Pradyumn Kumar Shukla

Specification of the social force pedestrian model by evolutionary adjustment to video tracking data

Based on suitable video recordings of interactive pedestrian motion and improved tracking software, we apply an evolutionary optimization algorithm to determine optimal parameter specifications for the social force model. The calibrated model is then used for large-scale pedestrian simulations of evacuation scenarios, pilgrimage, and urban environments.

On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods

In solving multi-objective optimization problems, evolutionary algorithms have been adequately applied to demonstrate that multiple and well-spread Pareto-optimal solutions can be found in a single simulation run. In this paper, we discuss and put together various different classical generating methods which are either quite well-known or are in oblivion due to publication in less accessible journals and some of which were even suggested before the inception of evolutionary methodologies. These generating methods specialize either in finding multiple Pareto-optimal solutions in a single simulation run or specialize in maintaining a good diversity by systematically solving a number of scalarizing problems. Most classical generating methodologies are classified into four groups mainly based on their working principles and one representative method from each group is chosen in the present study for a detailed discussion and for its performance comparison with a state-of-the-art evolutionary method. On visual comparisons of the efficient frontiers obtained for a number of two and three-objective test problems, the results bring out interesting insights about the strengths and weaknesses of these approaches. The results should motivate researchers to design hybrid multi-objective optimization algorithms which may be better than each of the individual methods.

Inefficient emergent oscillations in intersecting driven many-particle flows

Oscillatory flow patterns have been observed in many different driven many-particle systems. It seems reasonable to assume that the emergent oscillations in opposing flows are due to or related to an increased efficiency (throughput). In this contribution, however, we will study intersecting pedestrian and vehicle flows as an example for inefficient emergent oscillations. In the coupled vehicle–pedestrian delay problem, oscillating pedestrian and vehicle flows form when pedestrians cross the street with a small time gap to approaching cars, while both pedestrians and vehicles benefit, when they keep some overcritical time gap. That is, when the safety time gap of pedestrians is increased, the average delay time of pedestrians decreases and the vehicle flow goes up. This may be interpreted as a slower-is-faster effect. The underlying mechanism of this effect is explained.

On gradient based local search methods in unconstrained evolutionary multi-objective optimization

Evolutionary algorithms have been adequately applied in solving single and multi-objective optimization problems. In the single-objective case various studies have shown the usefulness of combining gradient based classical methods with evolutionary algorithms. However there seems to be limited number of such studies for the multi-objective case. In this paper, we take two classical methods for unconstrained multi-optimization problems and discuss their use as a local search operator in a state-of-the-art multi-objective evolutionary algorithm. These operators require gradient information which is obtained using finite difference method and using a stochastic perturbation technique requiring only two function evaluations. Computational studies on a number of test problems of varying complexity demonstrate the efficiency of resulting hybrid algorithms in solving a large class of complex multi-objective optimization problems. We also discuss a new convergence metric which is useful as a stopping criteria for problems having an unknown Pareto-optimal front.

Comparing classical generating methods with an evolutionary multi-objective optimization method

For the past decade, many evolutionary multi-objective optimization (EMO) methodologies have been developed and applied to find multiple Pareto-optimal solutions in a single simulation run. In this paper, we discuss three different classical generating methods, some of which were suggested even before the inception of EMO methodologies. These methods specialize in finding multiple Pareto-optimal solutions in a single simulation run. On visual comparisons of the efficient frontiers obtained for a number of two and three-objective test problems, these algorithms are evaluated with an EMO methodology. The results bring out interesting insights about the strengths and weaknesses of these approaches. Further investigations of such classical generating methodologies and their evaluation should enable researchers to design a hybrid multi-objective optimization algorithm which may be better than each individual method.

On the inexactness level of robust Levenberg–Marquardt methods

Recently, the Levenberg–Marquardt (LM) method has been used for solving systems of nonlinear equations with nonisolated solutions. Under certain conditions it converges Q-quadratically to a solution. The same rate has been obtained for inexact versions of the LM method. In this article the LM method will be called robust, if the magnitude of the regularization parameter occurring in its sub-problems is as large as possible without decreasing the convergence rate. For robust LM methods the article shows that the level of inexactness in the sub-problems can be increased significantly. As an application, the local convergence of a projected robust LM method is analysed.

On the Normal Boundary Intersection Method for Generation of Efficient Front

This paper is concerned with the problem of finding a representative sample of Pareto-optimal points in multi-objective optimization. The Normal Boundary Intersection algorithm is a scalarization scheme for generating a set of evenly spaced Efficient solutions. A drawback of this algorithm is that Pareto-optimality of solutions is not guaranteed. The contributions of this paper are two-fold. First, it presents alternate formulation of this algorithms, such that (weak) Pareto-optimality of solutions is guaranteed. This improvement makes these algorithm theoretically equivalent to other classical algorithms (like weighted-sum or ?-constraint methods), without losing its ability to generate a set of evenly spaced Efficient solutions. Second, an algorithm is presented so as to know beforehand about certain sub-problems whose solutions are not Pareto-optimal and thus not wasting computational effort to solve them. The relationship of the new algorithm with weighted-sum and goal programming method is also presented.

Electrical load management in smart homes using evolutionary algorithms

In this paper, we focus on a real world scenario of energy management of a smart home. External variable signals, reflecting the low voltage grids state, are used to address the challenge of balancing energy demand and supply. The problem is formulated as a nonlinear integer programming problem and a load management system, based on a customized evolutionary algorithm with local search, is proposed to control intelligent appliances, decentralized power plants and electrical storages in an optimized way with respect to the given external signals. The nonlinearities present in the integer programming problem makes it difficult for exact solvers. The results of this paper show the efficacy of evolutionary algorithms for solving such combinatorial problems.

Variable preference modeling using multi-objective evolutionary algorithms

Decision making in the presence of multiple and conflicting objectives requires preference from the decision maker. The decision makers preferences give rise to a domination structure. Till now, most of the research has been focussed on the standard domination structure based on the Pareto-domination principle. However, various real world applications like medical image registration, financial applications, multicriteria n-person games, among others, or even the preference model of decision makers frequently give rise to a so-called variable domination structure, in which the domination itself changes from point to point. Although variable domination is studied in the classical community since the early seventies, we could not find a single study in the evolutionary domain, even though, as the results of this paper show, multi-objective evolutionary algorithms can deal with the vagaries of a variable domination structure. The contributions of this paper are multiple-folds. Firstly, the algorithms are shown to be able to find a well-diverse set of the optimal solutions satisfying a variable domination structure. This is shown by simulation results on a number of test-problems. Secondly, it answers a hitherto open question in the classical community to develop a numerical method for finding a well-diverse set of such solutions. Thirdly, theoretical results are derived which facilitate the use of an evolutionary multi-objective algorithm. The theoretical results are of importance on their own. The results of this paper adequately show the niche of multi-objective evolutionary algorithms in variable preference modeling.

A Levenberg-Marquardt algorithm for unconstrained multicriteria optimization

To compute one of the nonisolated Pareto-critical points of an unconstrained multicriteria optimization problem a Levenberg-Marquardt algorithm is applied. Sufficient conditions for an error bound are provided to prove its fast local convergence. A globalized version is shown to converge to a Pareto-optimal point under convexity assumptions.