A distributionally robust optimization model for batch nonlinear switched time-delay system considering uncertain output measurements

We consider the optimistic bilevel optimization problem, known to have a wide range of applications in engineering, that we transform into a single-level optimization problem by means of the lower-level optimal value function reformulation. Subsequently, based on the partial calmness concept, we build an equation system, which is parameterized by the corresponding partial exact penalization parameter. We then design and analyze a Levenberg–Marquardt method to solve this parametric system of equations. Considering the fact that the selection of the partial exact penalization parameter is a critical issue when numerically solving a bilevel optimization problem by means of the value function reformulation, we conduct a careful experimental study to this effect, in the context of the Levenberg–Marquardt method, while using the Bilevel Optimization LIBrary (BOLIB) series of test problems. This study enables the construction of some safeguarding mechanisms for practical robust convergence of the method and can also serve as base for the selection of the penalty parameter for other bilevel optimization algorithms. We also compare the Levenberg–Marquardt method introduced in this paper to other existing algorithms of similar nature.

Bilevel optimization problems require every feasible upper-level solution to satisfy optimality of a lower-level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy development, transportation problems, and others. In the context of a bilevel single objective problem, there exists a number of theoretical, numerical, and evolutionary optimization results. However, there does not exist too many studies in the context of having multiple objectives in each level of a bilevel optimization problem. In this paper, we address bilevel multi-objective optimization issues and propose a viable algorithm based on evolutionary multi-objective optimization (EMO) principles. Proof-of-principle simulation results bring out the challenges in solving such problems and demonstrate the viability of the proposed EMO technique for solving such problems. This paper scratches the surface of EMO-based solution methodologies for bilevel multi-objective optimization problems and should motivate other EMO researchers to engage more into this important optimization task of practical importance.

The bilevel optimisation problem (BLP) is a subclass of optimisation problems in which one of the constraints of an optimisation problem is another optimisation problem. BLP is widely used to model hierarchical decision making where the leader and the follower correspond to the upper level and lower level optimisation problem, respectively. In BLP, the optimal solutions to the lower level optimisation problem are the feasible solutions to the upper level problem, which makes it particularly difficult to solve. This paper proposes a novel hardware architecture known as Recursive Pipelined Genetic Propagation (RPGP), to solve BLP efficiently on FPGA. RPGP features a graph of genetic operation nodes which can be scaled to exploit hardware resources. In addition, the topology of the RPGP graph can be changed at run-time to escape from local optima. We evaluate the proposed architecture on an Altera Stratix-V FPGA, using a benchmark bilevel optimisation problem set. Our experimental results show that RPGP can achieve a significant speed-up against previous work.

In this paper, we consider the problem of scheduling N robots interacting with a moving target. Both, the sequence of the robots and their trajectories are unknown and subject to optimization. Such type of problems appear in highly automated production plants and in the simulation of virtual factories. The purpose of the paper is to provide a mathematical model and to suggest a numerical solution approach. Our approach is based on the formulation of the problem as a bilevel optimization problem, where the lower level problem is an optimal control problem, while the upper level problem is a finite dimensional mixed-integer optimization problem. We approach the problem by exploitation of necessary optimality conditions for the lower level problem and by application of a Branch & Bound method for the resulting single level optimization problem. Two settings are taken into account. Firstly, no state constraints are assumed on the lower level problem, thus the local minimum principle applies directly. Secondly, the problem setting is augmented by pure state constraints, which are being handled by virtual controls in order to regularize the problem.

Investigation of the Doppler frequency shift effect on inter-channel switching time of free-space optically switched communication networks with distributed feedback laser array technique

When the lower-level optimal solution set-valued mapping of a bilevel optimization problem is not single-valued, we are faced with an ill-posed problem, which gives rise to the optimistic and pessimistic bilevel optimization problems, as tractable algorithmic frameworks. However, solving the pessimistic bilevel optimization problem is far more challenging than the optimistic one; hence, the literature has mostly been dedicated to the latter class of the problem. The Scholtes relaxation has appeared to be one of the simplest and most efficient ways to solve the optimistic bilevel optimization problem in its Karush-Kuhn-Tucker (KKT) reformulation or the corresponding more general mathematical program with complementarity constraints (MPCC). Inspired by such a success, this paper studies the potential of the Scholtes relaxation in the context of the pessimistic bilevel optimization problem. To proceed, we consider a pessimistic bilevel optimization problem, where all the functions involved are at least continuously differentiable. Then assuming that the lower-level problem is convex, the KKT reformulation of the problem is considered under the Slater constraint qualification. Based on this KKT reformulation, we introduce the corresponding version of the Scholtes relaxation algorithm. We then construct theoretical results ensuring that the limit of a sequence of global/local optimal solutions (resp. stationary points) of the aforementioned Scholtes relaxation is a global/local optimal solution (resp. stationary point) of the KKT reformulation of the pessimistic bilevel program. The results are accompanied by technical constructions ensuring that the Scholtes relaxation algorithm is well-defined or that the corresponding parametric optimization problem is more tractable. Furthermore, we perform some numerical experiments to assess the performance of the Scholtes relaxation algorithm using various examples. In particular, we study the effectiveness of the algorithm in obtaining solutions that can satisfy the corresponding C-stationarity concept.

