Abstract. In this paper, we show how Guided Local Search (GLS) can be applied to the SAT problem and show how the resulting algorithm can be naturally extended to solve the weighted MAX-SAT problem. GLS is a general, penalty-based metaheuristic, which sits on top of local search algorithms to help guide them out of local minima. GLS has been shown to be successful in solving a number of practical real life problems, such as the travelling salesman problem, BT's workforce scheduling problem, the radio link frequency assignment problem and the vehicle routing problem. We present empirical results of applying GLS to instances of the SAT problem from the DIMACS archive and also a small set of weighted MAX-SAT problem instances and compare them against the results of other local search algorithms for the SAT problem. Keywords: SAT problem, Local Search, Meta-heuristics, Optimisation 1.

We analyze visibility from static sensors in a dynamic scene with moving obstacles (people). Such analysis is considered in a probabilistic sense in the context of multiple sensors, so that visibility from even one sensor might be sufficient. Additionally, we analyze worst-case scenarios for high-security areas where targets are non-cooperative. Such visibility analysis provides important performance characterization of multi-camera systems. Furthermore, maximization of visibility in a given region of interest yields the optimum number and placement of cameras in the scene. Our analysis has applications in surveillance - manual or automated - and can be utilized for sensor planning in places like museums, shopping malls, subway stations and parking lots. We present several example scenes - simulated and real - for which interesting camera configurations were obtained using the formal analysis developed in the paper.

In this thesis, we develop constrained simulated annealing (CSA), a global optimization algorithm that asymptotically converges to constrained global minima (CGM dn ) with probability one, for solving discrete constrained nonlinear programming problems (NLPs). The algorithm is based on the necessary and sufficient condition for constrained local minima (CLM dn ) in the theory of discrete constrained optimization using Lagrange multipliers developed in our group. The theory proves the equivalence between the set of discrete saddle points and the set of CLM dn , leading to the first-order necessary and sufficient condition for CLM dn .

Abstract. Systems utilizing multiple sensors are required in many domains. In this paper, we specifically concern our-selves with applications where dynamic objects appear randomly and the system is employed to obtain some user-specified characteristics of such objects. For such systems, we deal with the tasks of determining measures for evaluating their performance and of determining good sensor configurations that would maximize such measures for better system performance. We introduce a constraint in sensor planning that has not been addressed earlier: visibility in the presence of random occluding objects. Two techniques are developed to analyze such visibility constraints: a probabilistic approach to determine “average ” visibility rates and a deterministic approach to address worst-case scenarios. Apart from this constraint, other important constraints to be considered include image resolution, field of view, capture orientation, and algorithmic constraints such as stereo matching and background appearance. Integration of such constraints is performed via the development of a probabilistic framework that allows one to reason about different occlusion events and integrates different multi-view capture and visibility constraints in a natural way. Integration of the thus obtained capture quality measure across the region of interest yields a measure for the effectiveness of a sensor configuration and maximization of such measure yields sensor configurations that are

GENET is a heuristic repair algorithm which demonstrates impressive efficiency in solving some large-scale and hard instances of constraint satisfaction problems (CSPs). In this paper, we draw a surprising connection between GENET and discrete Lagrange multiplier methods. Based on the work of Wah and Shang, we propose a discrete Lagrangian-based search scheme LSDL, defining a class of search algorithms for solving CSPs. We show how GENET can be reconstructed from LSDL.The dual viewpoint of GENET as a heuristic repair method and a discrete Lagrange multiplier method allows us to investigate variants of GENET from both perspectives. Benchmarking results confirm that first, our reconstructed GENET has the same fast convergence behavior as the original GENET implementation, and has competitive performance with other local search solvers DLM, WalkSAT, and WSAT(OIP), on a set of difficult benchmark problems. Second, our improved variant, which combines techniques from heuristic repair an...

In this thesis, we present a new theory of discrete constrained optimization using Lagrange multipliers and an associated first-order search procedure (DLM) to solve general constrained optimization problems in discrete, continuous and mixed-integer space. The constrained problems are general in the sense that they do not assume the differentiability or convexity of functions. Our proposed theory and methods are targeted at discrete problems and can be extended to continuous and mixed-integer problems by coding continuous variables using a floating-point representation (discretization). We have characterized the errors incurred due to such discretization and have proved that there exists upper bounds on the errors. Hence, continuous and mixed-integer constrained problems, as well as discrete ones, can be handled by DLM in a unified way with bounded errors.

Meta-heuristics are methods that sit on top of local search algorithms. They perform the function of avoiding or escaping a local optimum and/or premature convergence. The aim of this paper is to survey, compare and contrast meta-heuristics for local search. First, we present the technique of local search (or hill climbing as it is sometimes known). We then present a table displaying the attributes of all the different meta-heuristics. After this, we give a short description and discussion of each meta-heuristic with pseudo code. Finally, we describe why, in general, these techniques work and present some ideas of what is needed from the next generation of meta-heuristics.