As renewable energy penetration increases, managing demand-side flexibility becomes critical to ensure grid reliability and price stability. Demand response (DR) programs, especially those driven by dynamic pricing, are emerging as key tools in this transition. Retail electricity markets must integrate uncertain and volatile factors such as fluctuating consumer demand, wholesale prices, and generation costs. Designing pricing strategies that optimize consumer flexibility without inducing market inefficiencies requires a rigorous mathematical framework.

The authors propose a bilevel stochastic game-theoretical model where electricity retailers act as leaders setting dynamic tariffs, and consumers respond as rational followers optimizing their consumption. Two market structures are explored:

• Imperfect competition: Modeled as a Mathematical Program with Equilibrium Constraints (MPEC) where retailers exert market power.
• Perfect competition: Represented via Mixed-Integer Linear Programming (MILP) solving the KKT conditions jointly for all players.

The MPEC problem is solved using Artelys Knitro with numerical simulations based on real data from the European Energy Exchange (EEX). Artelys Knitro’s advanced optimization capabilities enable efficient handling of the non-linearity structure of the problem.

Authors: Arega Getaneh (Technical University of Denmark, Elektrovej, Denmark), Rossana Riccardi, Carlos Ruiz.

Emerging transportation systems such as ride-hailing and ride sharing are transforming urban mobility patterns and entail challenges to transportation planners. Switches between different transportation modes are rarely analyzed.

The goal of this paper is to model the interactions of different transportation modes such as public transport and solo driving, ride-hailing and ride sharing. The authors propose a traffic equilibrium model for a coupled morning-evening network, in which travelers can change the transportation mode between the morning and the evening commute.

The authors analyze the costs and the constraints of this framework and propose a variational inequality model with a nonlinear convex cost function, as well as an equivalent mixed complementarity problem (MiCP).

The authors rely on Artelys Knitro to solve the MiCP model. The presented coupled morning-evening solution is compared to decoupled models, which optimize first the morning commute then the evening one, or vice-versa. Results obtained on a well-established network example show that the least path costs and the calculated number of drivers in the proposed model are nearly 10% smaller than those obtained with decoupled models.

Authors: Wei Gu (University of Southern California, LosAngeles, CA, USA), Michael Zhang (University of California Davis, Davis,CA, USA), Maged Dessouky and Jong-Shi Pang (University of Southern California, LosAngeles, CA, USA)

Coordinating traffic at urban intersections is crucial in traffic control systems, and the advent of connected vehicles enables to consider more flexible paths and potentially improve efficiency.

The authors of this paper consider the area of a signal-free intersection as a bounded free space, where connected vehicles under automated driving (CVAD) are allowed to take free paths under the condition that the trajectories do not collide.

The authors’ model is as an extension of a nonlinear model predictive contouring control (NMPCC) which has the goal of both generating collision-free trajectories for the vehicles and optimizing the progress of the vehicles along their trajectories. The model involves constraints to avoid collisions and violations of intersection boundaries.

The model results in a Nonlinear Program (NLP). Artelys Knitro with the multistart option is exploited to solve it. Results show that this model allows shorter travel time with respect to a conventional approach, due to improved space utilization. The performance of the solution shows that even a real-time operation is feasible in the studied scenario.

Coordinating traffic at urban intersections is crucial in traffic control systems, and the advent of connected vehicles enables to consider more flexible paths and potentially improve efficiency.

The authors of this paper consider the area of a signal-free intersection as a bounded free space, where connected vehicles under automated driving (CVAD) are allowed to take free paths under the condition that the trajectories do not collide.

The authors’ model is as an extension of a nonlinear model predictive contouring control (NMPCC) which has the goal of both generating collision-free trajectories for the vehicles and optimizing the progress of the vehicles along their trajectories. The model involves constraints to avoid collisions and violations of intersection boundaries.

The model results in a Nonlinear Program (NLP). Artelys Knitro with the multistart option is exploited to solve it. Results show that this model allows shorter travel time with respect to a conventional approach, due to improved space utilization. The performance of the solution shows that even a real-time operation is feasible in the studied scenario.

Methanol is an important compound widely used in the chemical industry. Today, it is largely produced using fossil-based resources. Synthesizing methanol from renewable energy poses the challenge of the varying availability of green hydrogen as a feed stream. Conventional processes are not designed to consider such fluctuations.

