Metaheuristics for scheduling jobs with incompatible families on parallel batching machines

In this paper, we discuss the scheduling of jobs with incompatible families on parallel batching machines. The performance measure is total weighted tardiness. This research is motivated by a scheduling problem found in the diffusion and oxidation areas of semiconductor wafer fabrication where the machines can be modelled as parallel batch processors. Given that this scheduling problem is NP-hard, we suggest an ant colony optimization (ACO) and a variable neighbourhood search (VNS) approach. Both metaheuristics are hybridized with a decomposition heuristic and a local search scheme. We compare the performance of the two algorithms with that of a genetic algorithm (GA) based on extensive computational experiments. The VNS approach outperforms the ACO and GA approach with respect to time and solution quality.     

A Mixed Heuristic for Circuit Partitioning

As general-purpose parallel computers are increasingly being used to speed up different VLSI applications, the development of parallel algorithms for circuit testing, logic minimization and simulation, HDL-based synthesis, etc. is currently a field of increasing research activity. This paper describes a circuit partitioning algorithm which mixes Simulated Annealing (SA) and Tabu Search (TS) heuristics. The goal of such an algorithm is to obtain a balanced distribution of the target circuit among the processors of the multicomputer allowing a parallel CAD application for Test Pattern Generation to provide good efficiency. The results obtained indicate that the proposed algorithm outperforms both a pure Simulated Annealing and a Tabu Search. Moreover, the usefulness of the algorithm in providing a balanced workload distribution is demonstrated by the efficiency results obtained by a topological partitioning parallel test-pattern generator in which the proposed algorithm has been included. An extented algorithm that works with general graphs to compare our approach with other state of the art algorithms has been also included.     

A heterogeneous cooperative parallel search of branch-and-bound method and tabu search algorithm

In this study, we present a heterogeneous cooperative parallel search that integrates branch-and-bound method and tabu search algorithm. These two algorithms perform searches in parallel and cooperate by asynchronously exchanging information about the best solutions found and new initial solutions for tabu search. The rapid production of a good solution from the tabu search process provides the branch-and-bound process with a better feasible solution to accelerate the elimination of subproblems that do not contain an optimal solution. The new initial solution produced from the subproblem with a least-cost lower bound of the branch-and-bound method suggests the best potential area for tabu search to explore. We use a master-slave model to reduce the complexity of communication and enhance the performance of data exchange. A branch-and-bound process is used as the master process to control the exchange of information and the termination of computation. Several tabu search processes are executed simultaneously as the slave processes and cooperate by asynchronously exchanging information on the best solutions found and the new initial solutions by the master process of branch-and-bound. Based on the computation experiments of solving traveling salesman problems (TSP), the proposed heterogeneous parallel search algorithm outperforms a conventional parallel branch-and-bound method and a conventional parallel tabu search. We also present the computational results showing the efficiency of heterogeneous cooperative parallel search when we use more processors to accelerate search time. Thus, the proposed heterogeneous parallel search algorithm achieves linear accelerations.     

A Tabu Search Algorithm for the Quadratic Assignment Problem

Tabu search approach based algorithms are among the widest applied to various combinatorial optimization problems. In this paper, we propose a new version of the tabu search algorithm for the well-known problem, the quadratic assignment problem (QAP). One of the most important features of our tabu search implementation is an efficient use of mutations applied to the best solutions found so far. We tested this approach on a number of instances from the library of the QAP instances—QAPLIB. The results obtained from the experiments show that the proposed algorithm belongs to the most efficient heuristics for the QAP. The high efficiency of this algorithm is also demonstrated by the fact that the new best known solutions were found for several QAP instances.     