This paper addresses a bilevel optimization problem with a guaranteed (pessimistic) solution in a rather general form. The problem is reduced to a family of bilevel problems with optimistic solutions and perturbed follower's problems. For the quadratic-linear bilevel optimization problem, a reduction of the bilevel problem to a series of non-convex one-level optimization problems is proposed using the penalty method. Additionally, a solution method based on Global Search Theory (GST) is developed for the obtained problem. The GST consists of two stages: special local search and Global Search Scheme (GSS), which is based on Global Optimality Conditions (GOCs). The computational testing of the developed approach on specially constructed bilevel problems of high dimensions was successfully carried out. Finally, the computational testing on specially constructed bilevel problems of rather high dimensions was successfully carried out, that substantiate the developed approach.

Bi-level optimisation problems (BOPs) are a class of challenging problems with two levels of optimisation tasks. These problems allow to model a large number of real-life situations in which a first decision maker, hereafter the leader, optimises his objective by taking the follower's response to his decisions explicitly into account. In this context, a new proposed algorithm called CODBA-II was suggested to solve combinatorial BOPs. The latter was able to improve the quality of generated bi-level solutions regarding to recently proposed methods. In fact, a wide range of applications fit the bi-level programming framework and real-life implementations still scarce. For this reason, we propose in this paper a co-evolutionary decomposition-based bi-level algorithm for the bi-level knapsack optimisation problem. The computational algorithm turned out to be quite efficient on both computation time and solution quality regarding to other competitive EAs.

Dynamic traffic assignment (DTA) applications require traffic signal control data that are typically difficult to obtain and cumbersome to code in the required format. In addition, the evaluation of future scenarios requires future traffic signal settings consistent with the forecast demand. These signal settings are not known a priori and are costly to estimate. Intuitively, future signal timings need to be reasonably optimized so as to represent what the traffic management agency will do. In the literature, integration between traffic control and DTA models has been formulated as a bi-level or single-level optimization problem with system or user optimal constraints. Most existing solution procedures require certain nested structure with an inner-loop algorithm solving the problem of user-equilibrium or system-optimal assignment and the outer-loop algorithm searching for the optimal signal-timing settings. Most of these solution approaches remain only research tools without practical use because of computational intractability. This research proposes an efficient solution algorithm to the problem. An adaptive traffic signal control model is embedded in a simulation-based DTA model. For each inbound approach at an intersection of interest, the adaptive model uses upstream information and a dynamic rolling-horizon approach to project traffic flow conditions for a dynamic but short (projection) period. The adaptive model provides the signal settings during the entire process of traffic flow simulation and for every iteration of the solution algorithm. Thus, during the entire solution process, the experienced travel times and resulting traffic assignment flows are based on the adaptive (demand-responsive) signal settings, allowing the DTA flows and the adaptive signal settings to be generated simultaneously in a single-loop algorithmic structure. Simulation experiments illustrate the capabilities of the proposed approach.

Robust identification of nonlinear state-dependent impulsive switched system with switching duration constraints

Automated multi-objective system identification using grammar-based genetic programming

Uncertainties in variables and parameters cause optimization problems to move away from globally-optimal and uncertain solutions. Practitioners resort to finding robust and reliable solutions in such situations. Bilevel optimization problems involving a hierarchy of two nested optimization problems have received a growing attention in the recent past due to their relevance in practice. While a number of studies on bilevel solution methodologies and applications are available for a deterministic setup, but studies on uncertainties in bilevel optimization are rare. In this paper, we suggest methodologies for handling uncertainty in both lower and upper level variables that may occur from different practicalities. For the first time, we perform a systematic study demonstrating the effect of uncertainties in each level along with the definition of robustness and reliability in the context of bilevel optimization. The issues and complexities introduced due to such uncertainties are then studied through a number of test cases, for brevity, we only show results on three test cases. Finally, two real-world bilevel problems involving uncertainties in their variables are solved. The study provides foundations and demon- strates viable directions for further research in uncertainty-based bilevel optimization problems.

Digital Twin (DT) and mobile edge computing are two promising solutions for achieving latency-sensitive and computing-intensive applications in Industrial Internet of Things (IIoT). However, existing task offloading schemes with DT empowerment are faced with challenges, such as the spatio-temporal heterogeneity of edge server (ES) resources, resource-constrained ESs, and the explosive growth of data in emerging applications. This paper investigates the issues of task offloading and resource allocation under the assistance of DT and multiple ESs parallel collaboration. One novel scheme, abbreviated as Mes-PCORA, is proposed. With comprehensive information within the digital space, the Mes-PCORA scheme dynamically adjusts task allocation ratios across multiple ESs to achieve collaborative task offloading. The offloading request is formulated as a non-convex problem. To make the non-convex problem solvable in polynomial time, the original problem transformed into a bilevel optimization problem. Then, a bilevel iterative optimization approach is proposed. Specifically, the upper-level optimization problem is formulated as a multi-agent Markov Decision Process, and a deep reinforcement learning-based resource allocation algorithm is designed to solve it. Subsequently, for the lower-level optimization problem, it is solved by the interior point method. Numerical results demonstrate that the proposed scheme reduces the average task completion latency by 27.16%–63.44% and decreases the task offloading failure rate by 35.83%–73.95%, compared to state-of-the-art baselines.

Robust Nonlinear Model Predictive Control with Constraint Satisfaction: A Relaxation-based Approach

Optimization problems with composite functions consist of an objective function which is the sum of a smooth and a (convex) nonsmooth term. This particular structure is exploited by the class of proximal gradient methods and some of their generalizations like proximal Newton and quasi-Newton methods. The current literature on these classes of methods almost exclusively considers the case where also the smooth term is convex. Here we present a globalized proximal Newton-type method which allows the smooth term to be nonconvex. The method is shown to have nice global and local convergence properties, and some numerical results indicate that this method is very promising also from a practical point of view.