Confidence in heuristic solutions?

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

Energy efficient and economic renovation of residential buildings with low-temperature heating and air heat recovery

With the building sector accounting for around 40% of the total energy consumption in the EU, energy efficiency in buildings is and continues to be an important issue. Great progress has been made in reducing the energy consumption in new buildings, but the large stock of existing buildings with poor energy performance is probably an even more crucial area of focus. This thesis deals with energy efficiency measures that can be suitable for renovation of existing houses, particularly low-temperature heating systems and ventilation systems with heat recovery. The energy performance, environmental impact and costs are evaluated for a range of system combinations, for small and large houses with various heating demands and for different climates in Europe. The results were derived through simulation with energy calculation tools. Low-temperature heating and air heat recovery were both found to be promising with regard to increasing energy efficiency in European houses. These solutions proved particularly effective in Northern Europe as low-temperature heating and air heat recovery have a greater impact in cold climates and on houses with high heating demands. The performance of heat pumps, both with outdoor air and exhaust air, was seen to improve with low-temperature heating. The choice between an exhaust air heat pump and a ventilation system with heat recovery is likely to depend on case specific conditions, but both choices are more cost-effective and have a lower environmental impact than systems without heat recovery. The advantage of the heat pump is that it can be used all year round, given that it produces DHW. Economic and environmental aspects of energy efficiency measures do not always harmonize. On the one hand, lower costs can sometimes mean larger environmental impact; on the other hand there can be divergence between different environmental aspects. This makes it difficult to define financial subsidies to promote energy efficiency measures.