Probabilistic GRASP-Tabu Search algorithms for the UBQP problem

This paper presents two algorithms combining GRASP and Tabu Search for solving the Unconstrained Binary Quadratic Programming (UBQP) problem. We first propose a simple GRASP-Tabu Search algorithm working with a single solution and then reinforce it by introducing a population management strategy. Both algorithms are based on a dedicated randomized greedy construction heuristic and a tabu search procedure. We show extensive computational results on two sets of 31 large random UBQP instances and one set of 54 structured instances derived from the MaxCut problem. Comparisons with state-of-the-art algorithms demonstrate the efficacy of our proposed algorithms in terms of both solution quality and computational efficiency. It is noteworthy that the reinforced GRASP-Tabu Search algorithm is able to improve the previous best known results for 19 MaxCut instances.     

Honey bees mating optimization algorithm for the Euclidean traveling salesman problem

This paper introduces a new hybrid algorithmic nature inspired approach based on Honey Bees Mating Optimization for successfully solving the Euclidean Traveling Salesman Problem. The proposed algorithm for the solution of the Traveling Salesman Problem, the Honey Bees Mating Optimization (HBMOTSP), combines a Honey Bees Mating Optimization (HBMO) algorithm, the Multiple Phase Neighborhood Search-Greedy Randomized Adaptive Search Procedure (MPNS-GRASP) algorithm and the Expanding Neighborhood Search Strategy. Besides these two procedures, the proposed algorithm has, also, two additional main innovative features compared to other Honey Bees Mating Optimization algorithms concerning the crossover operator and the workers. The main contribution of this paper is that it shows that the HBMO can be used in hybrid synthesis with other metaheuristics for the solution of the TSP with remarkable results both to quality and computational efficiency. The proposed algorithm was tested on a set of 74 benchmark instances from the TSPLIB and in all but eleven instances the best known solution has been found. For the rest instances the quality of the produced solution deviates less than 0.1% from the optimum.     

Essential Particle Swarm Optimization queen with Tabu Search for MKP resolution

The Particle Swarm Optimization (PSO) algorithm is an innovative and promising optimization technique in evolutionary computation. The Essential Particle Swarm Optimization queen (EPSOq) is one of the recent discrete PSO versions that further simplifies the PSO principles and improves its optimization ability. Hybridization is a principle of combining two (or more) approaches in a wise way such that the resulting algorithm includes the positive features of both (or all) the algorithms. This paper proposes a new heuristic approach such that various features inspired from the Tabu Search are incorporated in the EPSOq algorithm in order to obtain another improved discrete PSO version. The implementation of this idea is identified with the acronym TEPSOq (Tabu Essential Particle Swarm Optimization queen). Experimentally, this approach is able to solve optimally large-scale strongly correlated 0–1 Multidimensional Knapsack Problem (MKP) instances. Computational results show that TEPSOq has outperforms not only the EPSOq, but also other existing PSO-based approaches and some other meta-heuristics in solving the 0–1 MKP. It was discovered also that this algorithm is able to locate solutions extremely close and even equal to the best known results available in the literature.     

Iterated Local Search for single-machine scheduling with sequence-dependent setup times to minimize total weighted tardiness

We present an Iterated Local Search (ILS) algorithm for solving the single-machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness. The proposed ILS algorithm exhibits several distinguishing features, including a new neighborhood structure called Block Move and a fast incremental evaluation technique, for evaluating neighborhood solutions. Applying the proposed algorithm to solve 120 public benchmark instances widely used in the literature, we achieve highly competitive results compared with a recently proposed exact algorithm and five sets of best solutions of state-of-the-art metaheuristic algorithms in the literature. Specifically, ILS obtains the optimal solutions for 113 instances within a reasonable time, and it outperforms the previous best-known results obtained by metaheuristic algorithms for 34 instances and matches the best results for 82 instances. In addition, ILS is able to obtain the optimal solutions for the remaining seven instances under a relaxed time limit, and its computational efficiency is comparable with the state-of-the-art exact algorithm by Tanaka and Araki (Comput Oper Res 40:344–352, 2013). Finally, on analyzing some important features that affect the performance of ILS, we ascertain the significance of the proposed Block Move neighborhood and the fast incremental evaluation technique.     

A hybrid clonal selection algorithm for the location routing problem with stochastic demands

In this paper, a new formulation of the Location Routing Problem with Stochastic Demands is presented. The problem is treated as a two phase problem where in the first phase it is determined which depots will be opened and which customers will be assigned to them while in the second phase, for each of the open depots a Vehicle Routing Problem with Stochastic Demands is solved. For the solution of the problem a Hybrid Clonal Selection Algorithm is applied, where, in the two basic phases of the Clonal Selection Algorithm, a Variable Neighborhood Search algorithm and an Iterated Local Search algorithm respectively have been utilized. As there are no benchmark instances in the literature for this form of the problem, a number of new test instances have been created based on instances of the Capacitated Location Routing Problem. The algorithm is compared with both other variants of the Clonal Selection Algorithm and other evolutionary algorithms.     

