Tapabrata Ray

Society and civilization: An optimization algorithm based on the simulation of social behavior

The ability to mutually interact is a fundamental social behavior in all human and insect societies. Social interactions enable individuals to adapt and improve faster than biological evolution based on genetic inheritance alone. This is the driving concept behind the optimization algorithm introduced in this paper that makes use of the intra and intersociety interactions within a formal society and the civilization model to solve single objective constrained optimization problems. A society corresponds to a cluster of points in the parametric space while a civilization is a set of all such societies. Every society has its set of better performing individuals (leaders) that help others to improve through information exchange. This results in the migration of a point toward a better performing point, analogous to an intensified local search. Leaders improve only through an intersociety information exchange that results in the migration of a leader from a society to another. This helps the better performing societies to expand and flourish.

A Swarm Metaphor for Multiobjective Design Optimization

This paper presents a new optimization algorithm to solve multiobjective design optimization problems based on behavioral concepts similar to that of a real swarm. The individuals of a swarm update their flying direction through communication with their neighboring leaders with an aim to collectively attain a common goal. The success of the swarm is attributed to three fundamental processes: identification of a set of leaders, selection of a leader for information acquisition, and finally a meaningful information transfer scheme. The proposed algorithm mimics the above behavioral processes of a real swarm. The algorithm employs a multilevel sieve to generate a set of leaders, a probabilistic crowding radius-based strategy for leader selection and a simple generational operator for information transfer. Two test problems, one with a discontinuous Pareto front and the other with a multi-modal Pareto front is solved to illustrate the capabilities of the algorithm in handling mathematically complex problems. Three well-studied engineering design optimization problems (unconstrained and constrained problems with continuous and discrete variables) are solved to illustrate the efficiency and applicability of the algorithm for multiobjective design optimization. The results clearly indicate that the swarm algorithm is capable of generating an extended Pareto front, consisting of well spread Pareto points with significantly fewer function evaluations when compared to the nondominated sorting genetic algorithm (NSGA).

MULTIOBJECTIVE DESIGN OPTIMIZATION BY AN EVOLUTIONARY ALGORITHM

Abstract This paper presents an evolutionary algorithm for generic multiobjective design optimization problems. The algorithm is based on nondominance of solutions in the objective and constraint space and uses effective mating strategies to improve solutions that are weak in either. Since the methodology is based on nondominance, scaling and aggregation affecting conventional penalty function methods for constraint handling does not arise. The algorithm incorporates intelligent partner selection for cooperative mating. The diversification strategy is based on niching which results in a wide spread of solutions in the parametric space. Results of the algorithm for the design examples clearly illustrate the efficiency of the algorithm in solving multidisciplinary design optimization problems.

A Pareto Corner Search Evolutionary Algorithm and Dimensionality Reduction in Many-Objective Optimization Problems

Many-objective optimization refers to the optimization problems containing large number of objectives, typically more than four. Non-dominance is an inadequate strategy for convergence to the Pareto front for such problems, as almost all solutions in the population become non-dominated, resulting in loss of convergence pressure. However, for some problems, it may be possible to generate the Pareto front using only a few of the objectives, rendering the rest of the objectives redundant. Such problems may be reducible to a manageable number of relevant objectives, which can be optimized using conventional multiobjective evolutionary algorithms (MOEAs). For dimensionality reduction, most proposals in the paper rely on analysis of a representative set of solutions obtained by running a conventional MOEA for a large number of generations, which is computationally overbearing. A novel algorithm, Pareto corner search evolutionary algorithm (PCSEA), is introduced in this paper, which searches for the corners of the Pareto front instead of searching for the complete Pareto front. The solutions obtained using PCSEA are then used for dimensionality reduction to identify the relevant objectives. The potential of the proposed approach is demonstrated by studying its performance on a set of benchmark test problems and two engineering examples. While the preliminary results obtained using PCSEA are promising, there are a number of areas that need further investigation. This paper provides a number of useful insights into dimensionality reduction and, in particular, highlights some of the roadblocks that need to be cleared for future development of algorithms attempting to use few selected solutions for identifying relevant objectives.

Differential Evolution with Dynamic Parameters Selection for Optimization Problems

Over the last few decades, a number of differential evolution (DE) algorithms have been proposed with excellent performance on mathematical benchmarks. However, like any other optimization algorithm, the success of DE is highly dependent on the search operators and control parameters that are often decided a priori. The selection of the parameter values is itself a combinatorial optimization problem. Although a considerable number of investigations have been conducted with regards to parameter selection, it is known to be a tedious task. In this paper, a DE algorithm is proposed that uses a new mechanism to dynamically select the best performing combinations of parameters (amplification factor, crossover rate, and the population size) for a problem during the course of a single run. The performance of the algorithm is judged by solving three well known sets of optimization test problems (two constrained and one unconstrained). The results demonstrate that the proposed algorithm not only saves the computational time, but also shows better performance over the state-of-the-art algorithms. The proposed mechanism can easily be applied to other population-based algorithms.

