Shivam Gupta

The k most vital arcs in the shortest path problem

The k most vital arcs in a network are those whose removal from the network results in the greatest increase in the shortest distance between two specified nodes. An exact algorithm is proposed to determine the k most vital arcs. Furthermore, an algorithm of time complexity equal to that of Dijkstras algorithm for the shortest path problem is developed to solve the single most vital arc problem.

Understanding knee points in bicriteria problems and their implications as preferred solution principles

A knee point is almost always a preferred trade-off solution, if it exists in a bicriteria optimization problem. In this article, an attempt is made to improve understanding of a knee point and investigate the properties of a bicriteria problem that may exhibit a knee on its Pareto-optimal front. Past studies are reviewed and a couple of new definitions are suggested. Additionally, a knee region is defined for problems in which, instead of one, a set of knee-like solutions exists. Edge-knee solutions, which behave like knee solutions but lie near one of the extremes on the Pareto-optimal front, are also introduced. It is interesting that in many problem-solving tasks, despite the existence of a number of solution methodologies, only one or a few of them are commonly used. Here, it is argued that often such common solution principles are knee solutions to a bicriteria problem formed with two conflicting goals of the underlying problem-solving task. The argument is illustrated on a number of tasks, such as regression, sorting, clustering and a number of engineering designs.

Unconstrained quadratic bivalent programming problem

Abstract A branching and pruning algorithm is proposed to minimize an unconstrained quadratic function of 0–1 variables. A local minimizing point is defined; and a necessary and sufficient condition for such a point is identified. The algorithm generates all such local minimizing points. The computational experience with the algorithm, which is encouraging, is also given.

k-Sum optimization problems

We consider a family of subsets of a finite set, each of cardinality n, as feasible solutions of a combinatorial optimization problem. Using weights associated with the elements of the given finite set, k-sum optimization problems and k-sum deviation problems are defined. We show that such problems can be solved efficiently if the n-sum problem can be solved efficiently. If the family F is the base system of a matroid, the k-sum optimization problem can be solved by a greedy algorithm. The solutions of k-sum optimization problems are used to give a new characterization of matroids. The k-sum spanning tree problem is also considered. Using an algorithm to obtain minmax spanning trees, a decomposition algorithm is proposed to solve such problems. This decomposition algorithm can also be used to improve the efficiency of most of the known minimum spanning tree algorithms.

A parametric algorithm for convex cost network flow and related problems

Abstract The convex cost network flow problem is to determine the minimum cost flow in a network when cost of flow over each arc is given by a piecewise linear convex function. In this paper, we develop a parametric algorithm for the convex cost network flow problem. We define the concept of optimum basis structure for the convex cost network flow problem. The optimum basis structure is then used to parametrize v, the flow to be transsshipped from source to sink. The resulting algorithm successively augments the flow on the shortest paths from source to sink which are implicitly enumerated by the algorithm. The algorithm is shown to be polynomially bounded. Computational results are presented to demonstrate the efficiency of the algorithm in solving large size problems. We also show how this algorithm can be used to (i) obtain the project cost curve of a CPM network with convex time-cost tradeoff functions; (ii) determine maximum flow in a network with concave gain functions; (iii) determine optimum capacity expansion of a network having convex arc capacity expansion costs.

OPTIMAL EXPANSION OF CAPACITATED TRANSSHIPMENT NETWORKS

Abstract In this paper, we address the problem of allocating a given budget to increase the capacities of arcs in a transshipment network to minimize the cost of flow in the network. The capacity expansion costs of arcs are assumed to be piecewise linear convex functions. We use properties of the optimum solution to convert this problem into a parametric network flow problem. The concept of optimum basis structure is used which allows us to consider piecewise linear convex functions without introducing additional arcs. The resulting algorithm yields an optimum solution of the capacity expansion problem for all budget levels less than or equal to the given budget. For integer data, the algorithm performs almost all computations in integers. Detailed computational results are also presented.

Group centre and group median of a network

Abstract The absolute centre and median of a network can be computed in polynomial time. We use a partition of the nodes to define group centre and group median of the network. These ideas can be used to unify the concepts of absolute centre and median. We give polynomially bounded algorithms to identify group centre and group median of a network. It may be observed that the introduction of partitions in some other combinatorial optimization problems, e.g. the assignment problem, changes the polynomial nature of the problem.

Compliance, network, security and the people related factors in cloud ERP implementation

Summary Cloud enterprise resource planning (ERP) is a buzz in the information technology domain. Small and medium enterprises (SMEs) do not have the financial budget to invest in on-premise ERP solution. The use of cloud-based services for SMEs has led to widespread diffusion of technology. The two big stakeholders in the cloud ERP are cloud user and cloud vendor. This paper brings out the factors that are under the influence of these two stakeholders. Critical success factors that are influenced by the people in the organization are considered for the study. Compliance, network, and security are the concerns that are under the control of cloud vendor. This study shows the factors that have an impact on the successful implementation of cloud ERP. An online questionnaire was designed and data from 208 respondents belonging to SMEs were collected. Structural equation modeling was used for data analysis. It was found that people-related factors and compliance had an impact toward the successful implementation of cloud-based services. Network and security factors did not show any significant impact on the implementation of cloud ERP. Copyright

Implementation of Cloud ERP - Moderating Effect of Compliance on the Organizational Factors

Cloud ERP has changed the way business can be done for Small and Medium Enterprises (SMEs). The two important benefits offered by Cloud ERP are: (a) SMEs can log into the internet from any place to access applications and data services at any point in the time. (b) Pay for the services that are used or needed. Although Cloud ERP has taken the IT world by storm and with all the advancement that has taken place so far, there are still issues and challenges that require to be addressed. This paper relates issues pertaining to Compliance with Organizational factors for successful implementation of Cloud ERP.

Solving dual problems using a coevolutionary optimization algorithm

In solving certain optimization problems, the corresponding Lagrangian dual problem is often solved simply because in these problems the dual problem is easier to solve than the original primal problem. Another reason for their solution is the implication of the weak duality theorem which suggests that under certain conditions the optimal dual function value is smaller than or equal to the optimal primal objective value. The dual problem is a special case of a bilevel programming problem involving Lagrange multipliers as upper-level variables and decision variables as lower-level variables. Another interesting aspect of dual problems is that both lower and upper-level optimization problems involve only box constraints and no other equality of inequality constraints. In this paper, we propose a coevolutionary dual optimization (CEDO) algorithm for co-evolving two populations—one involving Lagrange multipliers and other involving decision variables—to find the dual solution. On 11 test problems taken from the optimization literature, we demonstrate the efficacy of CEDO algorithm by comparing it with a couple of nested smooth and nonsmooth algorithms and a couple of previously suggested coevolutionary algorithms. The performance of CEDO algorithm is also compared with two classical methods involving nonsmooth (bundle) optimization methods. As a by-product, we analyze the test problems to find their associated duality gap and classify them into three categories having zero, finite or infinite duality gaps. The development of a coevolutionary approach, revealing the presence or absence of duality gap in a number of commonly-used test problems, and efficacy of the proposed coevolutionary algorithm compared to usual nested smooth and nonsmooth algorithms and other existing coevolutionary approaches remain as the hallmark of the current study.