Response surface methods based on kriging and radial basis function (RBF) interpolation have been successfully applied to solve expensive, i.e. computationally costly, global black-box nonconvex optimization problems. In this paper we describe extensions of these methods to handle linear, nonlinear, and integer constraints. In particular, algorithms for standard RBF and the new adaptive RBF (ARBF) are described. Note, however, while the objective function may be expensive, we assume that any nonlinear constraints are either inexpensive or are incorporated into the objective function via penalty terms. Test results are presented on standard test problems, both nonconvex problems with linear and nonlinear constraints, and mixed-integer nonlinear problems (MINLP). Solvers in the TOMLAB Optimization Environment (http://tomopt.com/tomlab/) have been compared, specifically the three deterministic derivative-free solvers rbfSolve, ARBFMIP and EGO with three derivative-based mixed-integer nonlinear solvers, OQNLP, MINLPBB and MISQP, as well as the GENO solver implementing a stochastic genetic algorithm. Results show that the deterministic derivative-free methods compare well with the derivativebased ones, but the stochastic genetic algorithm solver is several orders of magnitude too slow for practical use. When the objective function for the test problems is costly to evaluate, the performance of the ARBF algorithm proves to be superior.

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The benefit, in terms of social surplus, from introducing congestion charging schemes in urban networks are depending on the design of the charging scheme. The literature on optimal design of congestion pricing schemes is to a large extent based on static traffic assignment, which is known for its deficiency in correctly predict travel times in networks with severe congestion. Dynamic traffic assignment can better predict travel times in a road network, but are more computational expensive. Thus, previously developed methods for the static case cannot be applied straightforward. Surrogate-based optimization is commonly used for optimization problems with expensive-to-evaluate objective functions. In this paper we evaluate the performance of a surrogate-based optimization method, when the number of pricing schemes which we can afford to evaluate (due to the computational time) are limited to between 20 and 40. A static traffic assignment model of Stockholm is used for evaluating a large number of different configurations of the surrogate-based optimization method. Final evaluation is done with the dynamic traffic assignment tool VisumDUE, coupled with the demand model Regent, for a Stockholm network including 1 240 demand zones and 17 000 links. Our results show that the surrogate-based optimization method can indeed be used for designing a congestion charging scheme which return a high social surplus.

Increased recycling of nutrient-rich organic waste to meet crop nutrient needs is an essential component of a more sustainable food system. However, agricultural specialization continues to pose a significant challenge to balancing crop nutrient needs and the nutrient supply from animal manure and human excreta locally. For Sweden, this study found that recycling all excreta (in 2007) could meet up to 75% of crop nitrogen and 81% of phosphorus needs, but that this would exceed crop potassium needs by 67%. Recycling excreta within municipalities could meet 63% of crop P nutrient needs, but large regional differences and imbalances need to be corrected to avoid over or under fertilizing. Over 50% of the total nitrogen and phosphorus in excreta is contained in just 40% of municipalities, and those have a surplus of excreta nutrients compared to crop needs. Reallocation of surpluses (nationally optimized for phosphorus) towards deficit municipalities, would cost 192 million USD (for 24 079 km of truck travel). This is 3.7 times more than the total NPK fertilizer value being transported. These results indicate that Sweden could reduce its dependence on synthetic fertilizers through investments in excreta recycling, but this would likely require valuing also other recycling benefits.

We introduce a military aircraft mission planning problem where a given fleet of aircraft should attack a number of ground targets. Due to the nature of the attack, two aircraft need to rendezvous at the target, that is, they need to be synchronized in both space and time. At the attack, one aircraft is launching a guided weapon, while the other is illuminating the target. Each target is associated with multiple attack and illumination options. Further, there may be precedence constraints between targets, limiting the order of the attacks. The objective is to maximize the outcome of the entire attack, while also minimizing the mission timespan. We give a linear mixed-integer programming model of the problem, which can be characterized as a generalized vehicle routing problem with synchronization and precedence side constraints. Numerical results are presented for problem instances of realistic size.