Local Neighborhood Search Research Articles

Matheuristics for the lot sizing problem with back-ordering, setup carry-overs, and non-identical machines

Abstract In this study, the capacitated lot-sizing problem (CLSP) with back-ordering, setup carry-overs between periods, and non-identical parallel machines (CLSP-BOPM) is considered. The problem is one of the most general extensions of the well-known economic lot scheduling problems (ELSPs). Three matheuristics are designed and implemented starting from the ideas of variable neighborhood local search, local branching, and feasibility pump (FP), adapted and improved by considering the specific characteristics of the problem. Algorithms are tested on a set of medium to large problem instances. The FP algorithm outperforms all other algorithms and two different mixed-integer programming solvers as it requires a shorter computational time. To test the robustness of the algorithm, tests on three particular cases of the general problem, belonging to the family of discrete ELSPs, have been performed. Results from the proposed solver and a known specific state-of-the-art algorithm demonstrate substantial improvements.

Quantum-inspired cuckoo co-search algorithm for no-wait flow shop scheduling

Minimizing the makespan in no-wait flow shop scheduling problem (NWFSP) is widely applied in various industries. However, it is a NP-hard problem. A novel quantum-inspired cuckoo co-search (QCCS) algorithm is proposed to solve this problem. The QCCS algorithm consists of the following three phases: 1) Quantum representation of solution. 2) A quantum-inspired cuckoo search-differential evolution (QCS-DE) search. 3) Local neighborhood search (LNS) algorithm. Meanwhile, the convergence property of the QCCS algorithm is analyzed theoretically. The Taguchi experiments are further designed for the calibration of parameters. The QCCS algorithm was performed on Rec and Car benchmark instances and compared with the state-of-the-art algorithms, including GA-VNS, HGA, TS-PSO, TMIIG, where the superiority of the proposed algorithm is verified by numerical analyses. In addition, the in-depth statistical analysis demonstrates the effectiveness of the proposed algorithm. The numerical results verify that the proposed algorithm has strong optimization ability and can effectively solve the NWFSP with small and medium scale.

Cophenetic Median Trees.

Median tree inference under path-difference metrics has shown great promise for large-scale phylogeny estimation. Similar to these metrics is the family of cophenetic metrics that originates from a classic dendrogram comparison method introduced more than 50 years ago. Despite the appeal of this family of metrics, the problem of computing median trees under cophenetic metrics has not been analyzed. Like other standard median tree problems relevant in practice, as we show here, this problem is also NP-hard. NP-hard median tree problems have been successfully addressed by local search heuristics that are solving thousands of instances of a corresponding (local neighborhood) search problem. For the local neighborhood search problem under a cophenetic metric, the best known (naïve) algorithm has a time complexity that is typically prohibitive for effective heuristic searches. Building on the pioneering work on path-difference median trees, we develop efficient algorithms for Manhattan and Euclidean cophenetic search problems that improve on the naïve solution by a linear and a quadratic factor, respectively. We demonstrate the performance and effectiveness of the resulting heuristic methods in a comparative study using benchmark empirical datasets.

Delivering meals for multiple suppliers: Exclusive or sharing logistics service

We study a meal delivery problem faced by some logistics providers, which need to route vehicles in multiple trips to pick up meals from multiple suppliers and deliver to customers. Three types of logistics services are investigated: exclusive service and two novel sharing services. The delivery problems broadly belong to multi-trip routing with soft time windows and multiple refill locations. We develop two mainstream heuristics, iterated local search and adaptive large neighborhood search. Extensive case studies are conducted based on large-sized real-world instances. Managerial analysis shows that two sharing services generally yield much less total costs than the exclusive service.

