Decomposition Based Search - A theoretical and experimental evaluation

In this paper we present and evaluate a search strategy called Decomposition Based Search (DBS) which is based on two steps: subproblem generation and subproblem solution. The generation of subproblems is done through value ranking and domain splitting. Subdomains are explored so as to generate, according to the heuristic chosen, promising subproblems first. We show that two well known search strategies, Limited Discrepancy Search (LDS) and Iterative Broadening (IB), can be seen as special cases of DBS. First we present a tuning of DBS that visits the same search nodes as IB, but avoids restarts. Then we compare both theoretically and computationally DBS and LDS using the same heuristic. We prove that DBS has a higher probability of being successful than LDS on a comparable number of nodes, under realistic assumptions. Experiments on a constraint satisfaction problem and an optimization problem show that DBS is indeed very effective if compared to LDS.Comment: 16 pages, 8 figures. LIA Technical Report LIA00203, University of Bologna, 200

Scalable Parallel Numerical Constraint Solver Using Global Load Balancing

We present a scalable parallel solver for numerical constraint satisfaction problems (NCSPs). Our parallelization scheme consists of homogeneous worker solvers, each of which runs on an available core and communicates with others via the global load balancing (GLB) method. The parallel solver is implemented with X10 that provides an implementation of GLB as a library. In experiments, several NCSPs from the literature were solved and attained up to 516-fold speedup using 600 cores of the TSUBAME2.5 supercomputer.Comment: To be presented at X10'15 Worksho

OPERATIONAL PLANNING IN COMBINED HEAT AND POWER SYSTEMS

This dissertation presents methodologies for operational planning in Combined Heat and Power (CHP) systems. The subject of experimentation is the University of Massachusetts CHP system, which is a 22 MWe/640 MBh system for a district energy application. Systems like this have complex energy flow networks due to multiple interconnected thermodynamic components like gas and steam turbines, boilers and heat recovery steam generators and also interconnection with centralized electric grids. In district energy applications, heat and power requirements vary over 24 hour periods (planning horizon) due to changing weather conditions, time-of-day factors and consumer requirements. System thermal performance is highly dependent on ambient temperature and operating load, because component performances are nonlinear functions of these parameters. Electric grid charges are much higher for on-peak than off-peak periods, on-site fuel choices vary in prices and cheaper fuels are available only in limited quantities. In order to operate such systems in energy efficient, cost effective and least polluting ways, optimal scheduling strategies need to be developed. For such problems, Mixed-Integer Nonlinear Programming (MINLP) formulations are proposed. Three problem formulations are of interest; energy optimization, cost optimization and emission optimization. Energy optimization reduces system fuel input based on component nonlinear efficiency characteristics. Cost optimization addresses price fluctuations between grid on-peak and off-peak periods and differences in on-site fuel prices. Emission optimization considers CO2 emission levels caused by direct utilization of fossil fuels on-site and indirect utilization when importing electricity from the grid. Three solution techniques are employed; a deterministic algorithm, a stochastic search and a heuristic approach. The deterministic algorithm is the classical branch-and-bound method. Numerical experimentation shows that as planning horizon size increases linearly, computer processing time for branch-and-bound increases exponentially. Also in the problem formulation, fuel availability limitations lead to nonlinear constraints for which branch-and-bound in unable to find integer solutions. A genetic algorithm is proposed in which genetic search is applied only on integer variables and gradient search is applied on continuous variables. This hybrid genetic algorithm finds more optimal solutions than branch-and-bound within reasonable computer processing time. The heuristic approach fixes integer values over the planning horizon based on constraint satisfaction. It then uses gradient search to find optimum continuous variable values. The heuristic approach finds more optimal solutions than the proposed genetic algorithm and requires very little computer processing time. A numerical study using actual system operation data shows optimal scheduling can improve system efficiency by 6%, reduce cost by 11% and emission by 14%

Stochastic Constraint Programming

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number of complete algorithms and approximation procedures. Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables, and compare with other approaches for decision making under uncertainty.Comment: Proceedings of the 15th Eureopean Conference on Artificial Intelligenc

Developments in linear and integer programming

In this review we describe recent developments in linear and integer (linear) programming. For over 50 years Operational Research practitioners have made use of linear optimisation models to aid decision making and over this period the size of problems that can be solved has increased dramatically, the time required to solve problems has decreased substantially and the flexibility of modelling and solving systems has increased steadily. Large models are no longer confined to large computers, and the flexibility of optimisation systems embedded in other decision support tools has made on-line decision making using linear programming a reality (and using integer programming a possibility). The review focuses on recent developments in algorithms, software and applications and investigates some connections between linear optimisation and other technologies