Two-Level Weight Optimization of Composite Laminates Using Integer Programming

The stacking sequence optimization of laminated composite plates while maximizing the structural performance or minimizing the weight is a subject investigated extensively in the literature. Meanwhile, research on the optimization of laminates with cut-outs has been relatively limited. Cut-outs being an indispensable feature of structural components, this paper concentrates on the stacking sequence optimization of composite laminates in the presence of circular cut-outs. The buckling load of a laminate is used as a metric to quantify the structural performance. Here the laminates are modeled as carbon fiber-reinforced composites using the finite element analysis software, ABAQUS. For the optimization, the widely used harmony search algorithm is applied. In terms of design variables, ply thickness, and fiber orientation angles of the plies are used as continuously changing variables. In addition to the stacking sequence, another geometric variable to consider is the aspect ratio (ratio of the length of the longer sides to the length of the shorter sides of the plate) of the rectangular laminates. The optimization is carried out for three different aspect ratios. It is shown that, by using dispersed stacking sequences instead of the commonly used 0°/±45°/±90° fiber angle stacks, significantly higher buckling loads can be achieved. Furthermore, changing the cut-out geometry is found to have a significant effect on the structural performance.

Solving Integer Linear Programming (ILP) models generally lies in the category of NP-hard problems. Therefore, as the size of ILP models grows, the efficiency of exact algorithms for solving the models reduced significantly and for large models it is not possible to have the result. Genetic Algorithm (GA) is a metaheuristic method capable of adjusting and redesigning parameters and operations according to the characteristics of ILP models. Still GA has huge search space for large models and parallelization is a suitable technique to tackle this problem. This paper presents a scalable parallel GA to solve large ILP models derived from behavioral synthesis of digital circuits. We show that although models have non-binary variables, only binary variables are sufficient for coding chromosomes. We also use ”unknown” values for some genes to decrease the likelihood of inconsistency in the encoded constraints. Our experiments verify the efficiency and scalability of the proposed algorithm on multicore platforms. The proposed method outperforms IBM ILOG CPLEX 12.6 and MI-LXPM algorithm where the ILP models include 550 to 2258 int / binary decision variables. Also, the results indicate that the saturation point of using parallel processing elements for solving the large ILP models is at least 60.

A comparative analysis of linear fitting for non-linear functions on optimization: A case study: Air pollution problems

Similitude requirements and scaling laws for flutter prediction of angle-ply composite plates

This paper considers the power minimization problem in downlink of cloud radio access networks with limited fronthaul capacity. A joint design of beamforming, remote radio head (RRH) selection and RRH-user association that explicitly takes into account per- fronthaul capacity constraints is considered. The problem of interest is in fact a combinatorial program which is generally NP- hard. We naturally write the considered problem as a mixed integer program by introducing binary selection variables. The challenge is that even if these binary selection variables are relaxed to be continuous, the resulting problem is still nonconvex. For such a problem, finding a high- quality solution, rather than an optimal one, is a more realistic goal. Towards this end we propose two iterative algorithms to deal with combinatorial nature of the joint design problem. In the first method, by novel transformations, we iteratively approximate the continuous nonconvex constraints by convex conic ones using successive convex approximation framework. More explicitly the problem arrived at each iteration of the first method is a mixed-integer second order cone program (MISOCP) for which dedicated solvers are available. The second method is a simplified variant of the first one where we further relax the binary variables in each iteration to be continuous. That is to say, the second method merely requires solving a sequence of SOCPs. After convergence, we then perform a postprocessing procedure on the relaxed selection variables to search for a high-performance solution. Numerical results are presented to demonstrate the superiority of the proposed algorithms over existing methods based on sparse-inducing norm.

Although metaheuristic techniques have recently become popular in optimization, still they are not suitable for computationally expensive real-world problems, specifically when the problems have many input variables. Among these techniques, particle swarm optimization (PSO) is one of the most well-known population-based nature-inspired algorithms which can intelligently search huge spaces of possible arrangements of design variables to solve various complex problems. The candidate solutions and accordingly the required number of evaluated particles, however, dramatically increase with the number of design variables or the dimension of the problem. This study is a major modification to an original PSO for using all previously evaluated points aiming to increase the computational efficiency. For this purpose, a metamodeling methodology appropriate for so-called high-dimensional, expensive, black-box (HEB) problems is used to efficiently generate an approximate function from all particles calculated during the optimization process. Following the metamodel construction, a term named metamodeling acceleration is added to the velocity update formula in the original PSO algorithm using the minimum of the metamodel. The proposed strategy is called the metamodel guided particle swarm optimization (MGPSO) algorithm. The superior performance of the approach is compared with original PSO using several benchmark problems with different numbers of variables. The developed algorithm is then used to optimize the aerodynamic design of a gas turbine compressor blade airfoil as a challenging HEB problem. The simulation results illustrated the MGPSO’s capability to achieve more accurate results with a considerably smaller number of function evaluations.

