We discuss properties of acyclic graph evolution driven by node-firing. The research background and basic concepts of acyclic graph evolution are from the mutual exclusion problem in distributed environments. We proposed in our previous work a mutual exclusion protocol which is based on the notion of evolution trajectories of acyclic graphs. In this paper, we analyze firing concurrency and periodicity of the acyclic graph evolution, from graph theoretical point of views, and investigate topological conditions for assuring the number of firable nodes below a some fixed constant, at any instance of the evolution trajectory. A marked graph, a subclass of Petri nets, is often utilized as a proof tool in analysis.

In this paper we consider a sex-fair matching in the stable marriage problem. The sex-fair stable matching defined in this paper has a property that the sum of partner's ranks of individual men in their preference lists is as close as possible to the sum of partner's ranks of individual women in their preference lists. However, the sex-fair stable marriage problem is known as one of important open problems in the stable marriage problems. The main result of this paper is to propose a method for adapting a genetic algorithm (GA) to the sex-fair problem to find the sex-fair matching effectively. In the method we transform the sex-fair marriage problem into a graph problem whose decision version is shown to be NP-complete. The graph problem representation is suitable for GA application, that is, easier coding, easier and more effective definition of genetic operators. Computer experiment reports effectiveness of the GA solution.

This paper proposes a Petri net based mathematical programming approach to combinatorial optimization, in which we generate integer linear programming problems from Petri net models instead of the direct mathematical formulation. We treat two types of combinatorial optimization problems, ordinary problems and time-dependent problems. Firstly, we present autonomous Petri net modeling for ordinary optimization problems, where we obtain fundamental constraints derived from Petri net properties and additional problem-specific ones. Secondly, we propose a colored timed Petri net modeling approach to time-dependent problems, where we generate variables and constraints for time management and for resolving conflicts. Our Petri net approach can drastically reduce the difficulty of the mathematical formulation in a sense that (1) the Petri net modeling does not require deep knowledge of mathematical programming and technique of integer linear model formulations, (2) our automatic formulation allows us to generate large size of integer linear programming problems, and (3) the Petri net modeling approach is flexible for input parameter changes of the original problem.

The stable marriage problem is one of the basic problems proposed in 1962. In this paper, we consider a distributed stable marriage problem. This problem is applicable to cooperative works of autonomous robots in distributed environments. We show a Gale-Shapley based protocol to obtain stable matching and introduce autonomous mechanism for exchanging partners, called divorce process, in distributed environments. We report some interesting results of matching games by computer simulation.

This paper considers Cyclic Job-Shop Scheduling Problems (CJSSP) extended from the Job-Shop Scheduling Problem (JSSP). We propose an evolutionary computing method to solve the problem approximately by generating the Petri net structure for scheduling. The crossover proposed in this paper employs structural analysis of Petri net model, that is, the crossover improves the cycle time by breaking the bottle-neck circuit obtained by solving a linear programming problem. Experimental evaluation shows the effectiveness of our approach.

In this paper we consider a parallel and distributed computation of genetic algorithms on loosely-coupled multiprocessor systems. Loosely-coupled ones are more suitable for massively parallel processing and also more easily VLSI implementation than tightly-coupled ones. However, communication overhead on parallel processing is more serious for loosely-coupled ones. We propose in this paper a parallel and distributed execution method of genetic algorithm on loosely-coupled multiprocessor systems of fixed network topologies in which each processor element carries out genetic operations on its own chromosome set and communicates with only the neighbors in order to save communication overhead. We evaluate the proposed method on the multiprocessor systems with ring, torus, and hypercube topologies for benchmark problem instances. From the results, we find that the ring topology is more suitable for the proposed parallel and distributed execution since variety of chromosomes in the ring is kept much more than that in the others. Moreover, we also propose a new network topology called cone which is a hierarchical connection of ring topologies. We show its effectiveness by experimental evaluation.

This paper treats meta-heuristics for combinatorial optimization problems. The parallelization of meta-heuristics is then discussed in which we show that parallel processing has possibility of not only speeding up but also improving solution quality. Finally we extend the discussion of the combinatorial optimization into autonomous decentralized systems, say autonomous decentralized optimization. This notion becomes very important with the advancement of the network-connected system architecture.

This paper presents a genetic algorithm for designing at minimum cost a two-connected network topology such that the shortest cycle (referred to as a ring) to which each edge belongs does not exceed a given maximum number of hops. The genetic algorithm introduces a solution representation in which constraints such as connectivity and ring constraints are easily encoded. Furthermore, a problem specific crossover operator that ensures solutions generated through genetic evolution are all feasible is also proposed. Hence, both checking of the constraints and repair mechanism can be avoided thus resulting in increased efficiency. Experimental evaluation shows the effectiveness of the proposed GA.