An iterated local search heuristic for the split delivery vehicle routing problem

This paper concerns the Split Delivery Vehicle Routing Problem (SDVRP). This problem is a relaxation of the Capacitated Vehicle Routing Problem (CVRP) since the customers׳ demands are allowed to be split. We deal with the cases where the fleet is unlimited (SDVRP-UF) and limited (SDVRP-LF). In order to solve them, we implemented a multi-start Iterated Local Search (ILS) based heuristic that includes a novel perturbation mechanism. Extensive computational experiments were carried out on benchmark instances available in the literature. The results obtained are highly competitive, more precisely, 55 best known solutions were equaled and new improved solutions were found for 243 out of 324 instances, with an average and maximum improvement of 1.15% and 2.81%, respectively.     

求解0-1二次规划问题的迭代禁忌搜索算法

提出迭代禁忌算法求解0-1二次规划问题。在局部搜索过程中,使用禁忌搜索贪心跳坑策略,能够使算法有效跳出局部最优值的陷阱。采用国际上公认的30个算例作为算法测试实验集,与传统的禁忌搜索、模拟退火算法以及混合算法进行比较。实验结果表明,该算法在所有算例上都能够得到文献中报告的最优解,且计算效率明显优于其他算法。     

Self Controlling Tabu Search algorithm for the Quadratic Assignment Problem

This paper addresses the application of the principles of feedback and self-controlling software to the tabu search algorithm. We introduce two new reaction strategies for the tabu search algorithm. The first strategy treats the tabu search algorithm as a target system to be controlled and uses a control-theoretic approach to adjust the algorithm parameters that affect search intensification. The second strategy is a flexible diversification strategy which can adjust the algorithm’s parameters based on the search history. These two strategies, combined with tabu search, form the Self Controlling Tabu Search (SC-Tabu) algorithm. The algorithm is implemented and tested on the Quadratic Assignment Problem (QAP). The results show that the self-controlling features of the algorithm make it possible to achieve good performance on different types of QAP instances.     

A Hybrid Multi-Swarm Particle Swarm Optimization algorithm for the Probabilistic Traveling Salesman Problem

The Probabilistic Traveling Salesman Problem (PTSP) is a variation of the classic Traveling Salesman Problem (TSP) and one of the most significant stochastic routing problems. In the PTSP, only a subset of potential customers need to be visited on any given instance of the problem. The number of customers to be visited each time is a random variable. In this paper, a new hybrid algorithmic nature inspired approach based on Particle Swarm Optimization (PSO), Greedy Randomized Adaptive Search Procedure (GRASP) and Expanding Neighborhood Search (ENS) Strategy is proposed for the solution of the PTSP. The proposed algorithm is tested on numerous benchmark problems from TSPLIB with very satisfactory results. Comparisons with the classic GRASP algorithm, the classic PSO and with a Tabu Search algorithm are also presented. Also, a comparison is performed with the results of a number of implementations of the Ant Colony Optimization algorithm from the literature and in 13 out of 20 cases the proposed algorithm gives a new best solution.     

A comparative study of heuristic algorithms on Economic Lot Scheduling Problem

The Economic Lot Scheduling Problem (ELSP) has been well-researched for more than 40 years. As the ELSP has been generally seen as NP-hard, researchers have focused on the development of efficient heuristic approaches. In this paper, we consider the time-varying lot size approach to solve the ELSP. A computational study of the existing solution algorithms, Dobson’s heuristic, Hybrid Genetic algorithm, Neighborhood Search heuristics, Tabu Search and the newly proposed Simulated Annealing algorithm are presented. The reviewed methods are first tested on two well-known problems, those of Bomberger’s [Bomberger, E. E. (1966). A dynamic programming approach to a lot size scheduling problem. Management Science 12, 778–784] and Mallya’s [Mallya, R (1992). Multi-product scheduling on a single machine: A case study. OMEGA: International Journal of Management Science 20, 529–534] problems. We show the Simulated Annealing algorithm finds the best known solution to these problems. A similar comparison study is performed on various problem sets previously suggested in the literature. The results show that the Simulated Annealing algorithm outperforms Dobson’s heuristic, Hybrid Genetic algorithm and Neighborhood search heuristics on these problem sets. The Simulated Annealing algorithm also shows faster convergence than the best known Tabu Search algorithm, yet results in solutions of a similar quality. Finally, we report the results of the design of experiment study which compares the robustness of the mentioned meta-heuristic techniques.     

