This paper presents a generic reformulation framework for binary integer programs (BIPs) without imposing additional specifications for the objective function or constraints. To facilitate such generality, we introduce a set system approximation theory designed to identify the tightest inner and outer approximations for any binary solution space using special types of set systems. This development … Read more
Motivated by applications in cloud computing, we study interval scheduling problems exhibiting economies of scale. An instance is given by a set of jobs, each with start time, end time, and a function representing the cost of scheduling a subset of jobs on the same machine. Specifically, we focus on the max-weight function and non-negative, … Read more
This paper studies a general class of interdiction problems in which the solution space of both the leader and follower are characterized by two discrete sets denoted the leader’s strategy set and the follower’s structure set. In this setting, the interaction between any strategy-structure pair is assumed to be binary, in the sense that the … Read more
Some popular heuristics for combinatorial optimisation start by constructing a feasible solution to a dual of the problem. We show that such dual-based heuristics can exhibit highly counter-intuitive behaviour. In particular, for some problem classes, solving the dual exactly invariably leads to much worse primal solutions than solving the dual with a simple greedy heuristic. … Read more
We consider a probabilistic set covering problem where there is uncertainty regarding whether a selected set can cover an item, and the objective is to determine a minimum-cost combination of sets so that each item is covered with a pre-specified probability. To date, literature on this problem has focused on the special case in which … Read more
The set multicovering or set K-covering problem is an extension of the classical set covering problem, in which each object is required to be covered at least K times. The problem finds applications in the design of communication networks and in computational biology. We describe a GRASP with path-relinking heuristic for the set K-covering problem, … Read more
This paper investigates the role of dual information on the performances of heuristics designed for solving the set covering problem. After solving the linear programming relaxation of the problem, the dual information is used to obtain the two main approaches proposed here: (i) The size of the original problem is reduced and then the resulting … Read more
We present a biased random-key genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used … Read more
In this paper we present a cutting plane algorithm for the Set Covering problem. Cutting planes are generated by a “general” (i.e. not based on the “template paradigm”) separation algorithm based on the following idea: i) identify a suitably small subproblem defined by a subset of the constraints of the formulation; ii) run an exact … Read more
In this paper we address the following probabilistic version (PSC) of the set covering problem: min { cx | P (Ax>= xi) >= p, x_{j} in {0,1} j in N} where A is a 0-1 matrix, xi is a random 0-1 vector and p in (0,1] is the threshold probability level. In a recent development … Read more