https://web.stanford.edu/class/msande312/restricted/klos04facility.pdf

Facility location models for distribution system design

In this chapter we will introduce submodularity and some of its generalizations, illustrate how it arises in various applications, and discuss algorithms for optimizing submodular functions. Submodularity is a property of set functions with deep theoretical consequences and far-reaching applications. At first glance it seems very similar to concavity, in other ways it resembles convexity. It appears in a wide variety of applications: in Computer Science it has recently been identified and utilized in domains such as viral marketing [39], information gathering [44], image segmentation [10, 40, 36], document summarization [56], and speeding up satisfiability solvers [73]. Our emphasis in this chapter is on maximization; there are many important results and applications related to minimizing submodular functions that we do not cover. As a concrete running example, we will consider the problem of deploying sensors in a drinking water distribution network (see Figure 3.1) in order to detect contamination. In this domain, we may have a model of how contaminants, accidentally or maliciously introduced into the network, spread over time. Such a model then allows to quantify the benefit f(A) of deploying sensors at a particular set A of locations (junctions or pipes in the network) in terms of the detection performance (such as average time to detection). Based on this notion of utility, we then wish to find an optimal subset A ⊆ V of locations maximizing the utility, max A f(A) , subject to some constraints (such as bounded cost). This application requires solving a difficult real-world optimization problem, that can be handled with the techniques discussed in this chapter (Krause et al. [49] show in detail how submodular optimization can be applied in this domain.)

/pdf/submodular-function-maximization-1dos5dw1tz.pdf

Submodular Function Maximization

We present an exact partial enumerative algorithm for the maximum clique problem. The pruning device used is derived from graph colorings. Pruning of the search tree is accomplished not only by the number of colors used to color a tree subproblem but also by using information gained in the process of coloring. This leads to increased pruning which translates into improved computational performance. Experimental results on test problems are presented.

An exact algorithm for the maximum clique problem with accelerated pruning

The authors provide more efficient designs for conjoint choice experiments based on prior information elicited from managers about the parameters and their associated uncertainty. The authors use a Bayesian design procedure that assumes a prior distribution of likely parameter values and optimizes the design over that distribution. The authors propose a way to elicit prior information from managers and show in Monte Carlo studies that the procedure provides more efficient designs than the current procedures. The authors provide an empirical application, in which they elicit prior information on the parameter values and the associated uncertainty from managers. Here, the Bayesian design provides 30%–50% lower standard errors of the estimates and an expected predictive validity that is approximately 20% higher.

Designing conjoint choice experiments using managers' prior beliefs

A survey on new generation metaheuristic algorithms

Handbook of combinatorial optimization

The Data-Correcting (DC) Algorithm is a recursive branch-and-bound type algorithm, in which the data of a given problem instance are "heuristically corrected" at each branching in such a way that the new instance will be as close as possible to polynomially solvable and the result satisfies a prescribed accuracy (the difference between optimal and current solution). In this paper the DC algorithm is applied to determining exact or approximate global minima of supermodular functions. The working of the algorithm is illustrated by an instance of the Simple Plant Location (SPL) Problem. Computational results, obtained for the Quadratic Cost Partition Problem (QCP), show that the DC algorithm outperforms a branch-and-cut algorithm, not only for sparse graphs but also for nonsparse graphs (with density more than 40%), often with speeds 100 times faster.

/pdf/the-data-correcting-algorithm-for-the-minimization-of-57n3379z3v.pdf

The Data-Correcting Algorithm for the Minimization of Supermodular Functions

In this paper we present improvements to one of the most recent and fastest branch-and-bound algorithm for the maximum clique problem--MCS algorithm by Tomita et al. (Proceedings of the 4th international conference on Algorithms and Computation, WALCOM'10, pp. 191---203, 2010). The suggested improvements include: incorporating of an efficient heuristic returning a high-quality initial solution, fast detection of clique vertices in a set of candidates, better initial colouring, and avoiding dynamic memory allocation. Our computational study shows some impressive results, mainly we have solved p_hat1000-3 benchmark instance which is intractable for MCS algorithm and got speedups of 7, 3000, and 13000 times for gen400_p0.9_55, gen400_p0.9_65, and gen400_p0.9_75 instances correspondingly.

/pdf/improvements-to-mcs-algorithm-for-the-maximum-clique-problem-58dkt7qjt8.pdf

Improvements to MCS algorithm for the maximum clique problem

This chapter focuses on the p-median problem (PMP) and its properties. We consider a pseudo-Boolean formulation of the PMP, demonstrate its advantages and derive the most compact MILP formulation for the PMP within the class of mixed-Boolean linear programming formulations. Further, we develop two applications of the pseudo-Boolean approach: a construction of PMP instances that are expected to be complex for any solution algorithm and a definition of an equivalence relation for PMP instances. By equivalence we mean that solving one instance gives a solution for all the instances from its equivalence class. The proposed equivalence relation can be extended to any other problem modelled via the PMP, for example, the cell formation problem.

The p-Median Problem

https://pure.rug.nl/ws/files/3084577/01A14.pdf

Boris Goldengorin

Papers

Handbook of combinatorial optimization

The Data-Correcting Algorithm for the Minimization of Supermodular Functions

Improvements to MCS algorithm for the maximum clique problem

The p-Median Problem

Branch and peg algorithms for the simple plant location problem