This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These are incomparable to each other and two of them standard SDP relaxation OPF. Extensive computational experiments show that these have numerous advantages over existing convex in literature: (i) their solution quality is extremely close (the best one within 99.96% on average all IEEE test cases) consistently outperforms previously proposed quadratic OPF problem,...

In this paper, we examine a mixed integer linear programming reformulation for bilinear problems where each bilinearterm involves the product of nonnegative variable and continuous variable. This is obtained by first replacing general with its binary expansion then using McCormick envelopes to linearize resulting variables. We present convex hull underlying set. The effectiveness associated facet-defining inequalities are computationally evaluated on five classes instances.

It has been recently proven that the semidefinite programming (SDP) relaxation of optimal power flow problem over radial networks is exact under technical conditions such as not including generation lower bounds or allowing load over-satisfaction. In this paper, we investigate situation where are present. We show even for a two-bus one-generator system, SDP can have all possible approximation outcomes, (1) may be (2) inexact (3) feasible while OPF instance infeasible. provide complete...

We present a method to construct and analyse 3D models of underwater scenes using single cost-effective camera on standard laptop with (a) free or low-cost software, (b) no computer programming ability, (c) minimal man hours for both filming analysis. This study focuses four key structural complexity metrics: point-to-point distances, linear rugosity (R), fractal dimension (D), vector dispersion (1/k). the first assessment accuracy precision structure-from-motion (SfM) from an uncalibrated...

As the modern transmission control and relay technologies evolve, line switching has become an important option in power system operators' toolkits to reduce operational cost improve reliability. Most recent research relied on DC approximation of flow model optimal problem. However, it is known that may lead inaccurate solutions also overlook stability issues. In this paper, we focus problem with full AC model, abbreviated as (AC OTS). We propose a new exact formulation for OTS its...

We consider the integer L-shaped method for two-stage stochastic programs. To improve performance of algorithm, we present and combine two strategies. First, to avoid time-consuming exact evaluations second-stage cost function, propose a simple modification that alternates between linear mixed-integer subproblems. Next, better approximate shape general framework generate optimality cuts via cut-generating program considers information from all solutions found up any given stage method....

One of the most complicating factors in decentralized solution methods for a broad range power system optimization problems is modeling flow equations. Existing formulations direct current flows either have limited scalability or are very dense and unstructured, making them unsuitable large-scale studies. In this work, we present novel sparsified variant injection shift formulation, which has decomposable block-diagonal structure scales well large systems. We also propose method, based on...

We consider a class of linear programs involving set covering constraints which at most k are allowed to be violated. show that this program with violation is strongly 𝒩𝒫-hard. To improve the performance mixed-integer programming-based schemes for these problems, we introduce and analyze coefficient strengthening scheme, adapt an existing cutting plane technique, present branching technique. Through computational experiments, empirically verify techniques significantly effective in improving...

Recently minimal and extreme inequalities for continuous group relaxations of general mixed integer sets have been characterized. In this paper, we consider a stronger relaxation by allowing constraints, such as bounds, on the free variables in relaxation. We generalize number results infinite to characterize when there are two variables.

It is well-known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. In fact, USA Energy Policy Act 2005 (Section 1223) states U.S. should "encourage, as appropriate, deployment advanced technologies" including "optimized line configurations". As such, many authors have studied problem determining an optimal set to switch minimize cost meeting a given demand under direct current (DC) model flow. This...

The pq-relaxation for the pooling problem can be constructed by applying McCormick envelopes each of bilinear terms appearing in so-called pq-formulation problem. This relaxation strengthened using piecewise-linear functions that over- and under-estimate term. Although there is a significant amount empirical evidence to show such relaxations, which written as mixed-integer linear programs (MILPs), yield good bounds problem, best our knowledge, no formal result regarding quality these...

The goal of this software is to computationally ascertain how common it for the strong branching rule exhibit non-monotonicity in practice. We do so by applying cover cuts on randomly generated multi-dimensional knapsacks as well considering applied SCIP MIPLIB 2017 benchmark set. Our main insight from these experiments that if gap closed small, change tree size difficult predict, and often increases, possibly due inherent non-monotonicity. However, when a sufficiently large closed,...

Modern mixed-integer programming solvers use the branch-and-cut framework, where cutting planes are added to improve tightness of linear (LP) relaxation, with expectation that tighter formulation would produce smaller branch-and-bound trees. In this work, we consider question whether adding cuts will always lead trees for a given fixed branching rule. We formally call such property rule monotonicity. prove any which exclusively branches on fractional variables in LP solution is nonmonotonic....

Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension the duality theory for (see [M. Güzelsoy and T. K. Ralphs, Int. J. Oper. Res. (Taichung), 4 (2007), pp. 118--137], [G. L. Nemhauser A. Wolsey, Integer Combinatorial Optimization, Wiley-Interscience, New York, 1988]) to case particular, construct subadditive dual problems. Under simple condition on primal problem, show that strong holds.