited search locations. To maintain good solutions and diversity among solutions, opposition based learning has been implemented. The practical aspects i.e. value-point loading effect, avoidance of prohibited operating zones and ramp rate limits, generation limits of generators and satisfaction of power demand constraint are undertaken to solve economic power load dispatch problem. Heuristic search is exploited to handle equality constraints. The proposed algorithm is validated on standard benchmark functions and medium to large electric power systems. Results reveal that proposed technique is a potential method to solve economic load dispatch problems as it competes with recent algorithms undertaken for comparison.

Capacitated ring arborescence problems with profits

In this work, we introduce profit-oriented capacitated ring arborescence problems and present exact and heuristic algorithms. These combinatorial network design problems ask for optimized bi-level networks taking into account arc costs and node profits. Solutions combine circuits on the inner level with arborescences on the outer level of the networks. We consider the prize-collecting, the budget-constrained and the target-profit models and develop corresponding exact branch-and-cut algorithms based on mixed-integer formulations and valid inequalities. Iterated local search heuristics based on the exploration of problem-specific neighborhoods are elaborated to strengthen the upper bounds. For a set of hard literature derived instances with up to 51 nodes, we provide computational results which give evidence for the efficiency of the proposed approaches. Furthermore, we extensively analyze the performance of our methods, the obtained solution networks and the impact of the cutting planes on the obtained lower bounds.

Large scale continuous global optimization based on micro differential evolution with local directional search

Over the years, many optimization algorithms have been developed to solve large-scale optimization problems accurately and efficiently. In this regard, Memetic Algorithms offer robust and efficient framework that hybridizes the Evolutionary Algorithms with a local heuristic search. In this work, we propose micro Differential Evolution with a Directional Local Search (µDSDE) algorithm using a small population size to solve large scale continuous optimization problems. In this technique, the best individual retains its position, the second best individual undergoes mutation and crossover processes of DE, and the rest are reinitialized on the search space. Exploration of the search is carried out with the dispersal of the worst individuals whereas exploitation is performed through DE operators and Directional Local Search (DLS). We conducted extensive empirical studies using two test suites on Large Scale Global Optimization benchmark with up to 5000 dimensions. The results show that µDSDE considerably outperforms existing solutions in terms of the convergence rate and solution quality.