Crossing-constrained hierarchical drawings

We study the problem of computing hierarchical drawings of layered graphs when some pairs of edges are not allowed to cross. We show that deciding the existence of a drawing satisfying at least k non-crossing constraints from a given set is NP-hard, even if the graph is 2-layered and even when the permutation of the vertices on one side of the bipartition is fixed. We then propose simple constant-ratio approximation algorithms for the optimization version of the problem, which requires to find a maximum realizable subset of constraints, and we discuss how to extend the well-known hierarchical approach for creating layered drawings of directed graphs so as to minimize the number of edge crossings while maximizing the number of satisfied constraints.     

A genetic algorithm for the resource constrained multi-project scheduling problem

This paper presents a genetic algorithm for the resource constrained multi-project scheduling problem. The chromosome representation of the problem is based on random keys. The schedules are constructed using a heuristic that builds parameterized active schedules based on priorities, delay times, and release dates defined by the genetic algorithm. The approach is tested on a set of randomly generated problems. The computational results validate the effectiveness of the proposed algorithm.     

Minimizing weighted tardiness of job-shop scheduling using a hybrid genetic algorithm

Relative to job-shop scheduling problems that optimize makespan or flow time, due-date-related problems are usually much more computationally complex and are classified as strongly NP-hard. In this paper, a hybrid framework integrating a heuristic and a genetic algorithm (GA) is utilized for job-shop scheduling to minimize weighted tardiness. For each new generation of schedules, the GA determines the first operation of each machine, and the heuristic determines the assignment of the remaining operations. Schedules with inferior tardiness are discarded before the next round of evolution. Extensive numerical experiments were conducted for different levels of due-date tightness. The results show that the hybrid framework performs significantly better than does either a heuristic or GA alone. It is also found to be superior to a well-recognized heuristic improvement procedure (lead-time iterations). Specifically, the combination of the R&M heuristic and a GA outperforms a number of heuristics commonly used to minimize total tardiness and weighted total tardiness; this combination is, however, outperformed by the heuristic of Kreipl [Kreipl, S., 2000. A large step random walk for minimizing total weighted tardiness in a job shop. Journal of Scheduling 3, 125–138]. We also develop a generalized hybrid framework that can adapt to different job-shop problems—with or without sequence-dependent setups and with different objectives (e.g., makespan, tardiness, flow time). The new framework allows the interaction of parallel evolutions, extending the GA-heuristic environment to the solving of multi-objective scheduling problems.     

Solving the response time variability problem by means of a genetic algorithm

The response time variability problem (RTVP) is a hard scheduling problem that has recently been defined in the literature and has a wide range of real-world applications in mixed-model assembly lines, multithreaded computer systems, network environments and others. The RTVP arises whenever products, clients or jobs need to be sequenced in such a way that the variability in the time between the points at which they receive the necessary resources is minimized. Since the RTVP is a complex problem, heuristic and metaheuristic techniques are needed to solve it. The best results in the literature for the RTVP have been obtained with a psychoclonal algorithm. We propose a genetic algorithm (GA) that is adapted to solve the RTVP. A computational experiment is carried out and it is shown that, on average, the GA produces better results than the psychoclonal algorithm.     

Modeling fuzzy capacitated p-hub center problem and a genetic algorithm solution

Hub and spoke networks are used to switch and transfer commodities between terminal nodes in distribution systems at minimum cost and/or time. The p-hub center allocation problem is to minimize maximum travel time in networks by locating p hubs from a set of candidate hub locations and allocating demand and supply nodes to hubs. The capacities of the hubs are given. In previous studies, authors usually considered only quantitative parameters such as cost and time to find the optimum location. But it seems not to be sufficient and often the critical role of qualitative parameters like quality of service, zone traffic, environmental issues, capability for development in the future and etc. that are critical for decision makers (DMs), have not been incorporated into models. In many real world situations qualitative parameters are as much important as quantitative ones. We present a hybrid approach to the p-hub center problem in which the location of hub facilities is determined by both parameters simultaneously. Dealing with qualitative and uncertain data, Fuzzy systems are used to cope with these conditions and they are used as the basis of this work. We use fuzzy VIKOR to model a hybrid solution to the hub location problem. Results are used by a genetic algorithm solution to successfully solve a number of problem instances. Furthermore, this method can be used to take into account more desired quantitative variables other than cost and time, like future market and potential customers easily.     

