Abstract: We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.
Abstract: Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.
Abstract: Disasters are quite experienced in our days. They are
caused by floods, landslides, and building fires that is the main
objective of this study. To cope with these unexpected events,
precautions must be taken to protect human lives. The emphasis on
disposal work focuses on the resolution of the evacuation problem in
case of no-notice disaster. The problem of evacuation is listed as a
dynamic network flow problem. Particularly, we model the
evacuation problem as an earliest arrival flow problem with load
dependent transit time. This problem is classified as NP-Hard. Our
challenge here is to propose a metaheuristic solution for solving the
evacuation problem. We define our objective as the maximization of
evacuees during earliest periods of a time horizon T. The objective
provides the evacuation of persons as soon as possible. We
performed an experimental study on emergency evacuation from the
tunisian children’s hospital. This work prompts us to look for
evacuation plans corresponding to several situations where the
network dynamically changes.
Abstract: Genome rearrangement is an important area in computational biology and bioinformatics. The basic problem in genome rearrangements is to compute the edit distance, i.e., the minimum number of operations needed to transform one genome into another. Unfortunately, unsigned genome rearrangement problem is NP-hard. In this study an improved ant colony optimization algorithm to approximate the edit distance is proposed. The main idea is to convert the unsigned permutation to signed permutation and evaluate the ants by using Kaplan algorithm. Two new operations are added to the standard ant colony algorithm: Replacing the worst ants by re-sampling the ants from a new probability distribution and applying the crossover operations on the best ants. The proposed algorithm is tested and compared with the improved breakpoint reversal sort algorithm by using three datasets. The results indicate that the proposed algorithm achieves better accuracy ratio than the previous methods.
Abstract: A key element of many distribution systems is the
routing and scheduling of vehicles servicing a set of customers. A
wide variety of exact and approximate algorithms have been
proposed for solving the vehicle routing problems (VRP). Exact
algorithms can only solve relatively small problems of VRP, which is
classified as NP-Hard. Several approximate algorithms have proven
successful in finding a feasible solution not necessarily optimum.
Although different parts of the problem are stochastic in nature; yet,
limited work relevant to the application of discrete event system
simulation has addressed the problem. Presented here is optimization
using simulation of VRP; where, a simplified problem has been
developed in the ExtendSimTM simulation environment; where,
ExtendSimTM evolutionary optimizer is used to minimize the total
transportation cost of the problem. Results obtained from the model
are very satisfactory. Further complexities of the problem are
proposed for consideration in the future.
Abstract: Estimating the reliability of a computer network has been a subject of great interest. It is a well known fact that this problem is NP-hard. In this paper we present a very efficient combinatorial approach for Monte Carlo reliability estimation of a network with unreliable nodes and unreliable edges. Its core is the computation of some network combinatorial invariants. These invariants, once computed, directly provide pure and simple framework for computation of network reliability. As a specific case of this approach we obtain tight lower and upper bounds for distributed network reliability (the so called residual connectedness reliability). We also present some simulation results.
Abstract: Some fast exact algorithms for the maximum weight clique problem have been proposed. Östergard’s algorithm is one of them. Kumlander says his algorithm is faster than it. But we confirmed that the straightforwardly implemented Kumlander’s algorithm is slower than O¨ sterga˚rd’s algorithm. We propose some improvements on Kumlander’s algorithm.
Abstract: Virtualization-based server consolidation has been
proven to be an ideal technique to solve the server sprawl problem by
consolidating multiple virtualized servers onto a few physical servers
leading to improved resource utilization and return on investment. In
this paper, we solve this problem by using existing servers, which are
heterogeneous and diversely preferred by IT managers. Five practical
consolidation rules are introduced, and a decision model is proposed to
optimally allocate source services to physical target servers while
maximizing the average resource utilization and preference value. Our
model can be regarded as a multi-objective multi-dimension
bin-packing (MOMDBP) problem with constraints, which is strongly
NP-hard. An improved grouping generic algorithm (GGA) is
introduced for the problem. Extensive simulations were performed and
the results are given.
Abstract: This paper proposes a genetic algorithm based on a
new replacement strategy to solve the quadratic assignment problems,
which are NP-hard. The new replacement strategy aims to improve the
performance of the genetic algorithm through well balancing the
convergence of the searching process and the diversity of the
population. In order to test the performance of the algorithm, the
instances in QAPLIB, a quadratic assignment problem library, are
tried and the results are compared with those reported in the literature.
The performance of the genetic algorithm is promising. The
significance is that this genetic algorithm is generic. It does not rely on
problem-specific genetic operators, and may be easily applied to
various types of combinatorial problems.
