C. Patvardhan

A hybrid quantum evolutionary algorithm for solving engineering optimization problems

Evolutionary Algorithms (EA) have been successfully employed for solving difficult constrained engineering optimization problems. However, EA implementations often suffer from premature convergence due to the lack of proper balance between exploration and exploitation in the search process. This paper proposes a Hybrid Quantum inspired EA, which balances the exploration and exploitation in the search process by adaptively evolving the populations. It employs an adaptive quantum rotation based crossover operator designed by hybridizing a conventional crossover operator with the principles of Quantum Mechanics. The degree of rotation in this operator is determined adaptively. The proposed algorithm does not require either a mutation operator, to avoid premature convergence, or a local heuristic to improve convergence rate. Further, a parameter-tuning free hybrid technique is employed for handling constraints, which overcomes some limitations in the traditional techniques like penalty factor methods, by hybridizing Feasibility Rules method with Adaptive Penalty Factor method. It is implemented by using two populations, each evolving by applying one of the constraints handling techniques and swapping a part of the populations. A standard set of six diverse benchmark engineering design optimization problems have been used for testing the proposed algorithm. The algorithm exhibits superior performance than the existing state-of-the-art approaches.

Quantum-Inspired Evolutionary Algorithm for difficult knapsack problems

Quantum Inspired Evolutionary Algorithms (QIEAs) are Evolutionary Algorithms which use concepts and principles of quantum computing. The 0/1 knapsack problem (KP) is a well known combinatorial optimization problem that has been typically used to validate the performance of QIEAs. However, there are some variants of KPs called difficult knapsack problems (DKPs) that are known to be more difficult to solve. QIEAs have not yet been fully explored for solving these. In this work, an improved QIEA, called QIEA-PSA is presented. A novel method to initialize the qubit individuals based on heuristic information for the KP instance and a method for size reduction for each new generation are introduced in the presented QIEA-PSA. Experiments are carried out for several types of DKPs that are much larger in size than those attempted hitherto. QIEA-PSA provides much better solutions than QIEA with much lesser computation times. Even a serial implementation of QIEA-PSA competes favorably on the same problem instances with a parallel implementation of an exact algorithm given recently in literature. A comparison is made which shows QIEA-PSA outperforms a recently applied population based search technique to solve benchmark KP instances. The ideas used for developing QIEA-PSA are general and may be utilized with advantage on other problems.

A novel hybrid constraint handling technique for evolutionary optimization

Evolutionary Algorithms are amongst the best known methods of solving difficult constraint optimization problems, for which traditional methods are not applicable. However, there are no inbuilt or organic mechanisms available in Evolutionary Algorithms for handling constraints in optimization problems. These problems are solved by converting or treating them as unconstrained optimization problems. Several constraint handling techniques have been developed and reported in literature, of which, the penalty factor and feasibility rules are the most promising and widely used for such purposes. However, each of these techniques has its own advantages and disadvantages and often require fine tuning of one or more parameters, which in itself becomes an optimization problem. This paper presents a hybrid constraint handling technique for a two population adaptive coevolutionary algorithm, which uses a self determining and regulating penalty factor method as well as feasibility rules for handling constraints. Thus, the method overcomes the drawbacks in both the methods and utilizes their strengths to effectively and efficiently handle constraints. The simulation on ten benchmark problems demonstrates the efficacy of the approach.

Enhanced quantum evolutionary algorithms for difficult knapsack problems

Difficult knapsack problems are problems that are expressly designed to be difficult. In this paper, enhanced Quantum Evolutionary Algorithms are designed and their application is presented for the solution of the DKPs. The algorithms are general enough and can be used with advantage in other subset selection problems.

A high accuracy OCR system for printed Telugu text

Telugu is one of the oldest and most popular languages of India. The paper describes the design and development of a Telugu optical character recognition system for printed text (TOSP). Preprocessing tasks considered are: conversion of a grey scale image to a binary image; image rectification; skew detection and removal; segmentation of text into lines, words and basic symbols. Basic symbols are identified as the fundamental unit of segmentation and are recognized by neural recognizers. The recognizers are aided by an improvement module that uses additional logic to recognize confusing symbols correctly, resulting in increased recognition accuracy. The combinations of these basic symbols that together form characters and compound characters of Telugu are also determined to complete the recognition process. The special feature of TOSP is that it is designed to handle multiple sizes and multiple fonts. Further, the output produced by TOSP can be opened directly in any Indian language software that supports the facility for transliteration into Telugu script, and then edited. Several such software are popular and available.

