Descent Local Search Research Articles

A Reduced Variable Neighbourhood Search for the Beam Angle Optimisation Problem

Intensity Modulated Radiation Therapy (IMRT) is a widely used radiation therapy technique to treat cancer. The main goal in IMRT is to obtain a treatment plan that eliminates cancer cells from the tumour and, at the same time, damages as little as possible the Organs at Risk (OAR) around the tumour. To this end, we first need to seek the best possible set of beam angles, called beam angle configuration (BAC), to irradiate from. In this paper, we propose a reduced Variable Neighbourhood Search (rVNS) algorithm that explores the search space employing two different local search movements. Unlike traditional VNS algorithms, the rVNS we implement here does not need any transition rule to be implemented, as it includes both neighbourhoods moves at each iteration the rVNS we implement here does not need any transition rule to be implemented, as it includes two types of movements at each iteration. The first movement replaces each beam angle in the BAC by a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\pm 5^{\circ }$</tex-math></inline-formula> beam angle, while the second movement replaces each beam angle in the BAC by a randomly chosen beam angle. We try our approach We test our approach on a set of clinical prostate cases from a hospital in Chile. Results show that the rVNS produces better results than both steepest descent and next descent local search algorithms using the same neighbourhood definitions. The rVNS is showed shown to be faster than the Local Search algorithms and quite competitive w.r.t. the obtained treatment plans.

A matheuristic for tactical locomotive and driver scheduling for the Swiss national railway company SBB Cargo AG

AbstractAt the scale of Switzerland, the national railway company SBB Cargo AG has to schedule its locomotives and drivers in order to be able to pull all trains. Two objective functions are considered in a two-stage lexicographic fashion: (1) the locomotive and driver costs and (2) the driver time that is spent without driving. As the problem instances tend to reach really big sizes (up to 1900 trains), we propose to schedule locomotives and drivers in a sequential way, thus having a sequence of smaller problems to solve. Moreover, for smaller instances, we also propose to schedule jointly locomotives and drivers in an integrated way, therefore increasing the search space but possibly leading to better solutions. In this paper, we present a mathematical formulation and model for the problem. We also consider the contract-related constraints of the drivers, and we propose a way to integrate some time flexibility in the schedules. Next, we propose an innovative matheuristic to solve the problem, relying on a descent local search and a rolling horizon decomposition. An important goal of this method is to explore thoroughly at which extent a general-purpose solver can be used on this problem. Finally, the benefits of each aspect of the model and of the method are analyzed in detail on the results obtained for 20 real SBB Cargo AG instances.

A Receding Horizon Navigation and Control System for Autonomous Merchant Ships: Reducing Fuel Costs and Carbon Emissions under the Premise of Safety

In order to solve the multi-objective planning and trajectory tracking control problem related to maritime autonomous surface ships (MASSs), a new design scheme for autonomous navigation is proposed in this paper, with a receding horizon navigation and control (RHNC) system that contains navigation and control modules. In the navigation module, we designed a superposition field gradient descent local search algorithm based on the cost field, emission field, and guidance field to navigate the MASS reference path, and in the control module, we designed a nonlinear controller that can handle multiple constraints based on the NMPC framework. Under the new scheme, the navigation module completes local path planning to reduce costs and emissions, the control module accomplishes accurate trajectory tracking and real-time collision avoidance, and the information is transmitted in both directions between the two modules to collaboratively complete the MASS navigation and control tasks. We conducted a simulation study of the navigation algorithm and controller and the autonomous navigation system using a Kriso Container ship (KCS). The simulation results demonstrate the effectiveness of the proposed cooperative design scheme in reducing navigation costs and emissions and avoiding autonomous collision avoidances.

