Paradigm and Paradox in Topology Control of Power Grids

Corrective Transmission Switching can be used by the grid operator to relieve line overloading and voltage violations, improve system reliability, and reduce system losses. Power grid optimization by means of line switching is typically formulated as a mixed integer programming problem (MIP). Such problems are known to be computationally intractable, and accordingly, a number of heuristic approaches to grid topology reconfiguration have been proposed in the power systems literature. By means of some low order examples (3-bus systems), it is shown that within a reasonably large class of greedy heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence based on a large number of simulations using using IEEE 118- bus systems indicates that among three heuristics, a globally greedy heuristic is the most computationally intensive, but has the best chance of reducing generation costs while enforcing N-1 connectivity. It is argued that, among all iterative methods, the locally optimal switches at each stage have a better chance in not only approximating a global optimal solution but also greatly limiting the number of lines that are switched

Paradigm and paradox in topology control of power grids

Corrective Transmission Switching can be used by the grid operator to relieve line overloading and voltage violations, improve system reliability, and reduce system losses. Power grid optimization by means of line switching is typically formulated as a mixed integer programming problem (MIP). Such problems are known to be computationally intractable, and accordingly, a number of heuristic approaches to grid topology reconfiguration have been proposed in the power systems literature. By means of some low order examples (3-bus systems), it is shown that within a reasonably large class of “greedy” heuristics, none can be found that perform better than the others across all grid topologies. Despite this cautionary tale, statistical evidence based on a large number of simulations using IEEE 118-bus systems indicates that among three heuristics, a globally greedy heuristic is the most computationally intensive, but has the best chance of reducing generation costs while enforcing N-1 connectivity. It is argued that, among all iterative methods, the locally optimal switches at each stage have a better chance in not only approximating a global optimal solution but also greatly limiting the number of lines that are switched.First author draf

Empirical Analysis of Various Multi-Dimensional Knapsack Heuristics

Since the multidimensional knapsack problems are NP-hard problems, the exact solutions of knapsack problems often need excessive computing time and storage space. Thus, heuristic approaches are more practical for multidimensional knapsack problems as problems get large. This thesis presents the results of an empirical study of the performance of heuristic solution procedures based on the coefficients correlation structures and constraint slackness settings. In this thesis, the three representative greedy heuristics, Toyoda, Senju and Toyoda, and Loulou and Michaelides’ methods, are studied. The purpose of this research is to explore which heuristic of the three representative greedy heuristics performs best under certain combinations of conditions between constraint slackness and correlation structures. This thesis examines three heuristics over 1120 problems which are all the two-dimensional knapsack problems (2KPs) with 100 variables created by four constraint slackness settings and 45 feasible correlation structures. Then we analyze why the best heuristic behaves as it does as a function of problem characteristics. Finally we present two new heuristics using knowledge gained in the study. When these new heuristics are competitively tested against the three representative greedy heuristics, the results show the new heuristics perform better

An index for dynamic product promotion and the knapsack problem for perishable items

This paper introduces the knapsack problem for perishable items (KPPI), which concerns the optimal dynamic allocation of a limited promotion space to a collection of perishable items. Such a problem is motivated by applications in a variety of industries, where products have an associated lifetime after which they cannot be sold. The paper builds on recent developments on restless bandit indexation and gives an optimal marginal productivity index policy for the dynamic (single) product promotion problem with closed-form indices that yield estructural insights. The performance of the proposed policy for KPPI is investigated in a computational study.Dynamic promotion, Perishable items, Index policies, Knapsack problem, Festless bandits, Finite horizon, Marginal productivity index

Developing New Multidimensional Knapsack Heuristics Based on Empirical Analysis of Legacy Heuristics

The multidimensional knapsack problem (MKP) has been used to model a variety of practical optimization and decision-making applications. Due to its combinatorial nature, heuristics are often employed to quickly find good solutions to MKPs. While there have been a variety of heuristics proposed for the MKP, and a plethora of empirical studies comparing the performance of these heuristics, little has been done to garner a deeper understanding of heuristic performance as a function of problem structure. This dissertation presents a research methodology, empirical and theoretical results explicitly aimed at gaining a deeper understanding of heuristic procedural performance as a function of test problem characteristics. This work first employs an available, robust set of two-dimensional knapsack problems in an empirical study to garner performance insights. These performance insights are tested against a larger set of problems, five-dimensional knapsack problems specifically generated for empirical testing purposes. The performance insights are found to hold in the higher dimensions. These insights are used to formulate and test a suite of three new greedy heuristics for the MKP, each improving upon its successor. These heuristics are found to outperform available legacy heuristics across a complete spectrum of test problems. Problem reduction heuristics are examined and the subsequent performance insights garnered are used to derive a new problem reduction heuristic, which is then further extended to employ a local improvement phase. These problem reduction heuristics are also found to outperform currently available approaches. Available problem test sets are shown lacking along multiple dimensions of importance for viable empirical testing. A new problem generation methodology is developed and shown to overcome the current limitations in available problem test sets. This problem generation methodology is used to generate a new set of empirical test problems specifically designed for competitive computational tests. This new test set is shown to stress existing heuristics; not only does the computational time required by these legacy heuristics increase with problem size, but solution quality is found to decrease with problem size. However, the solution quality obtained by the suite of heuristics developed in this dissertation are shown to be unaffected by problem size thereby providing a level of robust solution quality not previously seen in heuristic development for the MKP. This research demonstrates that the test problems can have a profound, and sometimes misleading, impact on the general insights gained via empirical testing, provides six new quality heuristics, and two new robust sets of test problems, one focused on empirical testing, the other focused on competitive testing

Improved algorithms for machine allocation in manufacturing systems

In this paper we present two algorithms for a machine allocation problem occurring in manufacturing systems. For thetwo algorithms presented we prove worst-case performance ratios of 2 and 312, respectively. The machlne allocat~onproblem we consider is a general convex resource allocation problem, which makes the algorithms applicable to a varletyof resource allocation problems. Numerical results are presented for two real-life manufacturing systems.networks;manufacturing;allocation of machines;performance/productivity;queues