Order-based Representation Research Articles

IC Floorplanning Optimization using Simulated Annealing with Order-based Representation

Integrated Circuits (IC) floorplanning is an important step in the integrated circuit physical design; it influences the area, wire-length, delay etc of an IC. In this paper, Order Based (OB) representation has been proposed for fixed outline floorplan with Simulated Annealing (SA) algorithm. To optimize the IC floorplan, two physical quantities have been considered such as area, and wire-length for hard IP modules. Optimization of the IC floorplan works in two phases. In the first phase, floorplans are constructed by proposed representation without any overlapping among the modules. In the second phase, Simulated Annealing algorithm explores the packing of all modules in floorplan to find better optimal performances i.e. area and wire-length. The Experimental results on Microelectronic Center of North Carolina benchmark circuits show that our proposed representation with SA algorithm performs better for area and wire-length optimization than the other methods. The results are compared with the solutions derived from other algorithms. The significance of this research work is improvement in optimized area and wire-length for modern IC.

Unstructured network topology begets order-based representation by privileged neurons

How spiking activity reverberates through neuronal networks, how evoked and spontaneous activity interacts and blends, and how the combined activities represent external stimulation are pivotal questions in neuroscience. We simulated minimal models of unstructured spiking networks in silico, asking whether and how gentle external stimulation might be subsequently reflected in spontaneous activity fluctuations. Consistent with earlier findings in silico and in vitro, we observe a privileged subpopulation of ‘pioneer neurons’ that, by their firing order, reliably encode previous external stimulation. We also confirm that pioneer neurons are ‘sensitive’ in that they are recruited by small fluctuations of population activity. We show that order-based representations rely on a ‘chain’ of pioneer neurons with different degrees of sensitivity and thus constitute an emergent property of collective dynamics. The forming of such representations is greatly favoured by a broadly heterogeneous connection topology—a broad ‘middle class’ in degree of connectedness. In conclusion, we offer a minimal model for the representational role of pioneer neurons, as observed experimentally in vitro. In addition, we show that broadly heterogeneous connectivity enhances the representational capacity of unstructured networks.

An Efficient Genetic Algorithm for Large Scale Vehicle Routing Problem Subject to Precedence Constraints

The vehicle routing problem is a combinatorial optimization and integer programming problem seeking to service a number of customers with a fleet of vehicles. Vehicle routing problem has many applications in the fields of transportation, distribution and logistics. In this study, the vehicle routing problem subject to precedence constraints has been modeled as the Travelling Salesman Problem (TSP) with precedence constraints. Vehicle routing problem is difficult to solve using exact methods especially for large size instances due to computational expensive. Therefore, metaheuristic method based genetic algorithm has been developed to obtain feasible and optimal solution with less computation time. The conventional genetic algorithm procedure for TSP, with an order-based representation might generate invalid candidate solutions when precedence constraints are involved. In order to obtain feasible solution which does not violate precedence constraints, a route repair based topological sort technique is used and integrated in the genetic algorithm procedure. In this paper, a new algorithm is developed and the performances as well as the quality of the solution were evaluated against large scale test problems. The results from the computational experiments demonstrate that the algorithm with ‘earliest position’ task selection mechanism, linear order crossover and inversion mutation has better results in terms of number of generations and computation time to converge to optimal solution. The genetic operators used in this study are capable to introduce new fitter offspring and does not trapped in a local optimum. Therefore, it can be stated that the genetic algorithm approach developed in this study is efficient in solving large scale vehicle routing problem subject to precedence constraints with the objective of minimizing the distance travelled.

Reducing Premature Convergence Problem in Genetic Algorithm: Application on Travel Salesman Problem

Genetic algorithm (GA) is based on Darwin’s natural selection theory and is used extensively in combinatorial problems as these problems are demanding in terms of computational time. GA shows very good results in terms of both computational time and quality of solution for combinatorial problems as GAs have some traits that make them one of the best evolutionary algorithms (EAs). The use of both mutation and crossover operators make them, relative to other EAs, highly immune to be trapped in a local optima and thus less vulnerable to premature convergence problem. Traditionally, the solution for premature convergence problem is to maintain a certain degree of diversity of the GA’s population without affecting the convergence process itself. In this paper, this concept has been practiced where Frequency Crossover strategy (FC) along with nine different mutation strategies have been proposed and applied to travel salesman problem (TSP) to reduce the effect of premature convergence problem. Three sets of benchmark data have been used to test the effectiveness of this GA. The results showed that both the nine mutation types and the FC are essential for the proposed GA to perform well. While this GA has been applied on TSP in this paper, it is also believed that it is applicable on any problem that has an Order-Based chromosome representation.