Iterated greedy algorithms for a complex parallel machine scheduling problem

This paper addresses a complex parallel machine scheduling problem with jobs divided into operations and operations grouped in families. Non-anticipatory family setup times are held at the beginning of each batch, defined by the combination of one setup-time and a sequence of operations from a unique family. Other aspects are also considered in the problem, such as release dates for operations and machines, operation’s sizes, and machine’s eligibility and capacity. We consider item availability to define the completion times of the operations within the batches, to minimize the total weighted completion time of jobs. We developed Iterated Greedy (IG) algorithms combining destroy and repair operators with a Random Variable Neighborhood Descent (RVND) local search procedure, using four neighborhood structures to solve the problem. The best algorithm variant outperforms the current literature methods for the problem, in terms of average deviation for the best solutions and computational times, in a known benchmark set of 72 instances. New upper bounds are also provided for some instances within this set. Besides, computational experiments are conducted to evaluate the proposed methods’ performance in a more challenging set of instances introduced in this work. Two IG variants using a greedy repair operator showed superior performance with more than 70% of the best solutions found uniquely by these variants. Despite the simplicity, the method using the most common destruction and repair operators presented the best results in different evaluated criteria, highlighting its potential and applicability in solving a complex machine scheduling problem.

Matheuristics to optimize refueling and maintenance planning of nuclear power plants

Planning the maintenance of nuclear power plants is a complex optimization problem, involving a joint optimization of maintenance dates, fuel constraints and power production decisions. This paper investigates Mixed Integer Linear Programming (MILP) matheuristics for this problem, to tackle large size instances used in operations with a time scope of five years, and few restrictions with time window constraints for the latest maintenance operations. Several constructive matheuristics and a Variable Neighborhood Descent local search are designed. The matheuristics are shown to be accurately effective for medium and large size instances. The matheuristics give also results on the design of MILP formulations and neighborhoods for the problem. Contributions for the operational applications are also discussed. It is shown that the restriction of time windows, which was used to ease computations, induces large over-costs and that this restriction is not required anymore with the capabilities of matheuristics or local search to solve such size of instances. Our matheuristics can be extended to a bi-objective optimization extension with stability costs, for the monthly re-optimization of the maintenance planning in the real-life application.

Calibration of the descent local search algorithm parameters using orthogonal arrays

AbstractSolving optimization problems using heuristic algorithms requires the selection of its parameters. Traditionally, these parameters are selected by a trial and error process that cannot guarantee the quality of the results obtained because not all the potential combinations of parameters are checked. To fill this gap, this paper proposes the application of Taguchi's orthogonal arrays to calibrate the parameters of a heuristic optimization algorithm (the descent local search algorithm). This process is based on the study of the combinations of discrete values of the heuristic tool parameters and it enables optimization of the heuristic tool performance with a reduced computational effort. To check its efficiency, this methodology is applied to a technical challenge never studied before: the optimization of the tensioning process of cable‐stayed bridges. The statistical improvement of the heuristic tool performance is studied by the optimization of the tensioning process of a real cable‐stayed bridge. Results show that the proposed calibration technique provided robust values of the objective function (with lower minimum and mean values, and lower standard deviation) with reduced computational cost.

A Variable Neighborhood Search heuristic for rolling stock rescheduling

We present a Variable Neighborhood Search heuristic for the rolling stock rescheduling problem. Rolling stock rescheduling is needed when a disruption leads to cancellations in the timetable. In rolling stock rescheduling, one must then assign duties, i.e., sequences of trips, to the available train units in such a way that both passenger comfort and operational performance are taken into account. For our heuristic, we introduce three neighborhoods, which focus on swapping duties between train units, on improving the individual duties and on changing the shunting that occurs between trips, respectively. These neighborhoods are used for both a Variable Neighborhood Descent local search procedure and for perturbing the current solution in order to escape from local optima. Moreover, we show that the heuristic can be extended to the setting of flexible rolling stock turnings at ending stations by introducing a fourth neighborhood. We apply our heuristic to instances of Netherlands Railways (NS). The results show that the heuristic is able to find high-quality solutions within 1 ​min of solving time. This allows rolling stock dispatchers to use our heuristic in real-time rescheduling. • We consider the rescheduling of rolling stock after a disruption occurs. • We propose a Variable Neighborhood Search heuristic for rolling stock rescheduling. • We develop three innovative neighborhoods for local search and perturbation. • We apply the heuristic to real-world instances of Netherlands Railways (NS). • Solutions of high quality can be obtained within short computation times.