Routing a mix of conventional, plug-in hybrid, and electric vehicles

We introduce an electric vehicle routing problem combining conventional, plug-in hybrid, and electric vehicles. Electric vehicles are constrained in their service range by their battery capacity, and may require time-consuming recharging operations at some specific locations. Plug-in hybrid vehicles have two engines, an internal combustion engine and an electric engine using a built-in rechargeable battery. These vehicles can avoid visits to recharging stations by switching to fossil fuel. However, this flexibility comes at the price of a generally higher consumption rate and utility cost.To solve this complex problem variant, we design a sophisticated metaheuristic which combines a genetic algorithm with local and large neighborhood search. All route evaluations, within the approach, are based on a layered optimization algorithm which combines labeling techniques and greedy evaluation policies to insert recharging stations visits in a fixed trip and select the fuel types. The metaheuristic is finally hybridized with an integer programming solver, over a set partitioning formulation, so as to recombine high-quality routes from the search history into better solutions. Extensive experimental analyses are conducted, highlighting the good performance of the algorithm and the contribution of each of its main components. Finally, we investigate the impact of fuel and energy cost on fleet composition decisions. Our experiments show that a careful use of a mixed fleet can significantly reduce operational costs in a large variety of price scenarios, in comparison with the use of a fleet composed of a single vehicle class.

Scheduling of elective patients considering upstream and downstream units and emergency demand using robust optimization

Abstract Surgery is a vital process in Healthcare Centers (HCs). The importance of a surgery department is not only due to its direct impact on the health but also due to its high impact on the income and costs of HCs. Considering the upward trend of population aging in societies, increasing demand for surgery, and limited resources of HCs, providing an efficient schedule for Operating Room (OR) is essential. In this paper, a multi-objective mathematical model is proposed considering upstream and downstream units. The proposed model consists of three objectives in which the first one minimizes the number of deferred patients to the next planning horizon. The second one minimizes the waiting cost of scheduled patients and the cost of extra beds acquired in the ward, and the last one minimizes the idleness and overtime of ORs, lateness in operating children and earliness in operating patients far from HC. Then, the robust counterpart is proposed to evaluate some uncertain parameters, such as surgery t, Length of Stay (LoS) in upstream and downstream units and emergency demand. Since this problem is NP-hard, a new Mixed Integer Programming based Local Search Neighborhood (MIP-based LNS) algorithm is applied. Afterward, the effect of increasing number of slots on the CPU time is studied using a sensitivity analysis. Finally, a real case study entitled ‘Alborz Hospital’ is investigated. The obtained results show that applying the proposed model and increasing two beds in the Intensive Care Unit (ICU) could potentially decrease the number of deferred patients by 58.33% as compared to the traditional schedule (i.e., a schedule based on trial and error). Furthermore, the average idleness of ORs could be reduced by 36.58% as compared to the traditional schedule.

Integrated physician and clinic scheduling in ambulatory polyclinics

This paper presents an integrated physician and clinic scheduling problem arising in ambulatory cancer treatment polyclinics, where patients may be assessed by multiple physicians from different clinics in a single visit. The problem focuses on assigning clinic sessions and their associated physicians to shifts in a finite planning horizon. The complexity of this problem stems from the fact that several interdisciplinary clinics need to be clustered together, sharing limited resources. The problem is formulated as a multi-objective optimisation problem. Given the inherent complexity for optimally solving this problem with a standard optimisation software, we develop a hybrid algorithm based on iterated local search and variable neighbourhood descent methods to obtain high quality solutions. Computational results using a set of instances inspired from a case study in a hospital in Canada along with some managerial insights are reported and analysed.

A Differential Evolution Performance Comparison: Comparing How Various Differential Evolution Algorithms Perform in Designing Microstrip Antennas and Arrays

In this article, we have undertaken a performance comparison of different variants and hybridized schemes of differential evolution (DE) algorithms with respect to several antenna and array designs. These include DE/rand/1, self-adaptive DE (SADE), DE with global and local neighborhood search (DEGL), biogeography-based optimization with DE (BBODE), modified DE (MDE), MDE with p-best crossover strategy (MDE-pBX), improved DE (IDE), harmonic search DE (HSDE), DE with an individual dependent mechanism (DE-IDP-IDM), and adaptive DE with optimization-state estimation (ADE).

