Springer Science and Business Media LLC

Isoperimetric problems are of importance in engineering applications, where it is often desirable to maximize or minimize some physical variable by shape variation, subject to geometrical constraints, such as keeping an area or volume constant. The calculus of variations can offer a powerful tool for the solution of such problems where there is a governing variational minimum or maximum principle, e.g. Helmholtz's principle in slow viscous flow. In these problems the well-known Euler equations derived by the calculus of variations are supplemented with additional boundary conditions arising from the shape variation, as well as the usual physical boundary conditions. The exact solution of such unknown boundary problems can be difficult to find. A good approach then is to apply a complementary extremum principle that offers an algorithm for determining bounds on the exact extremal value of the original functional. This paper shows how this may be done in the case of the fundamental problem of the calculus of variations with variable endpoints. We apply this approach to a simple engineering problem of a stretched spring.

The application of optimization methods and algorithms to energy management is crucial when trying to find instantaneous compromises between various energy sources that can provide the power required by a powertrain. Because of the complexity of both the problem and the system structure, it is difficult to determine the optimal strategy in real time (on-line and using the onboard computer). This article tackles the problem of optimizing the power provided by various sources available to meet the power demand from the driver whilst minimizing the total hydrogen consumption during a journey. The real challenge is to find an energy management law applicable in real time on any power profile. This paper presents two new energy management methods: off-line “Dynamic Programming with Improved Constraints (DPIC)” and a real-time optimized decision-maker based on a two-levels optimized Fuzzy Logic (Fuzzy Switching of Fuzzy Rules—FSFR). DPIC produces better results than the classical discrete dynamic programming with state-of-the-art constraints, in terms of execution time and hydrogen consumption. FSFR is a real time energy management algorithm based on fuzzy rules learnt on specific profiles and real-time fuzzy switching of these fuzzy rules. Both methods are evaluated on different types of real world profiles (urban, road and highway profiles), to assess and confirm their effectiveness.

Distributed optimization using multiple computing agents in a localized and coordinated manner is a promising approach for solving large-scale optimization problems, e.g., those arising in model predictive control (MPC) of large-scale plants. However, a distributed optimization algorithm that is computationally efficient, globally convergent, amenable to nonconvex constraints remains an open problem. In this paper, we combine three important modifications to the classical alternating direction method of multipliers for distributed optimization. Specifically, (1) an extra-layer architecture is adopted to accommodate nonconvexity and handle inequality constraints, (2) equality-constrained nonlinear programming (NLP) problems are allowed to be solved approximately, and (3) a modified Anderson acceleration is employed for reducing the number of iterations. Theoretical convergence of the proposed algorithm, named ELLADA, is established and its numerical performance is demonstrated on a large-scale NLP benchmark problem. Its application to distributed nonlinear MPC is also described and illustrated through a benchmark process system.

Blackbox optimization deals with situations in which the objective function and constraints are typically computed by launching a time-consuming computer simulation. The subject of this work is the mesh adaptive direct search (mads) class of algorithms for blackbox optimization. We propose a way to dynamically scale the mesh, which is the discrete spatial structure on which mads relies, so that it automatically adapts to the characteristics of the problem to solve. Another objective of the paper is to revisit the mads method in order to ease its presentation and to reflect recent developments. This new presentation includes a nonsmooth convergence analysis. Finally, numerical tests are conducted to illustrate the efficiency of the dynamic scaling, both on academic test problems and on a supersonic business jet design problem.

The seed supply chain is one of most sophisticated elements of the agricultural value chain with long lead times, fragmented structure and high levels of uncertainty. Since the seed industry has received less attention in research compared with other sectors in the agriculture industry, it has enormous potential for improvement due to the lack of comprehensive mathematical optimization applications, increasing competition within the industry and decreasing spare arable land worldwide. All of the existing optimization applications in the seed supply chain have concerned land allocation at the farm level as well as regional level processing and distribution after harvesting. This research closes the gap between farm level planning and regional level distribution through optimization of seed production planning at a regional level, taking account of a number of complex constraints and practical preferences. Compared to a “business as usual” approach, the proposed application can save up to 16% of the total cost as well as 9% land usage and effectively mitigate major risks in the planning phase. The method is evaluated using Syngenta’s industrial case studies.

