In engineering applications one often has to trade-off among several objectives as, for example, the mechanical stability of a component, its efficiency, its weight and its cost. We consider a biobjective shape optimization problem maximizing the mechanical stability of a ceramic component under tensile load while minimizing its volume. Stability is thereby modeled using a Weibull-type formulation

Stratified models depend in an arbitrary way on a selected categorical feature that takes K values, and depend linearly on the other n features. Laplacian regularization with respect to a graph on the feature values can greatly improve the performance of a stratified model, especially in the low-data regime. A significant issue with Laplacian-regularized stratified models is that the model is K times

In this paper, we develop a novel evolutionary interactive method called interactive K-RVEA, which is suitable for computationally expensive problems. We use surrogate models to replace the original expensive objective functions to reduce the computation time. Typically, in interactive methods, a decision maker provides some preferences iteratively and the optimization algorithm narrows the search

This paper offers a novel approach for computing globally optimal solutions to the pump scheduling problem in drinking water distribution networks. A tailored integer linear relaxation of the original non-convex formulation is devised and solved by branch and bound where integer nodes are investigated through non-linear programming to check the satisfaction of the non-convex constraints and compute

Global warming and climate change call for urgent minimization of human activities on the environment. Therefore, there is a great need for the improvement of resource efficiencies by integrating various life-supporting systems. The challenge is on the energy, water and environment systems to integrate and become more sustainable. This field of research has received increased attention over the past

This work presents multi-objective optimization of an aspirating smoke detection system which uses the pipeline to transport air sample from the sampling points to the analysing module. On the basis of 3D computational fluid dynamics simulation it has been shown that the smoke transport will not always take place in the centre of the pipe and that one dimensional analysis is not able to provide information

Short-term open pit planners have to deal with the task of designing a feasible production schedule. This schedule must fulfill processing, mining and operational constraints and, at the same time, maximize the profit or total metal produced. It also must comply with the long-term production schedule and must incorporate new blasthole sampling data. This task is performed with little support of optimization

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 work, we provide a new Black–Scholes model, where the weak formulation at stake is done in the case of a general class of finite Radon measures. A numerical estimation of the parameters, by means of a gradient algorithm, shows that the estimated model is better as regards option pricing quality than the classical Black–Scholes one.

We present the closed-form solution to the problem of hedging price and quantity risks for energy retailers (ER), using financial instruments based on electricity price and weather indexes. Our model considers an ER who is intermediary in a regulated electricity market. ERs buy a fixed quantity of electricity at a variable cost and must serve a variable demand at a fixed cost. Thus ERs are subject

Variable order structures model situations in which the comparison between two points depends on a point-to-cone map. In this paper, inexact projected gradient methods for solving smooth constrained vector optimization problems on variable ordered spaces are presented. It is shown that every accumulation point of the generated sequences satisfies the first-order necessary optimality condition. Moreover

The impact of intermittent power production by Photovoltaic (PV) systems to the overall power system operation is constantly increasing and so is the need for advanced forecasting tools that enable understanding, prediction, and managing of such a power production. Solar power production forecasting is one of the enabling technologies, which can accelerate the transition to sustainable energy environment

In this paper, we study a numerical approach to compute a solution of the generalized Nash equilibrium problem (GNEP). The GNEP is a potent modeling tool that has been increasingly developing in recent decades. Much of this development has centered around applying variational methods to the so-called GNSC, a useful but restricted subset of GNEP where each player has the same constraint set. One popular

Most industrial optimization problems are sparse and can be formulated as block-separable mixed-integer nonlinear programming (MINLP) problems, defined by linking low-dimensional sub-problems by (linear) coupling constraints. This paper investigates the potential of using decomposition and a novel multiobjective-based column and cut generation approach for solving nonconvex block-separable MINLPs,

We investigate the computation of a sparse solution to an underdetermined system of linear equations using the Huber loss function as a proxy for the 1-norm and a quadratic error term à la Lasso. The approach is termed “penalized Huber loss”. The results of the paper allow to calculate a sparse solution using a simple extrapolation formula under a sign constancy condition that can be removed if one

A control problem for a linearized time-discrete regularized fracture propagation process is considered. The discretization of the problem is done using a conforming finite element method. In contrast to many works on discretization of PDE constrained optimization problems, the particular setting has to cope with the fact that the linearized fracture equation is not necessarily coercive. A quasi-best