A new bilevel formulation for the vehicle routing problem and a solution method using a genetic algorithm

The Vehicle Routing Problem (VRP) is one of the most well studied problems in operations research, both in real life problems and for scientific research purposes. During the last 50 years a number of different formulations have been proposed, together with an even greater number of algorithms for the solution of the problem. In this paper, the VRP is formulated as a problem of two decision levels. In the first level, the decision maker assigns customers to the vehicles checking the feasibility of the constructed routes (vehicle capacity constraints) and without taking into account the sequence by which the vehicles will visit the customers. In the second level, the decision maker finds the optimal routes of these assignments. The decision maker of the first level, once the cost of each routing has been calculated in the second level, estimates which assignment is the better one to choose. Based on this formulation, a bilevel genetic algorithm is proposed. In the first level of the proposed algorithm, a genetic algorithm is used for calculating the population of the most promising assignments of customers to vehicles. In the second level of the proposed algorithm, a Traveling Salesman Problem (TSP) is solved, independently for each member of the population and for each assignment to vehicles. The algorithm was tested on two sets of benchmark instances and gave very satisfactory results. In both sets of instances the average quality is less than 1%. More specifically in the set with the 14 classic instances proposed by Christofides, the quality is 0.479% and in the second set with the 20 large scale vehicle routing problems, the quality is 0.826%. The algorithm is ranked in the tenth place among the 36 most known and effective algorithms in the literature for the first set of instances and in the sixth place among the 16 algorithms for the second set of instances. The computational time of the algorithm is decreased significantly compared to other heuristic and metaheuristic algorithms due to the fact that the Expanding Neighborhood Search Strategy is used.     

A polynomial algorithm for the Hamiltonian cycle problem in semicomplete multipartite digraphs

We describe a polynomial algorithm for the Hamiltonian cycle problem for semicomplete multipartite digraphs. The existence of such an algorithm was conjectured in G. Gutin, Paths and cycles in digraphs. Ph. D. thesis, Tel Aviv Univ., 1993. (see also G. Gutin, J Graph Theory 19 (1995) 481–505). © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 111–132, 1998     

Performance of a genetic algorithm for the graph partitioning problem

The performance of the genetic algorithm (GA) for the graph partitioning problem (GPP) is investigated by comparison with standard heuristics on well-known benchmark graphs. In general, there is a case where a practical performance of a conventional genetic approach, which performs only simple operations without a local search strategy, is not sufficient. However, it is known that a combination of GA and local search can produce better solutions. From this practice, we incorporate a simple local search algorithm into the GA. In particular, the search ability of the GA is compared with standard heuristics such as multistart local search and simulated annealing, which use the same neighborhood structure of the simple local search, for solving the GPP. Experimental results show that the GA performs better than its competitors.     

Improving benders decomposition using a genetic algorithm

We develop and investigate the performance of a hybrid solution framework for solving mixed-integer linear programming problems. Benders decomposition and a genetic algorithm are combined to develop a framework to compute feasible solutions. We decompose the problem into a master problem and a subproblem. A genetic algorithm along with a heuristic are used to obtain feasible solutions to the master problem, whereas the subproblem is solved to optimality using a linear programming solver. Over successive iterations the master problem is refined by adding cutting planes that are implied by the subproblem. We compare the performance of the approach against a standard Benders decomposition approach as well as against a stand-alone solver (Cplex) on MIPLIB test problems.     

Cycles with two blocks in k‐chromatic digraphs

Let k and ℓ be positive integers. A cycle with two blocks is a digraph obtained by an orientation of an undirected cycle, which consists of two internally (vertex) disjoint paths of lengths at least k and ℓ, respectively, from a vertex to another one. A problem of Addario‐Berry, Havet and Thomassé [J. Combin. Theory Ser. B 97 (2007), 620–626] asked if, given positive integers k and ℓ such that , any strongly connected digraph D containing no has chromatic number at most . In this article, we show that such digraph D has chromatic number at most , improving the previous upper bound of Cohen et al. [Subdivisions of oriented cycles in digraphs with large chromatic number, to appear]. We also show that if in addition D is Hamiltonian, then its underlying simple graph is ‐degenerate and thus the chromatic number of D is at most , which is tight.     

Openly disjoint circuits through a vertex in regular digraphs

In 1985, Thomassen [14] constructed for every positive integer r, finite digraphs D of minimum degree δ(D)=r which do not contain a vertex x lying on three openly disjoint circuits, i.e. circuits which have pairwise exactly x in common. In 2005, Seymour [11] posed the question, whether an r-regular digraph contains a vertex x such that there are r openly disjoint circuits through x. This is true for r≤3, but does not hold for r≥8. But perhaps, in contrast to the minimum degree, a high regularity degree suffices for the existence of a vertex lying on r openly disjoint circuits also for r≥4. After a survey of these problems, we will show that every r-regular digraph with r≥7 has a vertex which lies on 4 openly disjoint circuits.     

