## 1 Introduction  
The disposal of the spent nuclear fuel is a challenging task where the careful planning and optimization of processes definitely pays dividends. The difficulty of the decision making is increased also by the fact that the disposal continues for the distant future and many parameters are still unknown. Indeed, the decisions made now have long term consequences. Thus, it is only reasonable to investigate different scenarios by utilizing multiobjective optimization from the different perspectives. The disposal is a topical issue since many of the countries utilizing nuclear power have not yet disposed of any spent nuclear fuel. Nevertheless, all of them have to do something for it sooner or later. Long-term storage in interim storage is not considered a safe or ethical solution [1]. At the same time, the geological disposal is stated to be widely accepted as a safe method [1]. Finland is going to be one of the first countries to dispose of the spent nuclear fuel by starting the disposal in 2020s [2]. The aim in the geological disposal is to isolate the spent nuclear fuel to the bedrock such that it has no more impacts on the environment than the regular background radiation. First, the fuel assemblies are removed from the reactor and stored in the water pool in the reactor hall in order to decrease the radiation and the decay heat power to the suitable level such that the assemblies can be transferred to the water pool in the interim storage facility for decades. When the assemblies are cool enough, they can be transferred to the encapsulation facility, where the assemblies are encapsulated into the copper-iron canisters. After that, the canister moves on towards the disposal facility, in depth of more than 400 m. The disposal facility consists of the central tunnel and several parallel disposal tunnels that are connected to the central tunnel. The canister is placed vertically in the hole on the floor of the disposal tunnel. Finally, the disposal tunnel is filled up and sealed. In this study, we divide the disposal process into three parts: the interim storage, the encapsulation facility, and the disposal facility. As the entire nuclear waste management is a large task, optimization related studies about it are usually focused on some smaller entities. Some of these entities are concentrated more on political or social aspects like to determine where to put a disposal repository [3] or how to route the transfer of the nuclear waste, or hazardous waste in general [4,5]. More safety-related aspects are the optimization of the nuclear safeguards [6,7] and the safety assessment of nuclear waste repositories [8]. In our study, we aim to produce a disposal schedule such that several goals related to all the interim storage, the encapsulation facility, and the disposal facility are taken into account simultaneously with multiobjective optimization. Other studies aiming at a disposal schedule are, for example, [9] where a single-objective mixed-integer linear programming (MILP) model minimizing the costs is given and [10] trying to achieve the minimal area of the disposal facility with a linear transportation model. Another research related to the disposal facility is discussed in [11], where the multiobjective MILP problem is given to optimize the nuclear waste placement in the disposal facility. In addition, there are attempts to optimize the loading of canisters in Finland [9,12], Slovenia [13], and Switzerland [14]. This study continues the work of [9], where the aim was to minimize the total costs of the disposal in Finland by selecting the schedule of the disposal. Here, this work has been continued by remodeling the situation as the nonsmooth multiobjective mixed-integer nonlinear programming (MINLP) problem. As a nonsmooth optimization problem [15, 16, 17], the objectives and the constraints are not necessarily continuously differentiable functions. This allows us to model the situation more accurately.