Implementation of parallel branch-and-bound algorithms – experiences with the graph partitioning problem

Parallel processing is one of the essential concepts in the attempts to increase the computational power available for solving continuous and discrete optimization problems. In the case where an optimization algorithm is search-based, crucial issues of parallel distributed implementations are work-load distribution and granularity, i.e. how to distribute the search space among processors and how to control the amount of processing between interprocessor communication. The present paper compares distributed implementations of two branch-and-bound algorithms for the graph partitioning problem: Given an undirected graph with an even number of edges and weights assigned to each edge, partition the vertices into two subsets of equal size such that the sum of the costs of edges connecting vertices in different subsets is as small as possible. The problem is known to be NP-complete. The two branch-and-bound methods compared differ in design strategy: One is based on time-consuming bound calculations leading to tight bounds and thus a narrow search tree with few nodes, whereas the other employs an easy bound calculation scheme leading to a larger search tree. Both have been implemented on an iPSC-hypercube with 32 processors. We investigate the influence of the design strategy on the performance of the algorithms.     

Parallel tabu search message-passing synchronous strategies for task scheduling under precedence constraints

This paper presents parallelization strategies for a tabu search algorithm for the task scheduling problem on heterogeneous processors under task precedence constraints. Parallelization relies exclusively on the decompostion of the solution space exploration. Four different parallel strategies are proposed and implemented on an asynchronous parallel machine under PVM: the master-slave model, with two different schemes for improved load balancing, and the single-program-multiple-data model, with single-token and multiple-token message passing schemes. The comparative analysis of these strategies shows that the tabu search approach for this problem is very suitable to the parallelization of the neighborhood search, with efficiency results almost always close to one for problems over a certain size.     

COSEARCH: A Parallel Cooperative Metaheuristic

In order to design a well-balanced metaheuristic for robustness, we propose the COSEARCH approach which manages the cooperation of complementary heuristic methods via an adaptive memory which contains a history of the search already done. In this paper, we present the idiosyncrasies of the COSEARCH approach and its application for solving large scale instances of the quadratic assignment problem (QAP). We propose an original design of the adaptive memory in order to focus on high quality regions of the search and avoid attractive but deceptive areas. For the QAP, we have hybridized three heuristic agents of complementary behaviours: a Tabu Search is used as the main search algorithm, a Genetic Algorithm is in charge of the diversification and a Kick Operator is applied to intensify the search. The evaluations have been executed on large scale network of workstations via a parallel environment which supports fault tolerance and adaptive dynamic scheduling of tasks.     

Adaptive Tabu Search for course timetabling

This paper presents an Adaptive Tabu Search algorithm (denoted by ATS) for solving a problem of curriculum-based course timetabling. The proposed algorithm follows a general framework composed of three phases: initialization, intensification and diversification. The initialization phase constructs a feasible initial timetable using a fast greedy heuristic. Then an adaptively combined intensification and diversification phase is used to reduce the number of soft constraint violations while maintaining the satisfaction of hard constraints. The proposed ATS algorithm integrates several distinguished features such as an original double Kempe chains neighborhood structure, a penalty-guided perturbation operator and an adaptive search mechanism. Computational results show the high effectiveness of the proposed ATS algorithm, compared with five reference algorithms as well as the current best known results. This paper also shows an analysis to explain which are the essential ingredients of the ATS algorithm.     

一种改进的禁忌搜索算法及其在连续全局优化中的应用

禁忌搜索算法是一种元启发式的全局优化算法,是局部搜索算法的一种推广,已被成功地应用于许多组合优化问题中。本文针对有界闭区域上的连续函数全局优化问题,提出了一种改进的禁忌搜索算法,并进行了理论分析和数值实验。数值实验表明,对于连续函数全局优化问题的求解该算法是可行有效的,并且结构简单,迭代次数较少,是一种较好的全局启发式优化算法。     

On the use of Monte Carlo simulation,cache and splitting techniques to improve the Clarke and Wright savings heuristics

This paper presents the SR-GCWS-CS probabilistic algorithm that combines Monte Carlo simulation with splitting techniques and the Clarke and Wright savings heuristic to find competitive quasi-optimal solutions to the Capacitated Vehicle Routing Problem (CVRP) in reasonable response times. The algorithm, which does not require complex fine-tuning processes, can be used as an alternative to other metaheuristics—such as Simulated Annealing, Tabu Search, Genetic Algorithms, Ant Colony Optimization or GRASP, which might be more difficult to implement and which might require non-trivial fine-tuning processes—when solving CVRP instances. As discussed in the paper, the probabilistic approach presented here aims to provide a relatively simple and yet flexible algorithm which benefits from: (a) the use of the geometric distribution to guide the random search process, and (b) efficient cache and splitting techniques that contribute to significantly reduce computational times. The algorithm is validated through a set of CVRP standard benchmarks and competitive results are obtained in all tested cases. Future work regarding the use of parallel programming to efficiently solve large-scale CVRP instances is discussed. Finally, it is important to notice that some of the principles of the approach presented here might serve as a base to develop similar algorithms for other routing and scheduling combinatorial problems.     