Large neighbourhood search with adaptive guided ejection search for the pickup and delivery problem with time windows

An effective and fast hybrid metaheuristic is proposed for solving the pickup and delivery problem with time windows. The proposed approach combines local search, large neighbourhood search and guided ejection search in a novel way to exploit the benefits of each method. The local search component uses a novel neighbourhood operator. A streamlined implementation of large neighbourhood search is used to achieve an effective balance between intensification and diversification. The adaptive ejection chain component perturbs the solution and uses increased or decreased computation time according to the progress of the search. While the local search and large neighbourhood search focus on minimising travel distance, the adaptive ejection chain seeks to reduce the number of routes. The proposed algorithm design results in an effective and fast solution method that finds a large number of new best-known solutions on a well-known benchmark dataset. Experiments are also performed to analyse the benefits of the components and heuristics and their combined use to achieve a better understanding of how to better tackle the subject problem.

Relaxation heuristics for the set multicover problem with generalized upper bound constraints

We consider an extension of the set covering problem (SCP) introducing (i) multicover and (ii) generalized upper bound (GUB) constraints. For the conventional SCP, the pricing method has been introduced to reduce the size of instances, and several efficient heuristic algorithms based on such reduction techniques have been developed to solve large-scale instances. However, GUB constraints often make the pricing method less effective, because they often prevent solutions from containing highly evaluated variables together. To overcome this problem, we develop heuristic algorithms to reduce the size of instances, in which new evaluation schemes of variables are introduced taking account of GUB constraints. We also develop an efficient implementation of a 2-flip neighborhood local search algorithm that reduces the number of candidates in the neighborhood without sacrificing the solution quality. In order to guide the search to visit a wide variety of good solutions, we also introduce a path relinking method that generates new solutions by combining two or more solutions obtained so far. According to computational comparison on benchmark instances, the proposed method succeeds in selecting a small number of promising variables properly and performs quite effectively even for large-scale instances having hard GUB constraints.

Three pseudo-utility ratio-inspired particle swarm optimization with local search for multidimensional knapsack problem

Abstract In this study, a three-ratio self-adaptive check and repair operator-inspired particle swarm optimization (3R-SACRO-PSO) with neighborhood local search is developed to solve the multidimensional knapsack problem (MKP). The proposed 3R-SACRO-PSO systematically alters substitute pseudo-utility ratios as the PSO method is executed. In addition, a local search scheme is introduced to improve solution quality. The proposed 3R-SACRO-PSO algorithm is tested using 168 different widely used benchmarks from the OR-Library to demonstrate and validate its performance. The control parameters for the performance test are determined through the Taguchi method. Experimental results parallel those of other PSO algorithms, and statistical test results show that the quality and efficiency of the proposed 3R-SACRO are better than those of the two-ratio SACRO method. Moreover, the proposed 3R-SACRO-PSO is on par with state-of-the-art PSO approaches. Thus, introducing the third pseudo-utility ratio into SACRO improves the performance of SACRO-based PSO. The neighborhood local search scheme further improves the solution quality in handling MKPs.

Evolutionary Hybrid Particle Swarm Optimization Algorithm for Solving NP-Hard No-Wait Flow Shop Scheduling Problems

The no-wait flow shop is a flowshop in which the scheduling of jobs is continuous and simultaneous through all machines without waiting for any consecutive machines. The scheduling of a no-wait flow shop requires finding an appropriate sequence of jobs for scheduling, which in turn reduces total processing time. The classical brute force method for finding the probabilities of scheduling for improving the utilization of resources may become trapped in local optima, and this problem can hence be observed as a typical NP-hard combinatorial optimization problem that requires finding a near optimal solution with heuristic and metaheuristic techniques. This paper proposes an effective hybrid Particle Swarm Optimization (PSO) metaheuristic algorithm for solving no-wait flow shop scheduling problems with the objective of minimizing the total flow time of jobs. This Proposed Hybrid Particle Swarm Optimization (PHPSO) algorithm presents a solution by the random key representation rule for converting the continuous position information values of particles to a discrete job permutation. The proposed algorithm initializes population efficiently with the Nawaz-Enscore-Ham (NEH) heuristic technique and uses an evolutionary search guided by the mechanism of PSO, as well as simulated annealing based on a local neighborhood search to avoid getting stuck in local optima and to provide the appropriate balance of global exploration and local exploitation. Extensive computational experiments are carried out based on Taillard’s benchmark suite. Computational results and comparisons with existing metaheuristics show that the PHPSO algorithm outperforms the existing methods in terms of quality search and robustness for the problem considered. The improvement in solution quality is confirmed by statistical tests of significance.