In this paper we propose a parallel and distributed computation of genetic local search with irregular topology in distributed environments. The scheme we propose in this paper is implemented with a tree topology established on an irregular network where each computing element carries out genetic local search on its own chromosome set and communicates with its parent when the best solution of each generation is updated. We evaluate the proposed algorithm by a simulation system implemented on a PC-cluster. We test our algorithm on four types topologies: star, line, balanced binary tree and sided binary tree, and investigate the influence of communication topology and delay on the evolution process.

Autonomous distributed scheduling is based on the autonomous decentralized optimization and recently focused as one of flexible scheduling techniques which can more cope with dynamically changing situation than traditional ones. This paper proposes an autonomous distributed scheduling scheme for the parallel machine scheduling problem. Through computer simulation, we observe that our proposed scheme can more quickly reduce the total deadline over-time than one in the literature and can adapt flexibly to unusual situation (addition of jobs).

This paper investigates migration effects of parallel genetic algorithms (GAs) on the line topology of heterogeneous computing resources. Evolution process of parallel GAs is evaluated experimentally on two types of arrangements of heterogeneous computing resources: the ascending and descending order arrangements. Migration effects are evaluated from the viewpoints of scalability, chromosome diversity, migration frequency and solution quality. The results reveal that the performance of parallel GAs strongly depends on the design of the chromosome migration in which we need to consider the arrangement of heterogeneous computing resources, the migration frequency and so on. The results contribute to provide referential scheme of implementation of parallel GAs on heterogeneous computing resources.

This paper proposes a scheme for automatic generation of mixed-integer programming problems for scheduling with multiple resources based on colored timed Petri nets. Our method reads Petri net data modeled by users, extracts the precedence and conflict relations among transitions, information on the available resources, and finally generates a mixed integer linear programming for exactly solving the target scheduling problem. The mathematical programing problems generated by our tool can be easily inputted to well-known optimizers. The results of this research can extend the usability of optimizers since our tool requires just simple rules of Petri nets but not deep mathematical knowledge.

This paper presents an evolutionary scheduling scheme for solving the job shop scheduling problem (JSSP) and other combinatorial optimization problems. The approach is based on a genetized-knowledge genetic algorithm (gkGA). The basic idea behind the gkGA is that knowledge of heuristics which are used in the GA is also encoded as genes alongside the genetic strings, referred to as chromosomes. Furthermore, during the GA selection, weaker heuristics die out while stronger ones survive for a given problem instance. We evaluate our evolutionary scheduling scheme based on the gkGA approach using well known benchmark instances for the JSSP. We observe that the gkGA based scheme is shown to consistently outperform the scheme based on ordinary GAs. In addition the gkGA-based scheme removes the problem of instance dependency.

This paper proposes an iterative parallel genetic algorithm with biased initial population to solve large-scale combinatorial optimization problems. The proposed scheme employs a master-slave collaboration in which the master node manages searched space of slave nodes and assigns seeds to generate initial population to slaves for their restarting of evolution process. Our approach allows us as widely as possible to search by all the slave nodes in the beginning period of the searching and then focused searching by multiple slaves on a certain spaces that seems to include good quality solutions. Computer experiment shows the effectiveness of our proposed scheme.

This paper treats mutual exclusion of a single shared-resource in distributed autonomous environments. The most important property of the autonomous network treated in this paper is its membership variability, that is, frequent occurrence of entries of new nodes and exits of old nodes. Thus, when the network is large-scale, it is not possible for each node to keet up the information of all other nodes. We in this paper design a mutual exclusion algorithm for distributed environments of autonomous nodes based on Chandy-Misra protocol for Dining Philosopher (diners) problems, which realizes a distributed implementation of the token ring method. We consider requirements of the communication topology that makes mutual exclusion possible, and propose entry and exit protocols for each node to perform them individualistically and autonomously.

In this paper, we propose the distributed stable marriage problem and apply it to planning for cooperative works of autonomous mobile robots and battery charger stations. We develop and analyze a distributed algorithm to determine the partner by message communication.

This paper proposes aspiration controls which restrains aspiration branches and keeps the original tabu-based searching by considering past and/or (predicted) future searching profiles. For implementation of the aspiration control we employ not only the short-term and long-term memory but also future memory which is first introduced in this paper as a new concept in the tabu search field. The tabu search with the aspiration control is also parallelized. Moreover two types of parallel cooperative searching scheme are proposed. Through computational experiment, we observe efficiency of our approach comparing to the traditional ones. Especially, we find that cooperative searching has possibility to improve the solution quality very well.