Depth-first Branch Research Articles

HMDS: A Makespan Minimizing DAG Scheduler for Heterogeneous Distributed Systems

The problem of scheduling Directed Acyclic Graphs in order to minimizemakespan(schedule length), is known to be a challenging and computationally hard problem. Therefore, researchers have endeavored towards the design of various heuristic solution generation techniques both for homogeneous as well as heterogeneous computing platforms. This work first presentsHMDS-Bl, a list-based heuristicmakespanminimization algorithm for task graphs on fully connected heterogeneous platforms. Subsequently,HMDS-Blhas been enhanced by empowering it with a low-overhead depth-first branch and bound based search approach, resulting in a new algorithm calledHMDS.HMDShas been equipped with a set of novel tunable pruning mechanisms, which allow the designer to obtain a judicious balance between performance (makespan) and solution generation times, depending on the specific scenario at hand. Experimental analyses using randomly generated DAGs as well as benchmark task graphs, have shown thatHMDSis able to comprehensively outperform state-of-the-art algorithms such asHEFT,PEFT,PPTS, etc., in terms of archivedmakespanswhile incurring bounded additional computation time overhead.

Toward a Search Strategy for Anytime Search in Linear Space Using Depth-First Branch and Bound

Depth-First Branch and Bound (DFBnB) is an anytime algorithm for solving combinatorial optimization problems. In this paper we present a weighted version of DFBnB, wDFBnB, which incorporates standard techniques for using weights in heuristic search and offers suboptimality guarantees. Our main contribution drawn from a preliminary evaluation is the observation that wDFBnB, used along with automated or hand-crafted weight schedules, can significantly outperform DFBnB both in terms of anytime behavior and convergence to the optimal. We think this small study calls for more research on the design of automated weight schedules that could provide superior anytime performance across a wider range of domains.

Anytime AND/OR Depth-First Search for Combinatorial Optimization

One popular and efficient scheme for solving exactly combinatorial optimization problems over graphical models is depth-first Branch and Bound. However, when the algorithm exploits problem decomposition using AND/OR search spaces, its anytime behavior breaks down. This paper 1) analyzes and demonstrates this inherent conflict between effective exploitation of problem decomposition (through AND/OR search spaces) and the anytime behavior of depth-first search (DFS), 2) presents a first scheme to address this issue while maintaining desirable DFS memory properties, 3) analyzes and demonstrates its effectiveness. Our work is applicable to any problem that can be cast as search over an AND/OR search space.

UAVs vs. Pirates

For the rising hazard of pirate attacks, unmanned aerial vehicle (UAV) swarm monitoring is a promising countermeasure. Previous monitoring methods have deficiencies in either adaptivity to dynamic events or simple but effective path coordination mechanisms, and they are inapplicable to the large-area, low-target-density, and long-duration persistent counter-piracy monitoring. This article proposes a self-organized UAV swarm counter-piracy monitoring method. Based on the pheromone map, this method is characterized by (1) a reservation mechanism for anticipatory path coordination and (2) a ship-adaptive mechanism for adapting to merchant ship distributions. A heuristic depth-first branch and bound search algorithm is designed for solving individual path planning. Simulation experiments are conducted to study the optimal number of plan steps and adaptivity scaling factor for different numbers of UAVs. Results show that merely decreasing revisit intervals cannot effectively reduce pirate attacks. Without the ship-adaptive mechanism, the proposed method reduces up to 87.2%, 43.2%, and 5.5% of revisit intervals compared to the Lèvy Walk method, the sweep method, and the baseline self-organized method, respectively, but cannot reduce pirate attacks; while with the ship-adaptive mechanism, the proposed method can reduce pirate attacks by up to 6.7% compared to the best of the baseline methods.

Optimal switching of switched systems with time delay in discrete time

This paper addresses a kind of optimal switching problem to minimize a quadratic cost functional for the discrete-time switched linear system with time delay. Since the dynamics is influenced by the switching sequence and the time delay, most existing gradient-based methods and relaxation techniques cannot be applied. In order to find the optimal solution, we first formulate the switched time-delay system into an equivalent switched system to separate the cross term of coefficient matrices. Based on the positive semi-definiteness of the system, we derive a series of lower bounds of the cost functional. By comparing them with the current optimal value, a depth-first branch and bound technique is proposed and the global optimal solution can be exactly obtained. Some numerical examples are demonstrated to verify the high efficiency of the method.