The optimal truss design using problem-oriented evolutionary algorithm is presented in the paper. The minimum weight structures subjected to stress and displacement constraints are searched. The discrete design variables are areas of members, selected from catalogues of available sections. The integration of the problem specific knowledge into the optimization procedure is proposed. The heuristic rules based on the concept of fully stressed design are introduced through special genetic operators, which use the information concerning the stress distribution of structural members. Moreover, approximated solutions obtained by deterministic, sequential discrete optimization methods are inserted into the initial population. The obtained hybrid evolutionary algorithm is specialized for truss design. Benchmark problems are calculated in numerical examples. The knowledge about the problem integrated into the evolutionary algorithm can enhance considerably the effectiveness of the approach and improve significantly the convergence rate and the quality of the results. The advantages and drawbacks of the proposed method are discussed.

Aerodynamic shape optimization of a helicopter rotor in hover is presented, using compressible CFD as the aerodynamic model. An efficient domain element shape parameterization method is used as the surface control and deformation method, and is linked to a radial basis function global interpolation, to provide direct transfer of domain element movements into deformations of the design surface and the CFD volume mesh, and so both the geometry control and volume mesh deformation problems are solved simultaneously. This method is independent of mesh type (structured or unstructured) or size, and optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced parallel gradient-based algorithm by finite-difference, resulting in a flexible method of ‘wrap-around’ optimization. This paper presents results of the method applied to hovering rotors using local and global design parameters, allowing a large geometric design space. Results are presented for two transonic tip Mach numbers, with minimum torque as the objective, and strict constraints applied on thrust, internal volume and root moments. This is believed to be the first free form design optimization of a rotor blade using compressible CFD as the aerodynamic model, and large geometric deformations are demonstrated, resulting in significant torque reductions, with off-design performance also improved.

Simulation-and-regression algorithms have become a standard tool for solving dynamic programs in many areas, in particular financial engineering and computational economics. In virtually all cases, the regression is performed on the state variables, for example on current market prices. However, it is possible to regress on decision variables as well, and this opens up new possibilities. We present numerical evidence of the performance of such an algorithm, in the context of dynamic portfolio choices in discrete-time (and thus incomplete) markets. The problem is fundamentally the one considered in some recent papers that also use simulations and/or regressions: discrete time, multi-period reallocation, and maximization of terminal utility. In contrast to that literature, we regress on decision variables and we do not rely on Taylor expansions nor derivatives of the utility function. Only basic tools are used, bundled in a dynamic programming framework: simulations—which can be black-boxed—as a representation of exogenous state variable dynamics; regression surfaces, as non-anticipative representations of expected future utility; and nonlinear or quadratic optimization, to identify the best portfolio choice at each time step. The resulting approach is simple, highly flexible and offers good performance in time and precision.

Concentrating solar power (CSP) tower technologies capture thermal radiation from the sun utilizing a field of solar-tracking heliostats. When paired with inexpensive thermal energy storage (TES), CSP technologies can dispatch electricity during peak-market-priced hours, day or night. The cost of utility-scale photovoltaic (PV) systems has dropped significantly in the last decade, resulting in inexpensive energy production during daylight hours. The hybridization of PV and CSP with TES systems has the potential to provide continuous and stable energy production at a lower cost than a PV or CSP system alone. Hybrid systems are gaining popularity in international markets as a means to increase renewable energy portfolios across the world. Historically, CSP-PV hybrid systems have been evaluated using either monthly averages of hourly PV production or scheduling algorithms that neglect the time-of-production value of electricity in the market. To more accurately evaluate a CSP-PV-battery hybrid design, we develop a profit-maximizing mixed-integer linear program ($${\mathcal {H}}$$) that determines a dispatch schedule for the individual sub-systems with a sub-hourly time fidelity. We present the mathematical formulation of such a model and show that it is computationally expensive to solve. To improve model tractability and reduce solution times, we offer techniques that: (1) reduce the problem size, (2) tighten the linear programming relaxation of ($${\mathcal {H}}$$) via reformulation and the introduction of cuts, and (3) implement an optimization-based heuristic (that can yield initial feasible solutions for ($${\mathcal {H}}$$) and, at any rate, yields near-optimal solutions). Applying these solution techniques results in a 79% improvement in solve time, on average, for our 48-h instances of ($${\mathcal {H}}$$); corresponding solution times for an annual model run decrease by as much as 93%, where such a run consists of solving 365 instances of ($${\mathcal {H}}$$), retaining only the first 24 h’ worth of the solution, and sliding the time window forward 24 h. We present annual system metrics for two locations and two markets that inform design practices for hybrid systems and lay the groundwork for a more exhaustive policy analysis. A comparison of alternative hybrid systems to the CSP-only system demonstrates that hybrid models can almost double capacity factors while resulting in a 30% improvement related to various economic metrics.