Effective local search algorithms for high school timetabling problems

This paper addresses the high school timetabling problem. The problem consists in building weekly timetables for meetings between classes and teachers with the goal of minimizing violations of specific requirements. In the last decades, several mixed-integer programs have been proposed and tested for this family of problems. However, medium and large size instances are still not effectively solved by these programs using state-of-the-art solvers and the scientific community has given special attention to the devising of alternative soft computing algorithms. In this paper, we propose a soft computing approach based on Iterated Local Search and Variable Neighborhood Search metaheuristic frameworks. Our algorithms incorporate new neighborhood structures and local search routines to perform an effective search. We validated the proposed algorithms on variants of the problem using seven public instances and a new dataset with 34 real-world instances including large cases. The results demonstrate that the proposed algorithms outperform the state-of-the-art approaches in both cases, finding the best solutions in 38 out of the 41 tested instances.

Multi-objective fuzzy flexible job shop scheduling using memetic algorithm

ABSTRACTMulti-objective flexible job shop scheduling problem with fuzzy processing time and fuzzy due date is a complicated combinatorial optimization problem. In this paper, a genetic global optimization is combined with a local search method to construct an effective memetic algorithm (MA) for simultaneously optimizing fuzzy makespan, average agreement index and minimal agreement index. First, a hybridization of different machine assignment methods with different operation sequence rules is proposed to generate a high-performance initial population. Second, the algorithm framework similar to the non-dominated sorting genetic algorithm II (NSGA-II) is adopted, in which a well-designed chromosome decoding method and two effective genetic operators are used. Then, a novel fuzzy Pareto dominance relationship based on the possibility degree and a modified crowding distance measure are defined and further employed to modify the fast non-dominated sorting. Next, a novel local search is incorporated into NSGA-II, where some candidate individuals are selected from the offspring population to experience variable neighbourhood local search by using the selection mechanism. In the experiment, the influence of four key parameters is investigated based on the Taguchi method of design of experiment. Finally, some comparisons are carried out with other existing algorithms on benchmark instances, and demonstrate the effectiveness of the proposed MA.

Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs

We present a data mining approach for reducing the search space of local search algorithms in a class of binary integer programs including the set covering and partitioning problems. The quality of locally optimal solutions typically improves if a larger neighborhood is used, while the computation time of searching the neighborhood increases exponentially. To overcome this, we extract variable associations from the instance to be solved in order to identify promising pairs of flipping variables in the neighborhood search. Based on this, we develop a 4-flip neighborhood local search algorithm that incorporates an efficient incremental evaluation of solutions and an adaptive control of penalty weights. Computational results show that the proposed method improves the performance of the local search algorithm for large-scale set covering and partitioning problems.

Linear classifier design under heteroscedasticity in Linear Discriminant Analysis

Under normality and homoscedasticity assumptions, Linear Discriminant Analysis (LDA) is known to be optimal in terms of minimising the Bayes error for binary classification. In the heteroscedastic case, LDA is not guaranteed to minimise this error. Assuming heteroscedasticity, we derive a linear classifier, the Gaussian Linear Discriminant (GLD), that directly minimises the Bayes error for binary classification. In addition, we also propose a local neighbourhood search (LNS) algorithm to obtain a more robust classifier if the data is known to have a non-normal distribution. We evaluate the proposed classifiers on two artificial and ten real-world datasets that cut across a wide range of application areas including handwriting recognition, medical diagnosis and remote sensing, and then compare our algorithm against existing LDA approaches and other linear classifiers. The GLD is shown to outperform the original LDA procedure in terms of the classification accuracy under heteroscedasticity. While it compares favourably with other existing heteroscedastic LDA approaches, the GLD requires as much as 60 times lower training time on some datasets. Our comparison with the support vector machine (SVM) also shows that, the GLD, together with the LNS, requires as much as 150 times lower training time to achieve an equivalent classification accuracy on some of the datasets. Thus, our algorithms can provide a cheap and reliable option for classification in a lot of expert systems.

