The Exact Weighted Independent Set Problem in Perfect Graphs and Related Classes

The exact weighted independent set (EWIS) problem consists in determining whether a given vertex-weighted graph contains an independent set of given weight. This problem is a generalization of two well-known problems, the NP-complete subset sum problem and the strongly NP-hard maximum weight independent set (MWIS) problem. Since the MWIS problem is polynomially solvable for some special graph classes, it is interesting to determine the complexity of this more general EWIS problem for such graph classes.We focus on the class of perfect graphs, which is one of the most general graph classes where the MWIS problem can be solved in polynomial time. It turns out that for certain subclasses of perfect graphs, the EWIS problem is solvable in pseudo-polynomial time, while on some others it remains strongly NP-complete. In particular, we show that the EWIS problem is strongly NP-complete for bipartite graphs of maximum degree three, but solvable in pseudo-polynomial time for cographs, interval graphs and chordal graphs, as well as for some other related graph classes.     

A hybrid iterated local search heuristic for the maximum weight independent set problem

This paper presents a hybrid iterated local search (ILS) algorithm for the maximum weight independent set (MWIS) problem, a generalization of the classical maximum independent set problem. Two efficient neighborhood structures are proposed and they are explored using the variable neighborhood descent procedure. Moreover, we devise a perturbation mechanism that dynamically adjusts the balance between intensification and diversification during the search. The proposed algorithm was tested on two well-known benchmarks (DIMACS-W and BHOSLIB-W) and the results obtained were compared with those found by state-of-the-art heuristics and exact methods. Our heuristic outperforms the best-known heuristic for the MWIS as well as the best heuristics for the maximum weight clique problem. The results also show that the hybrid ILS was capable of finding all known optimal solutions in milliseconds.     

Maximum weight independent sets in hole- and dart-free graphs

The Maximum Weight Independent Set (MWIS) problem on graphs with vertex weights asks for a set of pairwise nonadjacent vertices of maximum total weight. The complexity of the MWIS problem for hole-free graphs is unknown. In this paper, we first prove that the MWIS problem for (hole, dart, gem)-free graphs can be solved in $O\left(n^3\right)$-time. By using this result, we prove that the MWIS problem for (hole, dart)-free graphs can be solved in $O\left(n^4\right)$-time. Though the MWIS problem for (hole, dart, gem)-free graphs is used as a subroutine, we also give the best known time bound for the solvability of the MWIS problem in (hole, dart, gem)-free graphs.     

Multi-project scheduling with two-stage decomposition

We consider a non-preemptive, zero time lag multi-project scheduling problem with multiple modes and limited renewable and nonrenewable resources. A two-stage decomposition approach is adopted to formulate the problem as a hierarchy of 0-1 mathematical programming models. In stage one; each project is reduced to a macro-activity with macro-modes. The macro-activities are combined into a single macro-activity network over which the macro-activity scheduling problem (MP) is defined, where the objective is the maximization of the net present value with positive cash flows and the renewable resource requirements are time-dependent. An exact solution procedure and a genetic algorithm (GA) approach are proposed for solving the MP. A GA is also employed to generate an initial solution for the exact solution procedure. The first stage terminates with a post-processing procedure to distribute the remaining resource capacities. Using the start times and the resource profiles obtained in stage one, each project is scheduled in stage two for minimum makespan. Three new test problem sets are generated with 81, 84 and 27 problems each, and three different configurations of solution procedures are tested.     

A genetic algorithm approach to the product line design problem using the seller's return criterion: An extensive comparative computational study

In this paper we deal with the product line design problem employing the seller's marginal return criterion. Because this problem is NP-Hard, many researchers proposed heuristic methods. We present a genetic algorithm (GA) based heuristic for solving the above problem. In the implementation, the GA is initialized in two different ways. In the first way, the GA is initialized with a random population. We call this algorithm GA1. In the second way, the solution of the beam search (BS) method is included in the first population of the GA. We call this algorithm GA2. We compare GA1, a recently developed BS method and GA2 on randomly generated problems. GA1 seems to be substantially better than the BS method in terms of CPU time. Also, the solutions found by GA1 are substantially better than those found by the BS method in comparable times. In many cases, GA2 improves the solution found by the BS method. Consequently, it is a good second step of the BS method.     