A Parallel Grasp for the Steiner Tree Problem in Graphs Using a Hybrid Local Search Strategy

In this paper, we present a parallel greedy randomized adaptive search procedure (GRASP) for the Steiner problem in graphs. GRASP is a two-phase metaheuristic. In the first phase, solutions are constructed using a greedy randomized procedure. Local search is applied in the second phase, leading to a local minimum with respect to a specified neighborhood. In the Steiner problem in graphs, feasible solutions can be characterized by their non-terminal nodes (Steiner nodes) or by their key-paths. According to this characterization, two GRASP procedures are described using different local search strategies. Both use an identical construction procedure. The first uses a node-based neighborhood for local search, while the second uses a path-based neighborhood. Computational results comparing the two procedures show that while the node-based variant produces better quality solutions, the path-based variant is about twice as fast. A hybrid GRASP procedure combining the two neighborhood search strategies is then proposed. Computational experiments with a parallel implementation of the hybrid procedure are reported, showing that the algorithm found optimal solutions for 45 out of 60 benchmark instances and was never off by more than 4% of the optimal solution value. The average speedup results observed for the test problems show that increasing the number of processors reduces elapsed times with increasing speedups. Moreover, the main contribution of the parallel algorithm concerns the fact that larger speedups of the same order of the number of processors are obtained exactly for the most difficult problems.     

A Hybrid Particle Swarm Optimization Algorithm for the Redundancy Allocation Problem

The Redundancy Allocation Problem generally involves the selection of components with multiple choices and redundancy levels that produce maximum system reliability given various system level constraints as cost and weight. In this paper we investigate the series–parallel redundant reliability problems, when a mixing of components was considered. In this type of problem both the number of redundancy components and the corresponding component reliability in each subsystem are to be decided simultaneously so as to maximise the reliability of system. A hybrid algorithm is based on particle swarm optimization and local search algorithm. In addition, we propose an adaptive penalty function which encourages our algorithm to explore within the feasible region and near feasible region, and discourage search beyond that threshold. The effectiveness of our proposed hybrid PSO algorithm is proved on numerous variations of three different problems and compared to Tabu Search and Multiple Weighted Objectives solutions.     

Tabu Search for Frequency Assignment in Mobile Radio Networks

The main goal of the Frequency Assignment Problem in mobile radio networks consists of assigning a limited number of frequencies to each radio cell in a cellular network while minimizing electromagnetic interference due to the reuse of frequencies. This problem, known to be NP-hard, is of great importance in practice since better solutions will allow a telecommunications operator to manage larger cellular networks. This paper presents a new Tabu Search algorithm for this application. The algorithm is tested on realistic and large problem instances and compared with other methods based on simulated annealing, constraint programming and graph coloring algorithms. Empirical evidence shows that the Tabu algorithm is very competitive by giving the best solutions to the tested instances.     

Branch-and-bound and parallel computation: A historical note

This historical note summarizes what we believe to have been the first use of parallel processing to solve a combinatorial optimization problem by a branch-and-bound algorithm. In 1975, a branch-and-bound algorithm for the traveling salesman problem that used p parallel processors with shared memory was simulated on a single processor. The results show that the simultaneous exploration of several nodes of the search tree yields better feasible solutions earlier. This allows earlier pruning of branches and significantly reduces the number of nodes searched.     