Systematic Exploration of Larger Local Search Neighborhoods for the Minimum Vertex Cover Problem

We investigate the potential of exhaustively exploring larger neighborhoods in local search algorithms for Minimum Vertex Cover. More precisely, we study whether, for moderate values of k, it is feasible and worthwhile to determine, given a graph G with vertex cover C, if there is a k-swap S such that (C ∖ S) ∪ (S ∖ C) is a smaller vertex cover of G. First, we describe an algorithm running in ∆O(k) ⋅ n time for searching the k-swap neighborhood on n-vertex graphs with maximum degree ∆. Then, we demonstrate that, by devising additional pruning rules that decrease the size of the search space, this algorithm can be implemented so that it solves the problem quickly for k ≈ 20. Finally, we show that it is worthwhile to consider moderately-sized k-swap neighborhoods. For our benchmark data set, we show that when combining our algorithm with a hill-climbing approach, the solution quality improves quickly with the radius k of the local search neighborhood and that in most cases optimal solutions can be found by setting k=21.

Elite Opposition-Based Water Wave Optimization Algorithm for Global Optimization

Water wave optimization (WWO) is a novel metaheuristic method that is based on shallow water wave theory, which has simple structure, easy realization, and good performance even with a small population. To improve the convergence speed and calculation precision even further, this paper on elite opposition-based strategy water wave optimization (EOBWWO) is proposed, and it has been applied for function optimization and structure engineering design problems. There are three major optimization strategies in the improvement: elite opposition-based (EOB) learning strategy enhances the diversity of population, local neighborhood search strategy is introduced to enhance local search in breaking operation, and improved propagation operator provides the improved algorithm with a better balance between exploration and exploitation. EOBWWO algorithm is verified by using 20 benchmark functions and two structure engineering design problems and the performance of EOBWWO is compared against those of the state-of-the-art algorithms. Experimental results show that the proposed algorithm has faster convergence speed, higher calculation precision, with the exact solution being even obtained on some benchmark functions, and a higher degree of stability than other comparative algorithms.

Approach of hybrid GA for multi-objective job-shop scheduling

In recent years, scholars have made many research results on job-shop scheduling (JSP) problem, especially in single objective such as the maximum completion time. But most of the actual system scheduling problems are more than one object. Therefore, the research of multi-objective scheduling problem is very important and meaningful. In this paper, we proposed a multi-objective scheduling model which adopts weighted sum method to optimize two important indexes (makespan and total flow time). Genetic algorithm (GA) has diversified global search ability, while simulated annealing (SA) combined with tabu search (TS) have intensified capabilities in local neighborhood search. To overcome the drawback of the GA, we proposed a new hybrid GA (NewHGA) which produces initial solutions by GA firstly, and then take SA operator incorporate TS operator to search in the local space. By adding the novel local search strategy, the diversity of solutions will be improved greatly so that it can ensure the algorithm jump out of the local optimal value. We test this algorithm using the benchmark instances of different sizes taken from the OR-Library, and the results show that the algorithm is efficient than another hybrid algorithm.

Stability Analysis of Runway Schedules

By performing stability analysis on an optimal runway schedule, this paper derives a method to determine whether an optimized landing sequence of aircraft remains optimal after an arbitrary number of aircraft in that sequence are delayed by an arbitrary amount of time. We consider the problem of scheduling aircraft landing on a single runway with the objective of maximizing throughput under changing external conditions such as delays caused by weather. Instead of optimizing the schedule every time delays occur, stability criteria allow for fast evaluation of whether schedules remain optimal. This paper develops a method to compute stability regions for a set of schedules. Sensitivity analysis of the linear programming relaxation and a nonlinear relationship between the delay of individual aircraft and the incurred cost change for all landing sequences yield the stability information. Furthermore, the properties of a first-come–first-serve policy are studied by giving sufficient conditions and a heuristic condition for the optimality of first-come–first-serve sequences. The given results are shown to be also applicable to landing sequences obtained through local neighborhood search, sequences that obey a position shift constraint, and subsequences of landing sequences as used in a rolling horizon approach.