A genetic algorithm for robotic assembly line balancing

Flexibility and automation in assembly lines can be achieved by the use of robots. The robotic assembly line balancing (RALB) problem is defined for robotic assembly line, where different robots may be assigned to the assembly tasks, and each robot needs different assembly times to perform a given task, because of its capabilities and specialization. The solution to the RALB problem includes an attempt for optimal assignment of robots to line stations and a balanced distribution of work between different stations. It aims at maximizing the production rate of the line. A genetic algorithm (GA) is used to find a solution to this problem. Two different procedures for adapting the GA to the RALB problem, by assigning robots with different capabilities to workstations are introduced: a recursive assignment procedure and a consecutive assignment procedure. The results of the GA are improved by a local optimization (hill climbing) work-piece exchange procedure. Tests conducted on a set of randomly generated problems, show that the Consecutive Assignment procedure achieves, in general, better solution quality (measured by average cycle time). Further tests are conducted to determine the best combination of parameters for the GA procedure. Comparison of the GA algorithm results with a truncated Branch and Bound algorithm for the RALB problem, demonstrates that the GA gives consistently better results.     

基于遗传算法与贪婪策略的多港口集装箱配载研究

在物流运输行业中,集装箱运输已经成为我国长江沿岸各大港口的主要运输业务。集装箱的处理流程,尤其是集装箱的配载过程直接影响着班轮的运输效率,配载方案的制定对班轮运输起着至关重要的作用。本文针对多港口集装箱船的配载情况,利用CPLEX对该线性规划问题进行求解,并设计遗传算法和贪婪算法对长江沿岸多港口集装箱船配载情形进行对比。通过仿真实验,在小规模时遗传算法与CPLEX求解的精确解相同,验证了遗传算法的有效性。并且在大规模运输情形下,遗传算法得出的结果明显优于贪婪策略,进一步说明了遗传算法是行之有效的。得出的解决方案降低了班轮公司的运输成本,提高了港口的工作效率,对我国长江沿岸港口集装箱配载计划的制定具有一定的指导作用。     

Variable neighborhood search for minimum cost berth allocation

The berth allocation problem is to allocate space along the quayside to incoming ships at a container terminal in order to minimize some objective function. We consider minimization of total costs for waiting and handling as well as earliness or tardiness of completion, for all ships. We assume ships can arrive at any given time, i.e., before or after the berths become available. The resulting problem, which subsumes several previous ones, is expressed as a linear mixed 0–1 program. As it turns out to be too time-consuming for exact solution of instances of realistic size, a Variable Neighborhood Search (VNS) heuristic is proposed, and compared with Multi-Start (MS), a Genetic Search algorithm (GA) and a Memetic Search algorithm (MA). VNS provides optimal solutions for all instances solved to optimality in a previous paper of the first two authors and outperforms MS, MA and GA on large instances.     

101 Activities for Teaching Creativity and Problem Solving,Arthur B. VanGundy,Pfeiffer, J. Wiley,CA, USA (2004), p. xi + 391, £41.95, ISBN: 0-7879-7402-1

Many web sites (e.g. Hotmail, Yahoo) provide free services to the users while generating revenues from advertising. Advertising revenue is, therefore, critical for these sites. This in turn raises the question, how should advertisements at a web site be scheduled in a planning horizon to maximize revenue. Advertisements on the web are specified by geometry and display frequency and both of these factors need to be considered in developing a solution to the advertisement scheduling problem. Since this problem belongs to the class of NP-hard problems, we first develop a heuristic called LSMF to solve the problem. This heuristic is then combined with a genetic algorithm (GA) to develop a hybrid GA. The hybrid GA solution is first compared with the upper bound obtained by running CPLEX for the integer programming formulation of the problem. It is then also compared with an existing algorithm proposed in the literature. Our computational results show that the hybrid GA performs exceptionally well in the sense that it provides optimal or near optimal solution for a wide range of problem instances of realistic sizes and the improvements over existing algorithm are substantial. Finally we present a case study to illustrate how revenue could be significantly increased with a small improvement in the advertisement schedule. It is the first such study in this setup.     