A multiple-tree search procedure for the resource-constrained project scheduling problem

For over three decades, researchers have sought effective solution procedures for PERT/CPM types of scheduling problems under conditions of limited resource availability. This paper presents a procedure for this problem which takes advantage of the emerging technology provided by multiple parallel processors to find and verify an optimal schedule for a project under conditions of multiple resource constraints. In our approach, multiple solutions trees are searched simultaneously in the quest for a minimum duration schedule. Global upper and lower bound information in common memory is shared among processors, enabling one or several processors to prune potentially significant portions of its search tree based upon bounds discovered by a processor using a different search tree. Computational experience is reported both for problems in which resources are available in constant amounts per period, as well as the much more difficult problem in which the resources available are allowed to vary over the schedule horizon (e.g., travel, sick leave, assignment to other tasks or projects, and so forth). The modular multiple-tree search procedure described in this paper is quite general, permitting most types of existing serial search strategies to be adapted to this approach where multiple processors are available.     

New heuristics for over-constrained flight to gate assignments

We consider the over-constrained Airport Gate Assignment Problem where the number of flights exceed the number of gates available, and where the objectives are to minimize the number of ungated flights and the total walking distances. The problem is formulated as a binary quadratic programming problem. We design a greedy algorithm and use a Tabu Search meta-heuristic to solve the problem. The greedy algorithm minimizes ungated flights while we devise a new neighbourhood search technique, the Interval Exchange Move, which allows us flexibility in seeking good solutions, especially when flight schedules are dense in time. Experiments conducted give good results.     

Solution of the Cumulative Assignment Problem With a Well-Structured Tabu Search Method

The Cumulative Assignment Problem is an NP-complete problem obtained by substituting the linear objective function of the classic Linear Assignment Problem, with a non-linear cumulative function. In this paper we present a first attempt to solve the Cumulative Assignment Problem with metaheuristic techniques. In particular we consider two standard techniques, namely the Simulated Annealing and the Multi-Start methods, and we describe the eXploring Tabu Search: a new structured Tabu Search algorithm which uses an iterative multi-level approach to improve the search. The new method is analyzed through extensive computational experiments and proves to be more effective than the standard methods.     

A random 1-011-011-01algorithm for depth first search

In this paper we present a fast parallel algorithm for constructing a depth first search tree for an undirected graph. The algorithm is anRNC algorithm, meaning that it is a probabilistic algorithm that runs in polylog time using a polynomial number of processors on aP-RAM. The run time of the algorithm isO(T _MM(n) log³ n), and the number of processors used isP _MM (n) whereT _MM(n) andP _MM(n) are the time and number of processors needed to find a minimum weight perfect matching on ann vertex graph with maximum edge weightn.This research was done while the first author was visiting the Mathematical Research Institute in Berkeley. Research supported in part by NSF grant 8120790.Supported by Air Force Grant AFOSR-85-0203A.     

A Tabu Search heuristic procedure in Markov chain bootstrapping

Markov chain theory is proving to be a powerful approach to bootstrap finite states processes, especially where time dependence is non linear. In this work we extend such approach to bootstrap discrete time continuous-valued processes. To this purpose we solve a minimization problem to partition the state space of a continuous-valued process into a finite number of intervals or unions of intervals (i.e. its states) and identify the time lags which provide “memory” to the process. A distance is used as objective function to stimulate the clustering of the states having similar transition probabilities. The problem of the exploding number of alternative partitions in the solution space (which grows with the number of states and the order of the Markov chain) is addressed through a Tabu Search algorithm. The method is applied to bootstrap the series of the German and Spanish electricity prices. The analysis of the results confirms the good consistency properties of the method we propose.     

Metaheuristic methods based on Tabu search for assigning judges to competitions

Two metaheuristic methods based on Tabu search are introduced to assign judges to individual competitions in a tournament. The complexity of the mathematical formulation accounting for the assignment rules, leads us to use such an approach. The first metaheuristic includes two different Tabu searches that are combined with a diversification strategy. The second metaheuristic is applied to a penalized version of the original model formulated as an assignment problem. This metaheuristic is also based on a Tabu search procedure including a diversification strategy driven by the constraints violated. Numerical results are provided to indicate the efficiency of the methods to generate very good solutions.