A study of the loops control for reconfigurable computing with OpenCL in the LABS local search problem

In this article, we study the steepest descent local search (SDLS) algorithm that is used as the improvement step in the memetic algorithms for the search of low autocorrelation binary sequences (LABS). We address the method of reconfigurable computing, as the algorithm is of the field programmable gate array (FPGA) type as it features the integer operations, bit-wise data representation, regular execution flow, and huge computational complexity. It contains four levels of nested loops, but its direct parallel implementation as a custom processor leads to typical problems because the loops expose a dynamic range and too many iterations. This inhibits a simple parallel data path that is typically produced by the method of the loop unrolling. We have examined the four architectures that mitigate the found obstacles, and we provide the results of their implementation. The solutions take advantages of the loop pipelining, reordering of the loops, and dynamic reconfiguration. The recently available development tool was involved in our study as we have used the OpenCL (OCL) platform for FPGAs to draw practical conclusions. The given proposals are characterized by their performance and capacity for a problem size. Consequently, the speed/size trade-off is highlighted, as an FPGA size is a design constraint. The performance of the FPGA-based solutions is compared to the CPU speed, and the maximum reported speed-up is 750. Readers can further develop and/or use the presented OCL solutions for efficient LABS discovery as we provide the corresponding software repository.

Heuristic Techniques for the Design of Steel-Concrete Composite Pedestrian Bridges

The objective of this work was to apply heuristic optimization techniques to a steel-concrete composite pedestrian bridge, modeled like a beam on two supports. A program has been developed in Fortran programming language, capable of generating pedestrian bridges, checking them, and evaluating their cost. The following algorithms were implemented: descent local search (DLS), a hybrid simulated annealing with a mutation operator (SAMO2), and a glow-worms swarm optimization (GSO) in two variants. The first one only considers the GSO and the second combines GSO and DLS, applying the DSL heuristic to the best solutions obtained by the GSO. The results were compared according to the lowest cost. The GSO and DLS algorithms combined obtained the best results in terms of cost. Furthermore, a comparison between the CO2 emissions associated with the amount of materials obtained by every heuristic technique and the original design solution were studied. Finally, a parametric study was carried out according to the span length of the pedestrian bridge.

Inexact Multi-Objective Local Search Proximal Algorithms: Application to Group Dynamic and Distributive Justice Problems

We introduce and examine an inexact multi-objective proximal method with a proximal distance as the perturbation term. Our algorithm utilizes a local search descent process that eventually reaches a weak Pareto optimum of a multi-objective function, whose components are the maxima of continuously differentiable functions. Our algorithm gives a new formulation and resolution of the following important distributive justice problem in the context of group dynamics: In each period, if a group creates a cake, the problem is, for each member, to get a high enough share of this cake; if this is not possible, then it is better to quit, breaking the stability of the group.

Local Search Algorithms for the Beam Angles’ Selection Problem in Radiotherapy

One important problem in radiation therapy for cancer treatment is the selection of the set of beam angles radiation will be delivered from. A primary goal in this problem is to find a beam angle configuration (BAC) that leads to a clinically acceptable treatment plan. Further, this process must be done within clinically acceptable times. Since the problem of selecting beam angles in radiation therapy is known to be extremely hard to solve as well as time-consuming, both exact algorithms and population-based heuristics might not be suitable to solve this problem. In this paper, we compare two matheuristic methods based on local search algorithms, to approximately solve the beam angle optimisation problem (BAO). Although the steepest descent algorithm is able to find locally optimal BACs for the BAO problem, it takes too long before convergence, which is not acceptable in clinical practice. Thus, we propose to use a next descent algorithm that converges quickly to good quality solutions although no (local) optimality guarantee is given. We apply our two matheuristic methods on a prostate case which considers two organs at risk, namely, the rectum and the bladder. Results show that the matheuristic algorithm based on the next descent local search is able to quickly find solutions as good as the ones found by the steepest descent algorithm.

Heuristics in optimal detailed design of precast road bridges

This paper deals with the cost optimization of road bridges consisting of concrete slabs prepared in situ and two precast-prestressed U-shaped beams of self-compacting concrete. It shows the efficiency of four heuristic algorithms applied to a problem of 59 discrete variables. The four algorithms are the Descent Local Search (DLS), a threshold accepting algorithm with mutation operation (TAMO), the Genetic Algorithm (GA), and the Memetic Algorithm (MA). The heuristic optimization algorithms are applied to a bridge with a span length of 35m and a width of 12m. A performance analysis is run for the different heuristics, based on a study of Pareto optimal solutions between execution time and efficiency. The best results were obtained with TAMO for a minimum cost of 104184€. Among the key findings of the study, the practical use of these heuristics in real cases stands out. Furthermore, the knowledge gained from the investigation of the algorithms allows a range of values for the design optimization of such structures and pre-dimensioning of the variables to be recommended.