Solving TSP by considering processing time: Meta-heuristics and fuzzy approaches

In this paper, general properties of traveling salesman problem has been illustrated, then a model has been introduced to minimize Make-span (time interval which all of jobs will be done) with considering sequence-dependence setup times and processing time. Furthermore, fuzzy sets and its characteristics are applied to a Hard-solvable traveling salesman problem with considering processing times. As it can be seen, traveling salesman problems are NP-hard, so solving problem in huge dimensions is uncontrollably manageable and in other side these kinds of problems in real-world are unavoidable, so a local search can prove their importance. (However this Meta-heuristic methods may not reveal exact optimal solution, but they yield a near-exact optimal solution in undeniable reduced computational time). Here, some of most famous local searches have been explained in their common and normal form, which are Genetic Algorithm (GA), Tabu Search (TS), Simulated Annealing (SA), Ant Colony System (ACO). In rest, a comprehensive comparison through these methods has been shown. This normality in methods structure could help the article to hold no-side-taken and acceptable judgments. In final, point methods analysis and parameter tuning are held.     

A genetic algorithms simulation approach for the multi-attribute combinatorial dispatching decision problem

This paper presents a genetic algorithms (GA) simulation approach in solving a multi-attribute combinatorial dispatching (MACD) decision problem in a flow shop with multiple processors (FSMP) environment. The simulation is capable of modeling a non-linear and stochastic problem. GA are one of the commonly used metaheuristics and are a proven tool for solving complex optimization problems. The proposed GA simulation approach addresses a complex MACD problem. Its solution quality is illustrated by a case study from a multi-layer ceramic capacitor (MLCC) manufacturing plant. Because GA search results are often sensitive to the search parameters, this research optimized the GA parameters by using regression analysis. Empirical results showed that the GA simulation approach outperformed several commonly used dispatching rules. The improvements are ranging from 33% to 61%. On the other hand, the increased shop-floor-control complexity may hinder the implementation of the system. Finally, future research directions are discussed.     

Genetic algorithm approach on multi-criteria minimum spanning tree problem

Minimum Spanning Tree (MST) problem is of high importance in network optimization. The multi-criteria MST (mc-MST) is a more realistic representation of the practical problem in the real world, but it is difficult for the traditional network optimization technique to deal with. In this paper, a genetic algorithm (GA) approach is developed to deal with this problem. Without neglecting its network topology, the proposed method adopts the Prüfer number as the tree encoding and applies the Multiple Criteria Decision Making (MCDM) technique and nondominated sorting technique to make the GA search give out all Pareto optimal solutions either focused on the region near the ideal point or distributed all along the Pareto frontier. Compared with the enumeration method of Pareto optimal solution, the numerical analysis shows the efficiency and effectiveness of the GA approach on the mc-MST problem.     

An efficient genetic algorithm for the traveling salesman problem with precedence constraints

The traveling salesman problem with precedence constraints (TSPPC) is one of the most difficult combinatorial optimization problems. In this paper, an efficient genetic algorithm (GA) to solve the TSPPC is presented. The key concept of the proposed GA is a topological sort (TS), which is defined as an ordering of vertices in a directed graph. Also, a new crossover operation is developed for the proposed GA. The results of numerical experiments show that the proposed GA produces an optimal solution and shows superior performance compared to the traditional algorithms.     

A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge

This paper considers a two-stage distribution problem of a supply chain that is associated with a fixed charge. Two kinds of cost are involved in this problem: a continuous cost that linearly increases with the amount transported between a source and a destination, and secondly, a fixed charge, that incurs whenever there exists a transportation of a non-zero quantity between a source and a destination. The objective criterion is the minimisation of the total cost of distribution. A genetic algorithm (GA) that belongs to evolutionary search heuristics is proposed and illustrated. The proposed methodology is evaluated for its solution quality by comparing it with the approximate and lower bound solutions. Thus, the comparison reveals that the GA generates better solution than the approximation method and is capable of providing solution either equal or closer to the lower bound solution of the problem.     

Heuristic solution approaches for the cumulative capacitated vehicle routing problem

Cumulative capacitated vehicle routing problem (CCVRP) is an extension of the well-known capacitated vehicle routing problem, where the objective is minimization of sum of the arrival times at nodes instead of minimizing the total tour cost. This type of routing problem arises when a priority is given to customer needs or dispatching vital goods supply after a natural disaster. This paper focuses on comparing the performances of neighbourhood and population-based approaches for the new problem CCVRP. Genetic algorithm (GA), an evolutionary algorithm using particle swarm optimization mechanism with GA operators, and tabu search (TS) are compared in terms of required CPU time and obtained objective values. In addition, a nearest neighbourhood-based initial solution technique is also proposed within the paper. To the best of authors’ knowledge, this paper constitutes a base for comparisons along with GA, and TS for further possible publications on the new problem CCVRP.     

