Louis Caccetta

An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.

A globally and quadratically convergent method for absolute value equations

We investigate the NP-hard absolute value equation (AVE) Ax−|x|=b, where A is an arbitrary n×n real matrix. In this paper, we propose a smoothing Newton method for the AVE. When the singular values of A exceed 1, we show that this proposed method is globally convergent and the convergence rate is quadratic. Preliminary numerical results show that this method is promising.

A positive linear discrete-time model of capacity planning and its controllability properties

One of the most important concepts in production planning is that of the establishment of an overall or aggregate production plan. In this paper, the problem of establishing an aggregate production plan for a manufacturing plant is considered. A new dynamic discrete-time model of capacity planning utilizing concepts arising in positive linear systems (PLS) theory is proposed and its controllability property is analyzed. Controllability is a fundamental property of the system with direct implications not only in dynamic optimization problems (such as those arising in inventory and production control) but also in feedback control problems. Some new open problems regarding controllability of stationary and nonstationary PLS with linear constraints are posed in the paper. An optimal control problem for capacity planning is formulated and discussed.

Match factor for heterogeneous truck and loader fleets

The mining and construction industries have used match factor for many decades as an indicator of productivity performance. The term match factor is usually defined as the ratio of truck arrival rate to loader service time. This ratio relies on the assumption that the truck and loader fleets are homogeneous. That is, all the trucks are of the same type, and all the loaders are of the same type. In reality, mixed fleets are common. This paper proposes a method of defining match factor for heterogeneous fleets: in particular, a heterogeneous trucking fleet, a heterogeneous loading fleet, and the case where both truck and loader fleets are heterogeneous.

The SC1 property of an expected residual function arising from stochastic complementarity problems

The stochastic nonlinear complementarity problem has been recently reformulated as an expected residual minimization problem which minimizes an expected residual function defined by an NCP function. In this work, we show that the expected residual function defined by the Fischer-Burmeister function is an SC^1 function.

On the adjacency properties of paley graphs

In the application of graph theory to problems arising in network design, the requirements of the network can be expressed in terms of restrictions on the values of certain graph parameters such as connectivity, edge-connectivity, diameter, and independence number. In this paper, we focus on networks whose requirements translate into adjacency restrictions on the graph representing the network. More specifically, a graph G is said to have property P(m,n,k) if for any set of m + n distinct vertices there are at least k other vertices, each of which is adjacent to the first m vertices but not adjacent to any of the latter n vertices. The problem that arises is that of characterizing graphs having property P(m,n,k). In this paper, we present properties of graphs satisfying the adjacency property. In particular, for q 1(mod 4), a prime power, the Paley graph Gq of order q is the graph whose vertices are elements of the finite field q; two vertices are adjacent if and only if their difference is a quadratic residue. For any m, n, and k, we show that all sufficiently large Paley graphs satisfy P(m,n,k).

Convergence analysis of a block improvement method for polynomial optimization over unit spheres

Summary In this paper, we study the convergence property of a block improvement method (BIM) for the bi-quadratic polynomial optimization problem over unit spheres. We establish the global convergence of the method generally and establish its linear convergence rate under the second-order sufficient condition. We also extend the BIM to inhomogeneous polynomial optimization problems over unit spheres. Numerical results reported in this paper show that the method is promising. Copyright

Nonnegative polynomial optimization over unit spheres and convex programming relaxations

We consider approximation algorithms for nonnegative polynomial optimization over unit spheres. Such optimization models have wide applications, e.g., in signal and image processing, high order statistics, and computer vision. Since polynomial functions are nonconvex, the problems under consideration are all NP-hard. In this paper, based on convex polynomial optimization relaxations, we propose polynomial-time approximation algorithms with new approximation bounds. Numerical results are reported to show the effectiveness of the proposed approximation algorithms.

An Alternative Lagrange-Dual Based Algorithm for Sparse Signal Reconstruction

In this correspondence, we propose a new Lagrange-dual reformulation associated with an l1 -norm minimization problem for sparse signal reconstruction. There are two main advantages of our proposed approach. First, the number of the variables in the reformulated optimization problem is much smaller than that in the original problem when the dimension of measurement vector is much less than the size of the original signals; Second, the new problem is smooth and convex, and hence it can be solved by many state of the art gradient-type algorithms efficiently. The efficiency and performance of the proposed algorithm are validated via theoretical analysis as well as some illustrative numerical examples.

Parameter selection for nonnegative l 1 matrix/tensor sparse decomposition

For the nonnegative l 1 matrix/tensor sparse decomposition problem, we derive a threshold bound for the parameters beyond which all the decomposition factors are zero. The obtained result provides a guideline on selection for l 1 regularization parameters and extends the corresponding result on Lasso optimization problem.