A case for Tsai’s Modulus, an invariant-based approach to stiffness

In many applications, it is necessary to optimise the performance of hydrodynamic (HD) bearings. Many studies have proposed different strategies, but there remains a lack of conclusive research on the suitability of various optimisation methods. This study evaluates the most commonly used algorithms, including the genetic (GA), particle swarm (PSWM), pattern search (PSCH) and surrogate (SURG) algorithms. The effectiveness of each algorithm in finding the global minimum is analysed, with attention to the parameter settings of each algorithm. The algorithms are assessed on HD journal and thrust bearings, using analytical and numerical solutions for friction moment, bearing load-carrying capacity and outlet lubricant flow rate under multiple operating conditions. The results indicate that the PSCH algorithm was the most efficient in all cases, excelling in both finding the global minimum and speed. While the PSWM algorithm also reliably found the global minimum, it exhibited lower speed in the defined problems. In contrast, genetic algorithms and the surrogate algorithm demonstrated significantly lower efficiency in the tested problems. Although the PSCH algorithm proved to be the most efficient, the PSWM algorithm is recommended as the best default choice due to its ease of use and minimal sensitivity to parameter settings.

In this paper, new optimized multilevel biphase pulse compression codes (MBPCC) with low peak side lobe (PSL) and mean side lobes (MSL) have been investigated. Amplitude and phase coding have been used during the optimization process. In previous studies, biphase codes were optimized using genetic algorithm (GA). The robustness of genetic algorithm in solving optimization problems degrades simultaneously as the code length increases. Particle swarm optimization (PSO) algorithm has been used with MBPCC to solve this problem. PSO algorithm has the merits of rapid convergence to the global optimum. Complete description of PSO implementation process has been clarified. Swarm intelligence boasts a number of advantages due to the use of mobile agents. Set of novel codes with optimum PSL ranging between -27.06 dB and -38.26 dB for codes of length 5 up to 45 has been introduced. Optimization results obtained using both PSO and GA has been compared. Comparative study shows both the optimality and superiority of PSO algorithm over GA for different code lengths. MBPCC have a precision of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> (-30) dB, which can be feasibly implemented using digital attenuators at element level with optimum performance and hardware implementation facility.

Reliability optimization involves the simultaneous evaluation and selection of components and a system‐level design configuration that collectively meets all design constraints, and at the same time, optimizes some objective function, often system reliability or availability. Often these problems are very constrained because of physical or budgetary limitations. There are several variations of reliability optimization and there have been many attempts to determine optimal design configurations for different problem formulations. Applicable optimization methods include dynamic programming, integer programming, mixed integer and nonlinear programming, and metaheuristics, e.g., genetic algorithms (GA). Notable extensions to this problem include multistate reliability optimization and multiple‐objective system reliability optimization.

Centralized algorithms are widely used for optimization and control in power system applications. These algorithms require all the measurements and data to be accumulated at central location and hence suffer from single-point-of-failure. Additionally, these algorithms lack scalability with an increasing number of sensors and actuators, specially with the increasing integration of distributed energy resources (DERs). As the power system becomes a confluence of a diverse set of decision-making entities with a multitude of objectives, the preservation of privacy and operation of the system with limited information has been a growing concern. Distributed optimization techniques solve these challenges while also ensuring resilient computational solutions for the power system operation in the presence of both natural and man-made adversaries. A detailed discussion of possible applications of distributed optimization in power systems is provided in this work. However, there exist multiple challenges for accurate and computationally efficient distributed solutions. Commonly-used distributed optimization approaches include Lagrange relaxation, augmented Lagrangian, approximate network directions in conjunction with standard Lagrangian, auxiliary problem principle, alternating directions method of multipliers, optimality condition decomposition, proximal atomic coordination, and optimal feedback-based voltage control. A comprehensive classification of the distributed optimization problems has been discussed and detailed in this work. All of these algorithms have displayed efficient identification of global optimum solutions for convex continuous distributed optimization problems. The algorithms discussed so far are predominantly used to manage continuous state variables. Inclusion of integer variables in the decision support are needed for specific power system problems. Mixed integer programming (MIP) problem arises in a power system operation and control due to tap changing transformers, capacitors and switches. The global optimization techniques for MIPs are Branch and Bound, Branch and Cut, Cutting planes, Adaptive coordinate search, Nelder-Mead, Genetic algorithm etc. Although the above optimization techniques are able to solve NP-hard convexified MIP problems centrally, but are time consuming and do not scale well for large scale distributed problems. Decomposition and solution approach of distributed coordination can resolve the scalability issue. Despite the fact that a large body of work is present on the centralized solution methods for convexified MIP problems, the literature on distributed MIPs is relatively limited. The distributed optimization algorithms applied in power network to solve MIPs are reported here. ML based solutions can help to get faster convergence for distributed optimization or can replace optimization techniques depending on the problem as discussed in this work. Finally, a summary and path forward are provided, and the advancement needed in distributed optimization for the power grid is also presented.