Job Shop Scheduling by Branch and Bound Using Genetic Programming

A classical depth-first branch and bound (BB) method is adopted to minimize the makespan of job shops based on the disjunctive graph model. The engine of the BB is Giffler-Thompson’s active schedule generation method. The performance of the BB method highly depends on the selection of child nodes in earlier branching stages. To support the selection decision, several features of nodes are stored under the BB method, and the correct selection at each branching stage is informed by the mixed-integer linear programming model. The stored data of a test problem instance is analyzed by genetic programming (GP) to generate rules for selecting the correct nodes. The depth-first BB method guided by the generated rules by GP is applied for 42 benchmark instances and exhibits competitive performance when compared with the baseline rule that always selects the child node with the smallest lower bound on makespan.

Sport Tournament Automated Scheduling System

The organizer of sport events often facing problems such as wrong calculations of marks and scores, as well as difficult to create a good and reliable schedule. Most of the time, the issues about the level of integrity of committee members and also issues about errors made by human came into the picture. Therefore, the development of sport tournament automated scheduling system is proposed. The system will be able to automatically generate the tournament schedule as well as automatically calculating the scores of each tournament. The problem of scheduling the matches of a round robin and knock-out phase in a sport league are given focus. The problem is defined formally and the computational complexity is being noted. A solution algorithm is presented using a two-step approach. The first step is the creation of a tournament pattern and is based on known graph-theoretic method. The second one is an assignment problem and it is solved using a constraint based depth-first branch and bound procedure that assigns actual teams to numbers in the pattern. As a result, the scheduling process and knock down phase become easy for the tournament organizer and at the same time increasing the level of reliability.

Coalition Structure Generation Utilizing Graphical Representation of Partition Function Games

Forming effective coalition is a central research challenge in AI and multi-agent systems. The Coalition Structure Generation (CSG) problem is well-known as one of major research topics in coalitional games. The CSG problem is to partition a set of agents into coalitions so that the sum of utilities is maximized. This paper studies a CSG problem for partition function games (PFGs), where the value of a coalition differs depending on the formation of other coalitions generated by non-member agents. Traditionally, in PFGs, the input of a coalitional game is a black-box function called a partition function that maps an embedded coalition (a coalition and the coalition structure) to its value. Recently, a novel concise representation scheme called the Partition Decision Trees (PDTs) has been proposed. The PDTs is a graphical representation based on multiple rules. In this paper, we propose new algorithms that can solve a CSG problem by utilizing PDTs representation. More specifically, we modify PDTs representation to effectively handle negative value rules and apply the depth-first branch and bound algorithm. We experimentally show that our algorithm can solve a CSG problem well.

Searching for the M Best Solutions in Graphical Models

The paper focuses on finding the m best solutions to combinatorial optimization problems using best-first or depth-first branch and bound search. Specifically, we present a new algorithm m-A*, extending the well-known A* to the m-best task, and for the first time prove that all its desirable properties, including soundness, completeness and optimal efficiency, are maintained. Since best-first algorithms require extensive memory, we also extend the memory-efficient depth-first branch and bound to the m-best task. We adapt both algorithms to optimization tasks over graphical models (e.g., Weighted CSP and MPE in Bayesian networks), provide complexity analysis and an empirical evaluation. Our experiments confirm theory that the best-first approach is largely superior when memory is available, but depth-first branch and bound is more robust. We also show that our algorithms are competitive with related schemes recently developed for the m-best task.

Memory limited algorithms for optimal task scheduling on parallel systems

To fully benefit from a multi-processor system, tasks need to be scheduled optimally. Given that the task scheduling problem with communication delays, P|prec,cij|Cmax, is a well known strong NP-hard problem, exhaustive approaches are necessary. The previously proposed A* based algorithm retains its entire state space in memory and often runs out of memory before it finds an optimal solution. This paper investigates and proposes two memory limited optimal scheduling algorithms: Iterative Deepening A* (IDA*) and Depth-First Branch and Bound A* (BBA*). When finding a guaranteed near optimal schedule length is sufficient, the proposed algorithms can be combined, reporting the gap while they run. Problem specific pruning techniques, which are crucial for good performance, are studied for the two proposed algorithms. Extensive experiments are conducted to evaluate and compare the proposed algorithms with previous optimal algorithms.