Variable Neighborhood Search based algorithms for high school timetabling

This work presents the application of Variable Neighborhood Search (VNS) based algorithms to the High School Timetabling Problem. The addressed model of the problem was proposed by the Third International Timetabling Competition (ITC 2011), which released many instances from educational institutions around the world and attracted 17 competitors. Some of the VNS algorithm variants were able to outperform the winner of Third ITC solver, which proposed a Simulated Annealing – Iterated local Search approach. This result coupled with another reports in the literature points that VNS based algorithms are a practical solution method for providing high quality solutions for some hard timetabling problems. Moreover they are easy to implement with few parameters to adjust.     

Honey Bees Mating Optimization algorithm for large scale vehicle routing problems

Honey Bees Mating Optimization algorithm is a relatively new nature inspired algorithm. In this paper, this nature inspired algorithm is used in a hybrid scheme with other metaheuristic algorithms for successfully solving the Vehicle Routing Problem. More precisely, the proposed algorithm for the solution of the Vehicle Routing Problem, the Honey Bees Mating Optimization (HBMOVRP), combines a Honey Bees Mating Optimization (HBMO) algorithm with the Multiple Phase Neighborhood Search–Greedy Randomized Adaptive Search Procedure (MPNS–GRASP) and the Expanding Neighborhood Search (ENS) algorithm. Besides these two procedures, the proposed algorithm has, also, two additional main innovative features compared to other Honey Bees Mating Optimization algorithms concerning the crossover operator and the workers. Two sets of benchmark instances are used in order to test the proposed algorithm. The results obtained for both sets are very satisfactory. More specifically, in the fourteen classic instances proposed by Christofides, the average quality is 0.029% and in the second set with the twenty large scale vehicle routing problems the average quality is 0.40%.     

Tabu search vs. simulated annealing as a function of the size of quadratic assignment problem instances

Performance comparisons between algorithms have a long tradition in metaheuristic research. An early example is comparisons between Tabu Search (TS) and Simulated Annealing (SA) algorithms for tackling the Quadratic Assignment Problem (QAP). The results of these comparisons are to a certain extent inconclusive, even when focusing on only these two types of algorithms. While comparisons of SA and TS algorithms were based on rather small-sized instances, here we focus on possible dependencies of the relative performance between SA and TS algorithms on instance size. In fact, our experimental results show that the assertion whether one algorithm is better than the other can depend strongly on QAP instance size even if one focuses on instances with otherwise same characteristics.     

求解GCP问题的ILSBR算法

图着色问题（GCP,Graph Coloring Problem）是经典的NP-Hard组合优化问题之一。长期以来,人们一直在寻求快速、高效的启发式算法,以便在合理的计算时间内解决大规模问题。由于对规模较大的问题,目前的启发式算法尚不能在较短的时间内给出高质量的解,因此提出了一种基于全局最优解和局部最优解关系的ILS算法（ILSBR）。该算法的基本原理是通过对GCP问题的局部最优解和全局最优解之间关系的分析,发现对局部最优解的简单的相交操作能以很高的概率得到全局最优解的部分解。利用这些部分解构造一种新的扰动策略（RLG重着色）,并将其应用到传统的ILS算法中。在DIMACS标准集中,典型实例上的实验结果表明,采用RBILS算法在求解质量不变的情况下,求解速度上与目前的已知算法相比有较大的改进。     

Solving project scheduling problems with resource constraints via an event list-based evolutionary algorithm

There are various scheduling problems with resource limitations and constraints in the literature that can be modeled as variations of the Resource Constrained Project Scheduling Problem (RCPSP). This paper proposes a new solution representation and an evolutionary algorithm for solving the RCPSP. The representation scheme is based on an ordered list of events, that are sets of activities that start (or finish) at the same time. The proposed solution methodology, namely SAILS, operates on the event list and relies on a scatter search framework. The latter incorporates an Adaptive Iterated Local Search (AILS), as an improvement method, and integrates an event-list based solution combination method. AILS utilizes new enriched neighborhoods, guides the search via a long term memory and applies an efficient perturbation strategy. Computational results on benchmark instances of the literature indicate that both AILS and SAILS produce consistently high quality solutions, while the best results are derived for most problem data sets.     