Parameter estimation problems of mathematical models can often be formulated as nonlinear least squares problems. Typically these problems are solved numerically using iterative methods. The local minimiser obtained using these iterative methods usually depends on the choice of the initial iterate. Thus, the estimated parameter and subsequent analyses using it depend on the choice of the initial iterate

With arrival of advanced technologies, automated appliances in residential sector are still in unlimited growth. Therefore, the design of new management schemes becomes necessary to be achieved for the electricity demand in an effort to ensure safety of domestic installations. To this end, the Demand Side Management (DSM) is one of suggested solution which played a significant role in micro-grid and

This paper addresses the emerging practical requirement that wireless information and power transfer are employed simultaneously in a multiple-input single-output (MISO) secrecy channel. Transmit beamforming without artificial noise and that with artificial noise are considered. In addition, perfect and imperfect channel state information of both the legitimate receivers and eavesdroppers are investigated

Discrete variable topology optimization problems are usually solved by using solid isotropic material with penalization (SIMP), genetic algorithms (GA), or mixed-integer nonlinear optimization (MINLO). In this paper, we propose formulating discrete ply-angle and thickness topology optimization problems as a mixed-integer second-order cone optimization (MISOCO) problem. Unlike SIMP and GA methods, MISOCO

This paper presents a control system design methodology for the drill-string rotary drive and draw-works hoist system aimed at their coordinated control for the purpose of establishing a fully-automated mechatronic system suitable for borehole drilling applications. Both the drill-string rotary drive and the draw-works hoist drive are equipped with proportional-integral (PI) speed controllers, which

Planning the construction of new transport routes or power lines on terrain is usually carried out manually by engineers, with no guarantee of optimality. We introduce a new approach for the computation of an optimal trajectory for the construction of new transit routes and power lines between two locations on a submanifold \(U\subset \mathbb {R}^{3}\) representing the topography of a terrain. U is

This paper presents a novel trust-region method for the optimization of multiple expensive functions. We apply this method to a biobjective optimization problem in fluid mechanics, the optimal mixing of particles in a flow in a closed container. The three-dimensional time-dependent flows are driven by Lorentz forces that are generated by an oscillating permanent magnet located underneath the rectangular

Manufacturing remains one of the most energy intensive sectors, additionally, the energy used within buildings for heating, ventilation and air conditioning (HVAC) is responsible for almost half of the UK’s energy demand. Commonly, these are analysed in isolation from one another. Use of machine learning is gaining popularity due to its ability to solve non-linear problems with large data sets and

Compressor stations are the heart of every high-pressure gas transport network. Located at intersection areas of the network, they are contained in huge complex plants, where they are in combination with valves and regulators responsible for routing and pushing the gas through the network. Due to their complexity and lack of data compressor stations are usually dealt with in the scientific literature

This paper aimed to optimize the extraction of antioxidants from plum seeds (Prunus domestica L.) using ultrasound-assisted extraction. The Box–Behnken design was used for the optimization of the extraction process. The four extraction parameters, such as the extraction time (10–40 min), ethanol concentration (20–100%, v/v), liquid-to-solid ratio (10–30 cm3 g−1), and extraction temperature (30–70 °C)

We propose a sample average approximation-based outer-approximation algorithm (SAAOA) that can address nonconvex two-stage stochastic programs (SP) with any continuous or discrete probability distributions. Previous work has considered this approach for convex two-stage SP (Wei and Realff in Comput Chem Eng 28(3):333–346, 2004). The SAAOA algorithm does internal sampling within a nonconvex outer-approximation

Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimization formulations for computing a single sparse loading vector: we employ two norms

The application of mathematical optimization methods for water supply system design and operation provides the capacity to increase the energy efficiency and to lower the investment costs considerably. We present a system approach for the optimal design and operation of pumping systems in real-world high-rise buildings that is based on the usage of mixed-integer nonlinear and mixed-integer linear modeling

Individual technical components are usually well optimized. However, the design process of entire technical systems, especially in its early stages, is still dominated by human intuition and the practical experience of engineers. In this context, our vision is the widespread availability of software tools to support the human-driven design process with the help of modern mathematical methods. As a