The objective of this paper is to identify the optimal design of a multi-stage reactor for green methanol synthesis with inlet fluctuations. The authors model the reactor’s design parameters and operating conditions and propose an optimization problem to maximize the methanol yield, subject to a minimum carbon conversion rate. They solve the problem in the nominal steady-state and in a robust steady-state version, which is feasible for different inlet fluctuation values. However, through numerical simulations, they show that these models are not feasible when transient behavior is considered.

They hence propose a dynamic programming model that allows the feed distribution and shell temperatures of the reactor to change over time, depending on the varying value of the inlet stream. Experiments show that this problem is feasible for fluctuating inlet conditions.

All three optimization problems are continuous and nonlinear and require a discretization of the infinite dimensional problem to be solved. The authors exploit the power of Artelys Knitro with the multi-start option to solve all three of them.

Deployable structures typically consist of rigid elements connected via rotational joints which have compact rest states and deploy into 3D target surfaces. Such structures are widely used in industrial and consumer products, medical devices, aerospace applications, and civil installations.

The authors propose a new deployable material system, called umbrella mesh, that combines rigid linkage mechanisms and elastic beams to enable a wide variety of shapes. Umbrella meshes are composed of regular arrangements of parameterized cells. All cells cover the same area footprint, but the differing cell heights cause this area to expand by different amounts during deployment and result in a curved shape.

The authors provide a model to simulate the deployment of such structures and present an algorithm to optimize the free design parameters to best approximate a given target shape. These results are validated with physical prototypes and show that umbrella meshes allow to obtain surface geometries that are not possible with other existing methods.

The authors rely on Artelys Knitro to determine the optimal shape parameters for approximating a given target surface. The optimization problem is nonlinear, and the Artelys Knitro interior-point Conjugate gradient algorithm is exploited to rapidly converge to an optimal design.

Edge computing is becoming a complementary architecture to cloud computing. A key advantage of edge computing is that edge data centers are typically located much closer to users than traditional cloud data centers. This is especially relevant for applications with tight latency requirements, like virtual reality, autonomous vehicle or the Internet of Things. However, since edge clusters are often resource-constrained, there is a trade-off between network latency and server processing latency while deploying applications on both edge and cloud.

The authors propose an approach aiming at devising hybrid cloud/edge deployment plans guaranteeing an end-to-end latency (i.e., mean response time) lower than that of the pure cloud deployment counterparts, at minimal cost. For a given scenario with number and location of users and data centers, the method optimizes the number of servers per data center as well as the probability, for each possible pair user / data center, that a request from the user is scheduled to the data center. The resulting probability matrix enables the scheduler to realize the trade-off between edge processing and cloud processing.

Because the mean end-to-end response time is a highly nonlinear and nonconvex function of the number of servers and scheduling probabilities, the authors used the Interior-Point/Direct algorithm of Artelys Knitro with the multistart feature to solve a continuous relaxation of the problem before rounding. Results show that the proposed approach indeed produces deployment plans at least as efficient as cloud deployments for an equal or lower budget. In addition, the proposed method outperforms purely edge deployments (i.e., when users send their requests to the closest data center) by 11% to 24%.

The authors study the possibility of alleviating traffic congestion when activities of improvement (such as maintenance or rehabilitation) are executed on a public roadway facility, by exploiting excess road capacity along concurrent tolled roadway facilities operating in a public-private partnership. Increased access to the tolled facility is enabled by reducing or suspending tolls during periods of roadway improvement actions and appropriately compensating the tolled facility concessionaire for expected losses.

On the one hand, the public agency seeks to settle the maintenance schedule, toll price reduction and compensation, minimizing the total costs; on the other hand, the concessionaire seeks an optimal toll setting to maximize revenue, thus accepts or rejects the compensation proposed by the public agency, depending on whether it is greater or not to its lost opportunity to profit. Both stakeholders are beholden to the users, who can select the tolled route or the public one. This results in two bilevel problems – one for the agency, one for the concessionaire – and an iterative solution method is proposed to solve them. The solution of each problem is obtained at a Stackelberg equilibrium.

Each of the two bi-level problems is transformed in a single-level problem by adding optimality conditions. The first one is a nonconvex, mixed integer nonlinear program (MINLP), and the second one is a nonconvex nonlinear program (NLP). Both are solved with the nonlinear solver Artelys Knitro and for both the sequential quadratic programming method is exploited.

Results on a case-study show that carefully scheduling the improvement activities and simultaneously agreeing to reduce toll prices can lead to an 8% decrease in total travel time for users, with reduced costs for the public agency and no reduction in total revenue for the concessionaire.