Boosting learning and inference in Markov logic through metaheuristics

Markov Logic (ML) combines Markov networks (MNs) and first-order logic by attaching weights to first-order formulas and using these as templates for features of MNs. State-of-the-art structure learning algorithms in ML maximize the likelihood of a database by performing a greedy search in the space of structures. This can lead to suboptimal results because of the incapability of these approaches to escape local optima. Moreover, due to the combinatorially explosive space of potential candidates these methods are computationally prohibitive. We propose a novel algorithm for structure learning in ML, based on the Iterated Local Search (ILS) metaheuristic that explores the space of structures through a biased sampling of the set of local optima. We show through real-world experiments that the algorithm improves accuracy and learning time over the state-of-the-art algorithms. On the other side MAP and conditional inference for ML are hard computational tasks. This paper presents two algorithms for these tasks based on the Iterated Robust Tabu Search (IRoTS) metaheuristic. The first algorithm performs MAP inference and we show through extensive experiments that it improves over the state-of-the-art algorithm in terms of solution quality and inference time. The second algorithm combines IRoTS steps with simulated annealing steps for conditional inference and we show through experiments that it is faster than the current state-of-the-art algorithm maintaining the same inference quality.     

Hybrid metaheuristics for the Clustered Vehicle Routing Problem

The Clustered Vehicle Routing Problem (CluVRP) is a variant of the Capacitated Vehicle Routing Problem in which customers are grouped into clusters. Each cluster has to be visited once, and a vehicle entering a cluster cannot leave it until all customers have been visited. This paper presents two alternative hybrid metaheuristic algorithms for the CluVRP. The first algorithm is based on an Iterated Local Search algorithm, in which only feasible solutions are explored and problem-specific local search moves are utilized. The second algorithm is a hybrid genetic search, for which the shortest Hamiltonian path between each pair of vertices within each cluster should be precomputed. Using this information, a sequence of clusters can be used as a solution representation and large neighborhoods can be efficiently explored, by means of bi-directional dynamic programming, sequence concatenation, and appropriate data structures. Extensive computational experiments are performed on benchmark instances from the literature, as well as new large scale instances. Recommendations on the choice of algorithm are provided, based on average cluster size.     

Particle Swarm Optimization and Hill Climbing for the bandwidth minimization problem

In this paper, the problem of reducing the bandwidth of sparse matrices by permuting rows and columns is addressed and solved with a new hybrid heuristic which combines the Particle Swarm Optimization method with Hill Climbing (PSO-HC). This hybrid approach exploits a compact PSO in order to generate high-quality renumbering which is then refined by means of an efficient implementation of the HC local search heuristic. Computational experiments are carried out to compare the performance of PSO-HC with the well-known GPS algorithm, as well as some recently proposed methods, including WBRA, Tabu Search and GRASP_PR. PSO-HC proves to be extremely stable and reliable in finding good solutions to the bandwidth minimization problem, outperforming the currently known best algorithms in terms of solution quality, in reasonable computational time.     

Reconstructing permutation table to improve the Tabu Search for the PFSP on GPU

General-purpose computing on graphics processing unit (GPGPU) has been adopted to accelerate the running of applications which require long execution time in various problem domains. Tabu Search belonging to meta-heuristics optimization has been used to find a suboptimal solution for NP-hard problems within a more reasonable time interval. In this paper, we have investigated in how to improve the performance of Tabu Search algorithm on GPGPU and took the permutation flow shop scheduling problem (PFSP) as the example for our study. In previous approach proposed recently for solving PFSP by Tabu Search on GPU, all the job permutations are stored in global memory to successfully eliminate the occurrences of branch divergence. Nevertheless, the previous algorithm requires a large amount of global memory space, because of a lot of global memory access resulting in system performance degradation. We propose a new approach to address the problem. The main contribution of this paper is an efficient multiple-loop struct to generate most part of the permutation on the fly, which can decrease the size of permutation table and significantly reduce the amount of global memory access. Computational experiments on problems according with benchmark suite for PFSP reveal that the best performance improvement of our approach is about 100%, comparing with the previous work.     

Multiple Phase Neighborhood Search-GRASP for the Capacitated Vehicle Routing Problem

Greedy Randomized Adaptive Search Procedure (GRASP) has been proved to be a very efficient algorithm for the solution of the Traveling Salesman Problem. Also, it has been proved that expanding the local search with the use of two or more different local search strategies helps the algorithm to avoid trapping in a local optimum. In this paper, a new modified version of GRASP, called Multiple Phase Neighborhood Search-GRASP (MPNS-GRASP), for the solution of the Vehicle Routing Problem is proposed. In this method, a stopping criterion based on Lagrangean Relaxation and Subgradient Optimization is utilized. In addition, a different way for expanding the neighborhood search is used based on a new strategy, the Circle Restricted Local Search Moves strategy. The algorithm was tested on two sets of benchmark instances and gave very satisfactory results. In both sets of instances the results have solution qualities with average values near to the optimum values and in a number of them the algorithm finds the optimum. The computational time of the algorithm is decreased significantly compared to other heuristic and metaheuristic algorithms due to the fact that the new strategy, the Expanding Neighborhood Search Strategy, is used.