Weighted heuristic anytime search: new schemes for optimization over graphical models

Weighted heuristic search (best-first or depth-first) refers to search with a heuristic function multiplied by a constant w [31]. The paper shows, for the first time, that for optimization queries in graphical models the weighted heuristic best-first and weighted heuristic depth-first branch and bound search schemes are competitive energy-minimization anytime optimization algorithms. Weighted heuristic best-first schemes were investigated for path-finding tasks. However, their potential for graphical models was ignored, possibly because of their memory costs and because the alternative depth-first branch and bound seemed very appropriate for bounded depth. The weighted heuristic depth-first search has not been studied for graphical models. We report on a significant empirical evaluation, demonstrating the potential of both weighted heuristic best-first search and weighted heuristic depth-first branch and bound algorithms as approximation anytime schemes (that have sub-optimality bounds) and compare against one of the best depth-first branch and bound solvers to date.

Maximum-likelihood detection based on branch and bound algorithm for MIMO systems

Maximum likelihood detection for MIMO systems can be formulated as an integer quadratic programming problem. In this paper, we introduce depth-first branch and bound algorithm with variable dichotomy into MIMO detection. More nodes may be pruned with this structure. At each stage of the branch and bound algorithm, active set algorithm is adopted to solve the dual subproblem. In order to reduce the complexity further, the Cholesky factorization update is presented to solve the linear system at each iteration of active set algorithm efficiently. By relaxing the pruning conditions, we also present the quasi branch and bound algorithm which implements a good tradeoff between performance and complexity. Numerical results show that the complexity of MIMO detection based on branch and bound algorithm is very low, especially in low SNR and large constellations.

Effective algorithm for handling constraints in generator maintenance scheduling

An effective algorithm for handling constraints to solve the generator maintenance scheduling (GMS) problem is presented. The proposed algorithm of constraint logic programming (CLP) synthesises logic programming, constraint satisfaction technique (CST), and branch and bound search schemes to provide an efficient and flexible approach to the problem. The constraints of the problem cannot only be conveniently managed by the logic programming but also be actively used to reduce the search space by the CST. Once the infeasible solutions are pruned away from the search space, the depth-first branch and bound search strategy is then used for determining the optimal solution. The practical GMS problem of Taiwan Power (Taipower) system is solved by the proposed CLP algorithm for demonstrating its effectiveness. To exhibit the efficiency of the proposed algorithm, the results obtained are compared with those from the established methods of simulated annealing (SA) and lagrangian relaxation (LR).

Solving Vehicle Routing Problems Using Constraint Programming and Metaheuristics

Constraint Programming typically uses the technique of depth-first branch and bound as the method of solving optimization problems. Although this method can give the optimal solution, for large problems, the time needed to find the optimal can be prohibitive. This paper introduces a method for using local search techniques within a Constraint Programming framework, and applies this technique to vehicle routing problems. We introduce a Constraint Programming model for vehicle routing, and a system for integrating Constraint Programming and local search techniques. We then describe how the method can be accelerated by handling core constraints using fast local checks, while other more complex constraints are left to the constraint propagation system. We have coupled our local search method with a meta-heuristic to avoid the search being trapped in local minima. Several meta-heuristics are investigated ranging from a simple Tabu Search method to Guided Local Search. An empirical study over benchmark problems shows the relative merits of these techniques. Investigations indicate that the specific long-term memory technique used by Guided Local Search can be used as a diversification method for Tabu Search, resulting in significant benefit. Several new best solutions on the Solomon problems are found in relatively few iterations of our algorithm.

