Optimizing Greenhouse Heat Production in Lansingerland

Abstract

Many engineering problems require some objective to be optimized subject to certain constraints. For linear and convex optimization problems, techniques exist that can find the global minimum. For problems that have local minima or complex constraints, finding the global minimum is more difficult. An example of such a problem can be found in Lansingerland, where heat needs to be supplied by greenhouses. In this work a heat generation problem that has a local objective but complex constraints is solved using simulated annealing. The problem has the form of a demand supply problem and is applied in the context of generating heat for greenhouses in the region of Lansingerland. The objective is the costs that we want to keep as low as possible. The constraints arise from the network used to transport the heat, because the pressure in the pipes and valves of this network needs to be kept under control. Prior to coming up with a solution, the patterns of the heat demand are studied to decide what conditions the solutions should take into account. It was found that days follow a similar pattern and that the demand is higher in winter than in summer months. Furthermore the distribution of the heat demand over the different greenhouses is roughly equal for each day. Then, a look is taken at how a heat control can be solved using a stochastic optimization technique without considering variations during the day. Instead the problem is solved as if the heat demand for a single day is constant. We improve on canonical simulated annealing by making our mutations more intelligent than random. Two better approaches are shown to accomplish this. One starts by an analysis of trying different solutions to see what works best under what circumstances. This will be referred to as a smart mutation. The other approach varies the type of mutation based on earlier iterations. This will be referred to as an adaptive mutation. Both approaches show similar results, but since the adaptive mutation doesn't require much domain knowledge, this one is easier to apply to other problems. The influence of the starting point is also explored. In our setup it mattered a lot whether the initial point was already located in the feasible domain or not, for how quickly a solution can be found. We found that a good initial scenario should be one that already starts in the feasible domain. The best result was obtained by creating an initial scenario that for each greenhouse randomly decides to use the CHP or the RoCa. The mutation that gave best results in our case was the adaptive mutation, but it is expected that if more domain knowledge is added the smart mutation would be the best one. Finally, we will demonstrate how a heat control problem can be solved if the heat demand varies over time. In order to do so, a new way is introduced to segment time-series. This segmentation will be used to cluster the heat demand for a single day and to solve the problem for each segment individually. This improves the solution considerably, because it enables us to generate more heat at cold moments of the day like midnight, but to save on costs during the hot parts of the day.