Hybrid metaheuristic to solve the “one-to-many-to-one” problem

PurposeThe purpose of this paper is to present a specific variant of vehicle routing problem with simultaneous full pickup and delivery problem (VRPSFPD) known as one-to-many-to-one (1-M-1) problem with several vehicles, where every customer can receive and send goods simultaneously, which has added the notion of the totality for the pickup goods. Currently, hybrid metaheuristics have become more popular because they offer the best solutions to several combinatorial optimization problems. Therefore, due to the complexity of 1-M-1 a hybrid genetic algorithm with variable neighborhood descent (HGAVND) local search is proposed. To improve the solution provided by the HGAVND the authors suggest applying a structure OR-Opt. To test the performance of the algorithm the authors have used a set of benchmarks from the literature and apply the HGAVND algorithm to solve the real case of distribution of soft drink in Tunisia. The experimental results indicate that the algorithm can outperform all other algorithms proposed in literature with regard to solution quality and processing time. Moreover, the authors improve the best known solution of the majority of benchmark instances taken from the literature.Design/methodology/approachDue to the complexity of 1-M-1 a HGAVND local search is proposed.Originality/valueFirst, in the presence of full pickup constraints, the problem becomes more complex, this implies that the choice of a good metaheuristic can provide good results. Second, the best contribution consists in a specific variant of VRPSFPD problem as 1-M-1 which the paper present the first application of metaheuristics to solve the specific 1-M-1 and to apply it in real case of distribution of soft drink.

An adaptive guided variable neighborhood search based on honey-bee mating optimization algorithm for the course timetabling problem

A standard honey-bee mating optimization algorithm (HBMO) utilizes the steepest descent local search algorithm as a worker. The steepest descent algorithm has the advantage of being simple to understand, fast and is easy to implement. However, it can easily trapped in a local optimum and subsequently restrict the performance of HBMO. Furthermore, the type of neighborhood structures that are used within the local search algorithm might impact on the performance of algorithm. This work aimed to enhance the performance of HBMO by using an adaptive guided variable neighborhood search (AGVNS) as a worker. The AGVNS algorithm is a variant of variable neighborhood search algorithm that incorporates some problem-specific knowledge and utilizes an adaptive learning mechanism to find the most suitable neighborhood structure during the searching process. In order to evaluate the effectiveness of the proposed algorithm, the Socha course timetabling dataset has been chosen as the tested domain problem. The results demonstrated that the performance of the proposed algorithm is comparable to other approaches in the literature. Indeed, the proposed algorithm obtained the best results as compared to other approaches on some instances. These results indicate the effectiveness of combining HBMO and AGVNS for solving course timetabling problems, hence demonstrated that the AGVNS can enhance the performance of HBMO.

A SOLUTION FOR THE BI-OBJECTIVE VEHICLE ROUTING PROBLEM WITH TIME WINDOWS USING LOCAL SEARCH AND GENETIC ALGORITHMS

This paper deals with the vehicle routing problem with time windows (VRPTW). The VRPTW routes a set of vehicles to service customers having two-sided time windows, i.e. earliest and latest start of service times. The demand requests are served by capacitated vehicles with limited travel times to return to the depot. The purpose of this paper is to develop a hybrid algorithm that uses the modified push forward insertion heuristic (MPFIH), a λ-interchange local search descent method (λ-LSD) and a genetic algorithm to solve the VRPTW with two objectives. The first objective aims to determine the minimum number of vehicles required and the second is to find the solution that minimizes the total travel time. A set of well-known benchmark problems are used to compare the quality of solutions. The results show that the proposed algorithm provides effective solutions compared with best found solutions and better than another heuristic used for comparison.

The high performing backtracking algorithm and heuristic for the sequence-dependent setup times flowshop problem with total weighted tardiness

Although the sequence-dependent setup times flowshop problem with the total weighted tardiness minimization objective exists widely in industry, work on the problem has been scant in the existing literature. To the authors' best knowledge, the NEHEWDD heuristic and the Iterated Greedy (IG) algorithm with descent local search have been regarded as the high performing heuristic and the state-of-the-art algorithm for the problem, which are both based on insertion search. In this article firstly, an efficient backtracking algorithm and a novel heuristic (HPIS) are presented for insertion search. Accordingly, two heuristics are introduced, one is NEHEWDD with HPIS for insertion search, and the other is the combination of NEHEWDD and both the two methods. Furthermore, the authors improve the IG algorithm with the proposed methods. Finally, experimental results show that both the proposed heuristics and the improved IG (IG*) significantly outperform the original ones.