A combined branch-and-bound and genetic algorithm based approach for a flowshop scheduling problem

In this paper, we study the application of a meta-heuristic to a two-machine flowshop scheduling problem. The meta-heuristic uses a branch-and-bound procedure to generate some information, which in turn is used to guide a genetic algorithm's search for optimal and near-optimal solutions. The criteria considered are makespan and average job flowtime. The problem has applications in flowshop environments where management is interested in reducing turn-around and job idle times simultaneously. We develop the combined branch-and-bound and genetic algorithm based procedure and two modified versions of it. Their performance is compared with that of three algorithms: pure branch-and-bound, pure genetic algorithm, and a heuristic. The results indicate that the combined approach and its modified versions are better than either of the pure strategies as well as the heuristic algorithm.     

Intersection representation of digraphs in trees with few leaves

The leafage of a digraph is the minimum number of leaves in a host tree in which it has a subtree intersection representation. We discuss bounds on the leafage in terms of other parameters (including Ferrers dimension), obtaining a string of sharp inequalities. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 340–353, 1999     

Affinity genetic algorithm

Based on some phenomena from human society and nature, we propose a binary affinity genetic algorithm (aGA) by adopting the following strategies: the population is adaptively updated to avoid stagnation; the newly generated individuals will be ensured to survive for some generations in order for them to have time to show their good genes; new individuals and the old ones are balanced to have the advantages of both. In order to quantitatively analyze the selective pressure, the concept of selection degree and a simple linear control equation are introduced. We can maintain the diversity of the evolutionary population by controlling the value of the selection degree. Performance of aGA is further enhanced by incorporating local search strategies. Partially supported by a National Key Basic Research Project of China and by a USA NSF grant CCR-0201253.     

Elitist genetic algorithm for assignment problem with imprecise goal

The objective of this research paper is to solve a generalized assignment problem with imprecise cost(s)/time(s) instead of precise one by elitist genetic algorithm (GA). Here, the impreciseness of cost(s)/time(s) has been represented by interval valued numbers, as interval valued numbers are the best representation than others like random variable representation with a known probability distribution and fuzzy representation. To solve these types of problems, an elitist GA has been developed with interval valued fitness function. In this developed GA, the existing ideas about the order relations of interval valued numbers have been modified from the point of view of two types of decision making viz., optimistic decision making and pessimistic decision making. This modified approach has been used in the selection process for selecting better chromosomes/individuals for the next generation and in finding the best as well as the worst chromosomes/individuals in each generation. Here two new crossover schemes and two new mutation schemes have been introduced. In order to maintain the feasibility with crossover operations, a repair algorithm has been suggested. Extensive comparative computational studies based on different parameters of our developed algorithm on one illustrative example have also been reported.     

Aerospace design optimization using a steady state real-coded genetic algorithm

This study demonstrates the advantages of using a real coded genetic algorithm (GA) for aerospace engineering design applications. The GA developed for this study runs steady state, meaning that after every function evaluation the worst performer is determined and that worst performer is then thrown out and replaced by a new member that has been evaluated. The new member is produced by mating two successful parents through a crossover routine, and then mutating that new member. For this study three different preliminary design studies were conducted using both a binary and a real coded GA including a single stage solid propellant missile systems design, a two stage solid propellant missile systems design and a single stage liquid propellant missile systems design.     

A curve-fitting genetic algorithm for a styling application

Fitting curves in computer-aided geometric design is generally regarded as an optimisation problem. Depending on the application, the conditions to be satisfied can make the problem difficult to solve using classic methods, and for this reason, stochastic methods, such as genetic algorithms appear to be appropriate. This article considers a curve fitting problem, with the objective of generating shapes with specific curvature variations for use in the design of car bodies. To this end, a particular curve model was developed and implemented within a genetic algorithm. The main characteristics of this algorithm are described and its promising results are presented. The conclusion will show that this technique can be used as an alternative method in the design of car bodies.     

Single row facility layout problem using a permutation-based genetic algorithm

In this paper, a permutation-based genetic algorithm (GA) is applied to the NP-hard problem of arranging a number of facilities on a line with minimum cost, known as the single row facility layout problem (SRFLP). The GA individuals are obtained by using some rule-based as well as random permutations of the facilities, which are then improved towards the optimum by means of specially designed crossover and mutation operators. Such schemes led the GA to handle the SRFLP as an unconstrained optimization problem. In the computational experiments carried out with large-size instances of sizes from 60 to 80, available in the literature, the proposed GA improved several previously known best solutions.     

An alternative approach for unbalanced assignment problem via genetic algorithm

This paper presents an alternative approach using genetic algorithm to a new variant of the unbalanced assignment problem that dealing with an additional constraint on the maximum number of jobs that can be assigned to some agent(s). In this approach, genetic algorithm is also improved by introducing newly proposed initialization, crossover and mutation in such a way that the developed algorithm is capable to assign optimally all the jobs to agents. Computational results with comparative performance of the algorithm are reported for four test problems.