This paper describes a new parallel global surrogate-based algorithm Global Optimization in Parallel with Surrogate (GOPS) for the minimization of continuous black-box objective functions that might have multiple local minima, are expensive to compute, and have no derivative information available. The task of picking P new evaluation points for P processors in each iteration is addressed by sampling

We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic 1d partial differential equations. In addition, a pooling-type mixing model is required at the nodes of the network to treat the mixing of different water temperatures

To provide electric power supply to consumers even in abnormal situations, the equipment used in electric distribution systems, including distribution lines, have sufficient capacity margins. Maintenance and/or replacement of these lines involving network reconfigurations are routinely performed. Since the monetary costs of equipment investments are significant, downsizing the equipment is important

We consider two mathematical problems that are connected and occur in the layer-wise production process of a workpiece using wire-arc additive manufacturing. As the first task, we consider the automatic construction of a honeycomb structure, given the boundary of a shape of interest. In doing this, we employ Lloyd’s algorithm in two different realizations. For computing the incorporated Voronoi tesselation

Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity—the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard—practical instances of the problem usually involve a large to very large number of decision variables, typically of the order of millions for

In hydro predominant systems, the long-term hydrothermal scheduling problem (LTHS) is formulated as a multistage stochastic programming model. A classical optimization technique to obtain an operational policy is the stochastic dual dynamic programming (SDDP), which employs a forward step, for generating trial state variables, and a backward step to construct Benders-like cuts. To assess the quality

This paper concerns online portfolio selection problem. In this problem, no statistical assumptions are made about the future asset prices. Although existing universal portfolio strategies have been shown to achieve good performance, it is not easy, almost impossible, to determine upfront which strategy will achieve the maximum final cumulative wealth for online portfolio selection tasks. This paper

Based on the theoretical framework recently proposed by Bonifacius and Neitzel (Math Control Relat Fields 8(1):1–34, 2018. https://doi.org/10.3934/mcrf.2018001) we discuss the sequential quadratic programming (SQP) method for the numerical solution of an optimal control problem governed by a quasilinear parabolic partial differential equation. Following well-known techniques, convergence of the method

A global optimisation strategy based on the hybrid surrogate model method and the competitive mechanism-based multi-objective particle swarm optimisation (CMOPSO) algorithm was developed to improve the accuracy of the aerodynamic performance optimisation of a high-speed train running in open air without a crosswind. Free-form deformation was used to improve the optimisation efficiency without remodelling

Generating polyhedral outer approximations and solving mixed-integer linear relaxations remains one of the main approaches for solving convex mixed-integer nonlinear programming (MINLP) problems. There are several algorithms based on this concept, and the efficiency is greatly affected by the tightness of the outer approximation. In this paper, we present a new framework for strengthening cutting planes

In areas that require high performance components, such as the automotive, aeronautics and aerospace industries, optimization of the dynamic behavior of structures is sought through different approaches, such as the design of materials specific to the application, for instance through structural topology optimization. The bi-directional evolutionary structural optimization (BESO) method, in particular

Along with the advantages provided by the material and ease of assembly/disassembly, the ease of repair provided by minimum deformation after a collision and its sustainability highlight the preference of concrete barriers for roadside safety. However, concrete barriers, as rigid systems, are highly risky in case of a collision. Because the top priority of the application purpose is safety, it is desirable

Inverse problems are of great importance in some engineering texts and many industrial applications. Owing to this, we exhibit a method for numerically estimating two cases of the two-dimensional inverse problems in this research work. The considered inverse problem includes the time-dependent source control parameter r(t). This method is based on operational matrices of differential and integration

In this work, we consider a risk-averse ultimate pit problem where the grade of the mineral is uncertain. We derive conditions under which we can generate a set of nested pits by varying the risk level instead of using revenue factors. We propose two properties that we believe are desirable for the problem: risk nestedness, which means the pits generated for different risk aversion levels should be

A coupled topology and domain shape optimization framework is presented that is based on incorporating the shape design variables of the design domain in the Solid Isotropic Material with Penalization topology optimization method. The shape and topology design variables are incrementally updated in a sequential fashion, using a staggered numerical update scheme. Non-Uniform Rational B-Splines are employed