Designing construction processes in buildings by heuristic optimization

This paper describes a computer tool for calculating and validating loads on floor slabs and shores in the construction of multistorey buildings with in situ casting. Its chief novelty lies in its optimization unit, designed to produce appropriate and optimum construction processes, which was created by applying exact and heuristic methods: Random Walk (RW), Descent Local Search (DLS) and Simulated Annealing (SA). The system has shown that it can improve three of the most important aspects involved in construction: time, cost and safety. In some cases the optimal solutions were achieved while reducing up to 53% of the cost of the shoring system, in shorter construction time, and meeting all the usual requirements for the construction of this type of building.

Connecting a population dynamic model with a multi-period location-allocation problem for post-disaster relief operations

In this study, we propose a mathematical model and heuristics for solving a multi-period location-allocation problem in post-disaster operations, which takes into account the impact of distribution over the population. Logistics restrictions such as human and financial resources are considered. In addition, a brief review on resilience system models is provided, as well as their connection with quantitative models for post-disaster relief operations. In particular, we highlight how one can improve resilience by means of OR/MS strategies. Then, a simpler resilience schema is proposed, which better reflects an active system for providing humanitarian aid in post-disaster operations, similar to the model focused in this work. The proposed model is non-linear and solved by a decomposition approach: the master level problem is addressed by a non-linear solver, while the slave subproblem is treated as a black-box coupling heuristics and a Variable Neighborhood Descent local search. Computational experiments have been done using several scenarios, and real data from Belo Horizonte city in Brazil.

An immune-inspired algorithm for an unrelated parallel machines’ scheduling problem with sequence and machine dependent setup-times for makespan minimisation

This paper proposes an immune-inspired algorithm to the problem of minimising the makespan on unrelated parallel machines, with sequence dependent setup times. The initial population is generated through the construction phase of the Greedy Randomised Adaptive Search Procedure (GRASP). An evaluation function is proposed to help the algorithm escape from local optima. A Variable Neighbourhood Descent (VND) local search heuristic, which makes significant use of the characteristics of the problem, is proposed as a somatic hypermutation operator to accelerate the convergence of the algorithm. A population re-selection operator, which strategically keeps good quality solutions with a high level of dispersion in the search space, is also proposed. The experiments performed show that the proposed algorithm enables better results than those reported in recent literature studies.

A learning tabu search for a truck allocation problem with linear and nonlinear cost components

AbstractThe two‐level problem studied in this article consists of optimizing the refueling costs of a fleet of locomotives over a railway network. The goal consists of determining: (1) the number of refueling trucks contracted for each yard (truck assignment problem denoted TAP) and (2) the refueling plan of each locomotive (fuel distribution problem denoted FDP). As the FDP can be solved efficiently with existing methods, the focus is put on the TAP only. In a first version of the problem (denoted (P1)), various linear costs (e.g., fuel, fixed cost associated with each refueling, weekly operating costs of trucks) have to be minimized while satisfying a set of constraints (e.g., limited capacities of the locomotives and the trucks). In contrast with the existing literature on this problem, two types of nonlinear cost components will also be considered, based on the following ideas: (1) if several trucks from the same fuel supplier are contracted for the same yard, the supplier is likely to propose discounted prices for that yard (Problem (P2)); (2) if a train stops too often on its route, a penalty is incurred, which represents the dissatisfaction of the clients (Problem (P3)). Even if exact methods based on a mixed integer linear program formulation are available for (P1), they are not appropriate anymore to tackle (P2) and (P3). Various methods are proposed for the TAP: a descent local search, a tabu search, and a learning tabu search (LTS). The latter is a new type of local search algorithm. It involves a learning process relying on a trail system, and it can be applied to any combinatorial optimization problem. Results are reported and discussed for a large set of instances (for (P1), (P2), and (P3)), and show the good performance of LTS. © 2014 Wiley Periodicals, Inc. 62:32–45, 2015