Order-Based Representation in Random Networks of Cortical Neurons

The wide range of time scales involved in neural excitability and synaptic transmission might lead to ongoing change in the temporal structure of responses to recurring stimulus presentations on a trial-to-trial basis. This is probably the most severe biophysical constraint on putative time-based primitives of stimulus representation in neuronal networks. Here we show that in spontaneously developing large-scale random networks of cortical neurons in vitro the order in which neurons are recruited following each stimulus is a naturally emerging representation primitive that is invariant to significant temporal changes in spike times. With a relatively small number of randomly sampled neurons, the information about stimulus position is fully retrievable from the recruitment order. The effective connectivity that makes order-based representation invariant to time warping is characterized by the existence of stations through which activity is required to pass in order to propagate further into the network. This study uncovers a simple invariant in a noisy biological network in vitro; its applicability under in vivo constraints remains to be seen.

Evolutionary multi-objective portfolio optimization in practical context

This paper addresses evolutionary multi-objective portfolio optimization in the practical context by incorporating realistic constraints into the problem model and preference criterion into the optimization search process. The former is essential to enhance the realism of the classical mean-variance model proposed by Harry Markowitz, since portfolio managers often face a number of realistic constraints arising from business and industry regulations, while the latter reflects the fact that portfolio managers are ultimately interested in specific regions or points along the efficient frontier during the actual execution of their investment orders. For the former, this paper proposes an order-based representation that can be easily extended to handle various realistic constraints like floor and ceiling constraints and cardinality constraint. An experimental study, based on benchmark problems obtained from the OR-library, demonstrates its capability to attain a better approximation of the efficient frontier in terms of proximity and diversity with respect to other conventional representations. The experimental results also illustrated its viability and practicality in handling the various realistic constraints. A simple strategy to incorporate preferences into the multi-objective optimization process is highlighted and the experimental study demonstrates its capability in driving the evolutionary search towards specific regions of the efficient frontier.

Traffic grooming in unidirectional WDM ring networks using genetic algorithms

We propose a genetic algorithm (GA) with ( μ+ λ)-strategy to solve the traffic grooming problems in unidirectional SONET/WDM rings with arbitrary asymmetric traffic requirements. The objective is to optimally assign calls to wavelengths in order that the total number of SONET add/drop multiplexers (ADMs) is minimized while as few wavelengths as possible are used. We derive the theoretical lower and upper bounds on the numbers of both ADMs and wavelengths and summarize the general properties of the asymmetric traffic requirements in the ring. In applying GAs to solve the problem, we develop an order-based representation for the chromosome, introduce the concept of adaptive chromosome and propose a first fit approach incorporated with a greedy improvement algorithm to decode it. The order-mapped crossover and the inversion mutation are used to produce offspring. We also introduce the concept of the weighted average traversing length of each traffic and investigate the dependence of the average number of nodes at which per wavelength drops on both the weighted average traversing length and the average traffic requirement between each pair of nodes. Computer simulation results show that the algorithm proposed in this paper can significantly reduce the number of ADMs in solving the arbitrary asymmetric traffic grooming problems. A digital example shows that all the calls in the ring are nearly neatly paired after grooming.

Graph Coloring with Adaptive Evolutionary Algorithms

This paper presents the results of an experimental investigation on solving graph coloring problems with Evolutionary Algorithms (EAs). After testing different algorithm variants we conclude that the best option is an asexual EA using order-based representation and an adaptation mechanism that periodically changes the fitness function during the evolution. This adaptive EA is general, using no domain specific knowledge, except, of course, from the decoder (fitness function). We compare this adaptive EA to a powerful traditional graph coloring technique DSatur and the Grouping Genetic Algorithm (GGA) on a wide range of problem instances with different size, topology and edge density. The results show that the adaptive EA is superior to the Grouping (GA) and outperforms DSatur on the hardest problem instances. Furthermore, it scales up better with the problem size than the other two algorithms and indicates a linear computational complexity.

Hybrid Genetic Algorithms for a Rostering Problem

Hybrid Genetic Algorithms are described for a large-size real-life rostering problem (railway workers' job scheduling and roster optimization). The new algorithm uses an order-based representation which encodes as a chromosome the list of job units to schedule. First, a greedy algorithm is considered, which uses a randomly generated job units list, and satisfies only the constraints pertaining to the workers' job contract. Then, a genetic algorithm optimizes the global roster, minimizing its length and achieving some desired homogenizations. Finally, a second genetic algorithm (GA) is used to find the best parameter values for the first genetic algorithm. Thus, this work investigates the use of a GA together with a greedy algorithm and of a second GA to optimize the parameter values of the first GA. The results of significant tests on real data are reported. They compare favourably with the known results on Rostering Problems, both in terms of execution time and solution accuracy. This work considers a practical Rostering Problem concerning the Railway workers' rosters optimization. The size of the input data is very challenging: about 1000 duties (i.e. job-units called ‘links’) based on a large-size city location; 125 days to consider for roster optimization (summer rostering); the goal is to optimize the structure of the working-turn for any worker, and to minimize the global cost of the rosters. It should be emphasised that this is a very large problem: we will use GAs to solve the problem within an execution time in the order of a few minutes on a common workstation.