Document image denoising and binarization using Curvelet transform for OCR applications

Practically document images may have complex background in form of non-uniform illumination (shading) or an image in background. Such complex backgrounds result poor binarization causing character recognition errors. If such images are transmitted over a noisy analog channel, they are also corrupted by white Gaussian noise that makes binarization even worse. In this paper, a denoising and binarization scheme of document images to make them suitable for OCR using discrete Curvelet transform is presented. The proposed Curvelet based method is able to remove complex image background as well as white Gaussian noise and results in a better binarized document image as compared to other conventional methods. The ability of sparse representation and edge preservation of Curvelet transform helps better in text shape preservation even in the presence of noise. The proposed method is able to remove low frequency complex backgrounds and high frequency Gaussian noise and their combinations from document images and shows better performance in such noise combination cases when compared to commercial OCR packages.

A novel quantum evolutionary algorithm for quadratic Knapsack problem

The Quadratic Knapsack Problem (QKP) deals with maximizing a quadratic objective function subject to given constraints on the capacity of the Knapsack. We assume all coefficients to be non-negative and all variables to be binary. Solution to QKP generalizes the problem of finding whether a graph contains a clique of given size. We propose in this paper a Novel Quantum Evolutionary Algorithm (NQEA) for QKPs. These algorithms are general enough and can be used for similar subsection of problems. We report in this paper solutions which lie in less than 1% of the optimal solutions. We also show that our algorithm is scalable to much larger problem sizes and is capable of exploiting the search space to its maximum.

Is stochastic ranking really better than Feasibility Rules for constraint handling in Evolutionary Algorithms

Evolutionary Algorithms have been widely used to solve difficult constrained optimization problems. However, Evolutionary algorithms are intrinsically unconstrained optimization techniques. Constraint handling is mostly incorporated additionally and its choice has great bearing on the quality of the solution. Stochastic Ranking was introduced as an improvement over Feasibility Rules for handling constraints in Evolutionary Optimization. It is widely believed that stochastic ranking is currently the best-known technique for handling constraints. However, a fair comparative study has never been attempted in the literature, where by the performance of both the constraint handling technique is compared on the same Evolutionary Algorithm. This paper fairly compares the performance of both the constraint handling techniques on the same Evolutionary Algorithm over a set of parameters like feasibility rate, successful run, success rate and success performance in addition to objective function value and number of function evaluations. The results put a question mark over the belief that Feasibility Rules are worse than Stochastic Ranking.

A New QEA Computing Near-Optimal Low-Discrepancy Colorings in the Hypergraph of Arithmetic Progressions

We present a new quantum-inspired evolutionary algorithm, the attractor population QEA (apQEA). Our benchmark problem is a classical and difficult problem from Combinatorics, namely finding low-discrepancy colorings in the hypergraph of arithmetic progressions on the first n integers, which is a massive hypergraph (e.g., with approx. 3.88 ×1011 hyperedges for n = 250 000). Its optimal low-discrepancy coloring bound \(\Theta(\sqrt[4]{n})\) is known and it has been a long-standing open problem to give practically and/or theoretically efficient algorithms. We show that apQEA outperforms known QEA approaches and the classical combinatorial algorithm (Sarkozy 1974) by a large margin. Regarding practicability, it is also far superior to the SDP-based polynomial-time algorithm of Bansal (2010), the latter being a breakthrough work from a theoretical point of view. Thus we give the first practical algorithm to construct optimal colorings in this hypergraph, up to a constant factor. We hope that our work will spur further applications of Algorithm Engineering to Combinatorics.

Parallel improved quantum inspired evolutionary algorithm to solve large size Quadratic Knapsack Problems

Quadratic Knapsack Problem (QKP), an extension of the canonical simple Knapsack Problem, is NP Hard in the stronger sense. No pseudo-polynomial time algorithm is known to exist which can solve QKP instances. QKP has been studied intensively due to its simple structure yet challenging difficulty and numerous applications. A few attempts have been made to solve large size instances of QKP due to its complexity. Quantum Inspired Evolutionary Algorithm (QIEA) provides a generic framework that has often been carefully tailored for a given problem to obtain an effective implementation. In this work, an improved and parallelized QIEA, dubbed IQIEA-P is presented. Several additional features make it more balanced in exploration and exploitation and thus have better applicability. Computational experiments are presented on large QKP instances of 1000 and 2000 items. The improvements are inherently parallelizable and, therefore, good speedups are obtained on a multi-core machine. No parallel algorithm is available for QKP. The solutions provided by QIEA-P are competitive with those obtained from the state of the art algorithm