In this paper, we present a comprehensive and in-depth investigation on the optimization of Proportional-Integral (PI) controller tuning for achieving stability and desired overshoot in the step response. The main objective of this study is to compare the effectiveness of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) techniques in finding the optimal parameters for the PI controller. The PI controller is a widely used control algorithm that plays a crucial role in many industrial processes. Its tuning greatly affects the system's performance, particularly in terms of stability and overshoot. Therefore, finding the optimal tuning parameters is of utmost importance. To address this optimization problem, we propose the utilization of two popular metaheuristic algorithms, GA and PSO. These algorithms are known for their ability to efficiently search through large solution spaces and find near-optimal solutions. By applying these algorithms to the PI controller tuning problem, we aim to determine which technique yields better results in terms of stability and overshoot tuning. In our comparative study, we provide a detailed explanation of both GA and PSO algorithms, focusing on their working principles and mathematical formulations. We also describe how these algorithms can be applied to the PI controller tuning problem. Furthermore, we highlight the key differences between GA and PSO, shedding light on their strengths and weaknesses. To assess the performance of GA and PSO, we conduct several experiments using different benchmark functions and step response models. We measure the stability and overshoot metrics for various parameter settings obtained through GA and PSO. By thoroughly analyzing the obtained results, we draw meaningful conclusions regarding the effectiveness of each technique. Our findings demonstrate that both GA and PSO exhibit promising results in optimizing PI controller tuning. These observations provide valuable insights and guidelines for choosing the appropriate algorithm based on specific control requirements. In conclusion, this comparative study is thought to contribute to the field of control systems engineering by offering a comprehensive analysis of GA and PSO techniques in the context of PI controller tuning. By highlighting their strengths and weaknesses, it is aimed to provide researchers and practitioners with valuable information for making informed decisions when optimizing control parameters for stability and overshoot reduction purposes.

Optimisation of fixture layout is critical to reduce geometric and form error of the workpiece during the machining process. In this paper the optimal placement of fixture elements (locator and clamp locations) under dynamic conditions is investigated using evolutionary techniques. The application of the newly developed particle swarm optimisation (PSO) algorithm and widely used genetic algorithm (GA) is presented to minimise elastic deformation of the workpiece considering its dynamic response. To improve the performances of GA and PSO, an improved GA (IGA) obtained by basic GA (GA) with sharing and adaptive mutation and an improved PSO (IPSO) obtained by basic PSO (PSO) incorporated into adaptive mutation are developed. ANSYS parametric design language (APDL) of finite element analysis is employed to compute the objective function for a given fixture layout. Three layout optimisation cases derived from the high speed slot milling case are used to test the effectiveness of the GA, IGA, PSO and IPSO based approaches. The comparisons of computational results show that IPSO seems superior to GA, IGA and PSO approaches with respect to the trade-off between global optimisation capability and convergence speed for the presented type problems.

Grid-edge technology can unlock flexibility from consumers to contribute to meeting the growing need for flexibility in European energy systems. Furthermore, power-to-heat technology such as heat pumps and thermal energy storage has been shown to both decarbonise heat and enable the cost-effective integration of more renewable electricity into the grid. The consumer's reaction to price signals in this context presents the opportunity to simultaneously unlock operational cost reductions for consumers and localised implicit demand-side flexibility to benefit grid operators.In this paper, the prediction accuracy, run-time, and reliability of several (metaheuristic) optimisation algorithms to derive optimal operation schedules for heat pump-based grid-edge technology are investigated. To compare effectiveness, an optimisation effectiveness indicator OEI is defined. Particle Swarm Optimisation (PSO) and Genetic Algorithm (GA) were found to be most effective and robust in yielding quasi-optimal minima for the non-linear, multi-modal, and discontinuous cost function. GA optimisation with binary variables is 5–15 times more effective than with continuous variables. Using continuous variables, PSO is more effective than GA due to smaller optimisation error, shorter run-time, and higher reliability (smaller standard deviation). Simulated Annealing and Direct (Pattern) Search were found to be not very effective.

Maritime patrol tasks assignment optimization of multiple USVs under endurance constraint