Using genetic algorithms for the coordinated scheduling problem of a batching machine and two-stage transportation

This paper considers a coordinated scheduling problem. For the first-stage transportation there is a crane available to transport the product from the warehouse to a batching machine. For the second-stage transportation there is a vehicle available to deliver the completed jobs from the machine shop floor to the customer. The coordinated scheduling problem of production and transportation deals with sequencing the transportation of the jobs and combining them into batches to be processed. The problem of minimizing the sum of the makespan and the total setup cost was proven by Tang and Gong [1] to be strongly NP-hard. This paper proposes two genetic algorithm (GA) approaches for this scheduling problem, with different result representations. The experimental results demonstrate that a regular GA and a modified GA (MGA) can find near-optimal solutions within an acceptable amount of computational time. Among the two proposed metaheuristic approaches, the MGA is superior to the GA both in terms of computing time and the quality of the solution.     

An empirical study of hybrid genetic algorithms for the set covering problem

The purpose of this paper is to explore the computational performance of several hybrid algorithms that are extensions of a basic genetic algorithm (GA) approach for solving the set covering problem (SCP). We start by making several enhancements to a GA for the SCP that was proposed by Beasley and Chu. Next, several hybrid solution approaches are introduced that combine the GA with various local neighbourhood search approaches, with a form of the greedy randomized adaptive search procedure, and with an estimation of distribution algorithms approach. Using Beasley's library of SCPs extensive computational results are generated for the hybrid solution approaches defined in this paper. Statistical analyses of the results are performed.     

Combining Metaheuristics and Exact Methods for Solving Exactly Multi-objective Problems on the Grid

This paper presents a parallel hybrid exact multi-objective approach which combines two metaheuristics – a genetic algorithm (GA) and a memetic algorithm (MA), with an exact method – a branch and bound (B&B) algorithm. Such approach profits from both the exploration power of the GA, the intensification capability of the MA and the ability of the B&B to provide optimal solutions with proof of optimality. To fully exploit the resources of a computational grid, the hybrid method is parallelized according to three well-known parallel models – the island model for the GA, the multi-start model for the MA and the parallel tree exploration model for the B&B. The obtained method has been experimented and validated on a bi-objective flow-shop scheduling problem. The approach allowed to solve exactly for the first time an instance of the problem – 50 jobs on 5 machines. More than 400 processors belonging to 4 different administrative domains have contributed to the resolution process during more than 6 days.      

Enumeration of Pareto optimal multi-criteria spanning trees – a proof of the incorrectness of Zhou and Gen's proposed algorithm

The minimum spanning tree (MST) problem is a well-known optimization problem of major significance in operational research. In the multi-criteria MST (mc-MST) problem, the scalar edge weights of the MST problem are replaced by vectors, and the aim is to find the complete set of Pareto optimal minimum-weight spanning trees. This problem is NP-hard and so approximate methods must be used if one is to tackle it efficiently. In an article previously published in this journal, a genetic algorithm (GA) was put forward for the mc-MST. To evaluate the GA, the solution sets generated by it were compared with solution sets from a proposed (exponential time) algorithm for enumerating all Pareto optimal spanning trees. However, the proposed enumeration algorithm that was used is not correct for two reasons: (1) It does not guarantee that all Pareto optimal minimum-weight spanning trees are returned. (2) It does not guarantee that those trees that are returned are Pareto optimal. In this short paper we prove these two theorems.     

Using genetic algorithm to solve dynamic cell formation problem

In this paper, solving a cell formation (CF) problem in dynamic condition is going to be discussed using genetic algorithm (GA). Previous models presented in the literature contain some essential errors which will decline their advantageous aspects. In this paper these errors are discussed and a new improved formulation for dynamic cell formation (DCF) problem is presented. Due to the fact that CF is a NP-hard problem, solving the model using classical optimization methods needs a long computational time. Therefore the improved DCF model is solved using a proposed GA and the results are compared with the optimal solution and the efficiency of the proposed algorithm is discussed and verified.