In this study we present an optimization problem where machine scheduling and personnel allocation decisions are solved simultaneously. The machine scheduling consists of solving a variant of the job shop problem where jobs are allocated in batches and multitasking is allowed. On the other hand, the personnel allocation problem searches for the optimal allocation of human resources to support the facility

Storage planning and utilization are among the most important considerations of practical batch process scheduling. Modeling the available storage options appropriately can be crucial in order to find practically applicable solutions with the best objective value. In general, there are two main limitations on storage: capacity and time. This paper focuses on the latter and investigates different techniques

The present paper addresses the robustness and convergence behavior of the direct limit analysis (LA) based methodology developed for the topology design of continuum structures subject to prescribed statically and plastically admissible loads. The design methodology, based on a direct method formulation of the static LA problem, has recently been proposed for continuous topology optimization and its

This paper aims to obtain a strong convergence result for a Douglas–Rachford splitting method with inertial extrapolation step for finding a zero of the sum of two set-valued maximal monotone operators without any further assumption of uniform monotonicity on any of the involved maximal monotone operators. Furthermore, our proposed method is easy to implement and the inertial factor in our proposed

One crucial advantage of additive manufacturing regarding the optimization of lattice structures is that there is a reduction in manufacturing constraints compared to classical manufacturing methods. To make full use of these advantages and to exploit the resulting potential, it is necessary that lattice structures are designed using optimization. Against this backdrop, two mixed integer programs are

We present a convection–diffusion inverse problem that aims to identify an unknown number of sources and their locations. We model the sources using a binary function, and we show that the inverse problem can be formulated as a large-scale mixed-integer nonlinear optimization problem. We show empirically that current state-of-the-art mixed-integer solvers cannot solve this problem and that applying

The assessment of the ecological impact of different powertrain concepts is of increasing relevance considering the enormous efforts necessary to limit the global warming effect due to the man-made climate change. Within this contribution, we adopt existing methods for the optimization of electric and hybrid electric powertrains using a vehicle simulation environment and derive a method to identify

The paper concerns with the two numerical methods for approximating solutions of a monotone and Lipschitz variational inequality problem in a Hilbert space. We here describe how to incorporate regularization terms in the projection method, and then establish the strong convergence of the resulting methods under certain conditions imposed on regularization parameters. The new methods work in both cases

We present a novel parameter space exploration algorithm for three classes of multiparametric problems, namely linear (mpLP), quadratic (mpQP), and mixed-integer linear (mpMILP). We construct subsets of the parameter space in the form of simplices through Delaunay triangulation to facilitate identification of the optimal partitions that describe the solution space. The presented exploration strategy

In this paper, we focus on multiobjective two-level simple recourse programming problems, in which multiple objective functions are involved in each level, shortages and excesses arising from the violation of the constraints with discrete random variables are penalized, and the sum of the objective function and the expectation of the amount of the penalties is minimized. To deal with such problems

We propose a semismooth Newton-type method for nonsmooth optimal control problems. Its particular feature is the combination of a quasi-Newton method with a semismooth Newton method. This reduces the computational costs in comparison to semismooth Newton methods while maintaining local superlinear convergence. The method applies to Hilbert space problems whose objective is the sum of a smooth function

The employment of industrial robot systems especially in the automotive industry noticeably changed the view of production plants and led to a tremendous increase in productivity. Nonetheless, rising technological complexity, the parallelization of production processes, as well as the crucial need for respecting specific safety issues pose new challenges for man and machine. Our goal is to develop

The objective of this research is to efficiently solve complicated high dimensional optimization problems by using machine learning technologies. Recently, major optimization targets have been changed to more complicated ones such as discontinuous and high dimensional optimization problems. It is necessary to solve the high-dimensional optimization problems to obtain an innovate design from topology

Particle swarm optimization (PSO) is one of the most commonly used stochastic optimization algorithms for many researchers and scientists of the last two decades, and the pattern search (PS) method is one of the most important local optimization algorithms. In this paper, we test three methods of hybridizing PSO and PS to improve the global minima and robustness. All methods let PSO run first followed

The synthesis of energy systems is a two-stage optimization problem where design decisions have to be implemented here-and-now (first stage), while for the operation of installed components, we can wait-and-see (second stage). To identify a sustainable design, we need to account for both economical and environmental criteria leading to multi-objective optimization problems. However, multi-objective