Abstract: This paper presents a heuristic approach to solve the Generalized Assignment Problem (GAP) which is NP-hard. It is worth mentioning that many researches used to develop algorithms for identifying the redundant constraints and variables in linear programming model. Some of the algorithms are presented using intercept matrix of the constraints to identify redundant constraints and variables prior to the start of the solution process. Here a new heuristic approach based on the dominance property of the intercept matrix to find optimal or near optimal solution of the GAP is proposed. In this heuristic, redundant variables of the GAP are identified by applying the dominance property of the intercept matrix repeatedly. This heuristic approach is tested for 90 benchmark problems of sizes upto 4000, taken from OR-library and the results are compared with optimum solutions. Computational complexity is proved to be O(mn2) of solving GAP using this approach. The performance of our heuristic is compared with the best state-ofthe- art heuristic algorithms with respect to both the quality of the solutions. The encouraging results especially for relatively large size test problems indicate that this heuristic approach can successfully be used for finding good solutions for highly constrained NP-hard problems.
Abstract: Estimating the lifetime distribution of computer networks in which nodes and links exist in time and are bound for failure is very useful in various applications. This problem is known to be NP-hard. In this paper we present efficient combinatorial approaches to Monte Carlo estimation of network lifetime distribution. We also present some simulation results.
Abstract: We study the spatial design of experiment and we want to select a most informative subset, having prespecified size, from a set of correlated random variables. The problem arises in many applied domains, such as meteorology, environmental statistics, and statistical geology. In these applications, observations can be collected at different locations and possibly at different times. In spatial design, when the design region and the set of interest are discrete then the covariance matrix completely describe any objective function and our goal is to choose a feasible design that minimizes the resulting uncertainty. The problem is recast as that of maximizing the determinant of the covariance matrix of the chosen subset. This problem is NP-hard. For using these designs in computer experiments, in many cases, the design space is very large and it's not possible to calculate the exact optimal solution. Heuristic optimization methods can discover efficient experiment designs in situations where traditional designs cannot be applied, exchange methods are ineffective and exact solution not possible. We developed a GA algorithm to take advantage of the exploratory power of this algorithm. The successful application of this method is demonstrated in large design space. We consider a real case of design of experiment. In our problem, design space is very large and for solving the problem, we used proposed GA algorithm.
Abstract: The Block Sorting problem is to sort a given
permutation moving blocks. A block is defined as a substring
of the given permutation, which is also a substring of the
identity permutation. Block Sorting has been proved to be
NP-Hard. Until now two different 2-Approximation algorithms
have been presented for block sorting. These are the best known
algorithms for Block Sorting till date. In this work we present
a different characterization of Block Sorting in terms of a
transposition cycle graph. Then we suggest a heuristic,
which we show to exhibit a 2-approximation performance
guarantee for most permutations.
Abstract: This paper presents a heuristic to solve large size 0-1 Multi constrained Knapsack problem (01MKP) which is NP-hard. Many researchers are used heuristic operator to identify the redundant constraints of Linear Programming Problem before applying the regular procedure to solve it. We use the intercept matrix to identify the zero valued variables of 01MKP which is known as redundant variables. In this heuristic, first the dominance property of the intercept matrix of constraints is exploited to reduce the search space to find the optimal or near optimal solutions of 01MKP, second, we improve the solution by using the pseudo-utility ratio based on surrogate constraint of 01MKP. This heuristic is tested for benchmark problems of sizes upto 2500, taken from literature and the results are compared with optimum solutions. Space and computational complexity of solving 01MKP using this approach are also presented. The encouraging results especially for relatively large size test problems indicate that this heuristic can successfully be used for finding good solutions for highly constrained NP-hard problems.
Abstract: This study compares three meta heuristics to minimize makespan (Cmax) for Hybrid Flow Shop (HFS) Scheduling Problem with Parallel Machines. This problem is known to be NP-Hard. This study proposes three algorithms among improvement heuristic searches which are: Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS). SA and TS are known as deterministic improvement heuristic search. GA is known as stochastic improvement heuristic search. A comprehensive comparison from these three improvement heuristic searches is presented. The results for the experiments conducted show that TS is effective and efficient to solve HFS scheduling problems.
Abstract: All practical real-time scheduling algorithms in multiprocessor systems present a trade-off between their computational complexity and performance. In real-time systems, tasks have to be performed correctly and timely. Finding minimal schedule in multiprocessor systems with real-time constraints is shown to be NP-hard. Although some optimal algorithms have been employed in uni-processor systems, they fail when they are applied in multiprocessor systems. The practical scheduling algorithms in real-time systems have not deterministic response time. Deterministic timing behavior is an important parameter for system robustness analysis. The intrinsic uncertainty in dynamic real-time systems increases the difficulties of scheduling problem. To alleviate these difficulties, we have proposed a fuzzy scheduling approach to arrange real-time periodic and non-periodic tasks in multiprocessor systems. Static and dynamic optimal scheduling algorithms fail with non-critical overload. In contrast, our approach balances task loads of the processors successfully while consider starvation prevention and fairness which cause higher priority tasks have higher running probability. A simulation is conducted to evaluate the performance of the proposed approach. Experimental results have shown that the proposed fuzzy scheduler creates feasible schedules for homogeneous and heterogeneous tasks. It also and considers tasks priorities which cause higher system utilization and lowers deadline miss time. According to the results, it performs very close to optimal schedule of uni-processor systems.