ENGINEERING DESIGN OPTIMIZATION USING A SWARM WITH AN INTELLIGENT INFORMATION SHARING AMONG INDIVIDUALS

Abstract In this paper a new swarm algorithm for single objective design optimization problems is presented. A swarm is a collection of individuals having a common goal to reach the best value (minimum or maximum) of a function. Among the individuals in a swarm, there are some better performers (leaders) who set the direction of search for the rest of the individuals. An individual that is not in the better performer list (BPL) improves its performance by deriving information from its closest neighbour in the BPL. In an unconstrained problem, the objective values are used to generate the BPL while a multilevel Pareto ranking scheme is implemented to generate the BPL for constrained problems. The information sharing strategy also ensures that all the individuals in the swarm are unique as in a real swarm, where at a given time instant two individuals cannot share the same location. The uniqueness among the individuals result in a set of near optimal individuals at the final stage that is useful for sensitivity analysis. Three well-studied engineering design examples are solved to illustrate the benefits of the proposed swarm strategy

A Decomposition-Based Evolutionary Algorithm for Many Objective Optimization

Decomposition-based evolutionary algorithms have been quite successful in solving optimization problems involving two and three objectives. Recently, there have been some attempts to exploit the strengths of decomposition-based approaches to deal with many objective optimization problems. Performance of such approaches are largely dependent on three key factors: 1) means of reference point generation; 2) schemes to simultaneously deal with convergence and diversity; and 3) methods to associate solutions to reference directions. In this paper, we introduce a decomposition-based evolutionary algorithm wherein uniformly distributed reference points are generated via systematic sampling, balance between convergence and diversity is maintained using two independent distance measures, and a simple preemptive distance comparison scheme is used for association. In order to deal with constraints, an adaptive epsilon formulation is used. The performance of the algorithm is evaluated using standard benchmark problems, i.e., DTLZ1-DTLZ4 for 3, 5, 8, 10, and 15 objectives, WFG1-WFG9, the car side impact problem, the water resource management problem, and the constrained ten-objective general aviation aircraft design problem. Results of problems involving redundant objectives and disconnected Pareto fronts are also included in this paper to illustrate the capability of the algorithm. The study clearly highlights that the proposed algorithm is better or at par with recent reference direction-based approaches for many objective optimization.

A socio-behavioural simulation model for engineering design optimization

This paper proposes a method for solving single objective constrained optimization problems by way of a socio-behavioural simulation model. The essence of the methodology is derived from the concept that the behaviour of an individual changes and improves due to social interaction with the society leaders. Leaders are identified after all individuals of a society are Pareto ranked according to constraint satisfaction. At the higher end, leaders of all societies interact among themselves for the overall improvement of the societies. Such overall improvement of individual societies leads to a better civilization. Four well-studied single objective constrained optimization problems have been solved to show the efficacy of the proposed methodology.

Infeasibility Driven Evolutionary Algorithm for Constrained Optimization

Real life optimization problems often involve one or more constraints and in most cases, the optimal solutions to such problems lie on constraint boundaries. The performance of an optimization algorithm is known to be largely dependent on the underlying mechanism of constraint handling. Most population based stochastic optimization methods prefer a feasible solution over an infeasible solution during their course of search. Such a preference drives the population to feasibility first before improving its objective function value which effectively means that the solutions approach the constraint boundaries from the feasible side of the search space. In this chapter, we introduce an evolutionary algorithm that explicitly maintains a small percentage of infeasible solutions close to the constraint boundaries during its course of evolution. The presence of marginally infeasible solutions in the population allows the algorithm to approach the constraint boundary from the infeasible side of the search space in addition to its approach from the feasible side of the search space via evolution of feasible solutions. Furthermore, “good” infeasible solutions are ranked higher than the feasible solutions, thereby focusing the search for the optimal solutions near the constraint boundaries. The performance of the proposed algorithm is compared with Non-dominated Sorting Genetic Algorithm II (NSGA-II) on a set of single and multi-objective test problems. The results clearly indicate that the rate of convergence of the proposed algorithm is better than NSGA-II on the studied test problems. Additionally, the algorithm provides a set of marginally infeasible solutions which are of great use in trade-off studies.

Design synthesis of path generating compliant mechanisms by evolutionary optimization of topology and shape

This work demonstrates the successful synthesis of path generating compliant mechanisms by the process of topology and shape design optimization. As geometric topology variation of continuum structures is difficult to treat and analysis of the displacement path or trajectory of such structures is computationally intensive, a highly effective and efficient optimal design procedure is needed. This paper describes the use of a recently developed morphological geometric representation scheme coupled with an evolutionary algorithm to synthesize the mechanism. The scheme uses arrangements of skeleton and flesh to define structural geometry, which facilitates transmission of topological/shape characteristics across generations in the evolutionary process and will not render any geometrically invalid designs. The evolutionary algorithm solves the problem as a discrete optimization problem, with a proficient constraint handling capability.