Scheduling Sport Tournaments using Constraint Logic Programming

We tackle the problem of scheduling the matches of a round robin tournament for a sport league. We formally define the problem, state its computational complexity, and present a solution algorithm using a two-step approach. The first step is the creation of a tournament pattern and is based on known graph-theoretic results. The second one is an assignment problem and it is solved using a constraint-based depth-first branch and bound procedure that assigns actual teams to numbers in the pattern. The procedure is implemented using the finite domain library of the constraint logic programming language \eclipse. Experimental results show that, in practical cases, the optimal solution of the assignment problem (which is not necessarily optimal for the overall problem) can be found in reasonable time, despite the fact that the problem is NP-complete. In addition, a local search procedure has been developed in order to provide, when necessary, an approximate solution in shorter time.

A new thermal unit commitment approach using constraint logic programming

The authors propose a constraint logic programming (CLP) algorithm to solve the thermal unit commitment (UC) problem in this paper. The algorithm combines the characteristics of the logic programming with the constraint satisfaction as well as the depth-first branch and bound search techniques to provide an efficient and flexible approach to the UC problem. Through the constraint satisfaction techniques, the constraints, which consist of the upper bound on the objective value, are propagated as much as possible to actively reduce the search space of the UC problem in a priori way. Consequently, the optimal solution can be acquired in a very early stage. To demonstrate the effectiveness of the proposed approach, the practical thermal UC problem of Taiwan Power (Taipower) 38-unit system over a 24-hour period is solved by the CLP algorithm implemented in CHIP language. The results obtained are compared with those from the established methods of the dynamic programming, the Lagrangian relaxation as well as the simulated annealing.

Scheduling a project to maximize its net present value: An integer programming approach

We describe an integer programming algorithm for determining scheduled start and finish times for the activities of a project subject to resource limitations during each period of the schedule duration. The objective is to maximize the net present value of the project to the firm. A depth-first branch and bound solution procedure searches over the feasible set of finish or completion times for each of the activities of the project. Fathoming criteria based upon the concept of a network cut originally developed to solve the duration minimization version of this problem are extended in this paper to solve the net present value problem. These fathoming decision rules prevent many potentially inferior solutions from being explicitly evaluated. Computational experience reported demonstrates the efficacy of the approach.

Reducing reexpansions in iterative-deepening search by controlling cutoff bounds

It is known that a best-first search algorithm like A∗ [5, 6] requires too much space (which often renders it unusable) and a depth-first search strategy does not guarantee an optimal cost solution. The iterative-deepening algorithm IDA∗ [4] achieves both space and cost optimality for a class of tree searching problems. However, for many other problems, it takes too much of computation time due to excessive reexpansion of nodes. This paper presents a modification of IDA∗ to an admissible iterative depth-first branch and bound algorithm IDA∗_CR for trees which overcomes this drawback of IDA∗ and operates much faster using the same amount of storage. Algorithm IDA∗_CRA, a bounded suboptimal cost variation of IDA∗_CR is also presented in order to reduce the execution time still further. Results with the 0/1 Knapsack Problem, Traveling Salesman Problem, and the Flow Shop Scheduling Problem are shown.

An Algorithm for the Manufacturing Equipment Selection Problem

Abstract This paper provides a unified framework in which product and process demands can be related to manufacturing system requirements. A nonlinear cost minimization model is developed that can be used by facility planners to guide the analyses underlying the equipment selection problem. The approach extends current work by accounting for machine flexibility. The objective is to determine how many of each machine type to purchase, as well as what fraction of the time each piece of equipment will be configured for a particular type of operation. The resultant problem is solved with a depth-first branch and bound routine that employs a greedy set covering heuristic to find good feasible solutions. This permits early fathoming and greatly contributes to the efficiency of the algorithm. A small example is presented to highlight the computations. This is followed by a discussion of me results for a series of test problems designed to evaluate overall algorithmic performance. We show mat 16 process, 25 machine problems can be readily solved in less than 6 minutes on a microcomputer.

Optimal and canonical solutions of the change making problem

Given a set of different coin-types, the change-making problem consists in assembling a changes c so as to minimize the number of coins utilized; this problem can arise in practice in some classes of uni-dimensional cargo-loading and cutting-stock problems. The paper presents a depth-first branch and bound algorithm, which makes use of a new dominance criterion; the superiority of this algorithm over Chang-Gill's and Wright's is shown through extensive computational comparisons. Moreover the performance and the applicability of a heuristic algorithm are analyzed.