Multi-start Optimization Research Articles

Optimization of CZM parameters of Norway spruce tested in mode I using multistart simplex method

The paper addresses the advanced fracture analysis of the SEN-TPB test on Norway Spruce in three anatomical directions: tangential (T), radial (R) and tangential–radial (TR). It utilizes reverse engineering to obtain cohesive zone model (CZM) parameters, which are then compared to the experimental values obtained using the compliance-based beam method (CBBM) and additional standard material tensile tests perpendicular to the grain. The optimization employs force–displacement curves to find their optimal fit using the multistart simplex optimization method. Results indicate that CZM modeling can be relatively problematic when realistic values are used; however, the best agreement with experimental data is observed for the group of cracks in the TR direction. A fundamental issue with CZM modeling in the elastic part has been identified and discussed. The sensitivity of the problem to various parameters was assessed, and an energy balance in the CZM at Fmax was performed. This work contributes to knowledge about realistic modeling of the interface and a fundamental understanding of fracture in wood.

Efficient simultaneous optimization approach for the synthesis of large-scale heat-integrated water networks

This study develops a generalized superstructure and a compact mixed-integer nonlinear programming (MINLP) model for achieving efficient energy and water utilization in designing integrated process water systems with large sizes. Utilizing non-isothermal mixing reduces the need for many heat exchangers for indirect heat recovery. Hence, an exchanger-centric modeling strategy for heat integration is embraced over a hot–cold streams matching-based approach. A novel two-step approach is proposed to address the nonconvex and nonlinear challenges and ensure the efficiency of getting high-quality solutions. Initially, a targeting model incorporating linear heat integration is adopted to reduce the superstructure and partially initialize the design model. Subsequently, in the synthesizing stage, a two-level global search procedure is devised, integrating adaptive exchanger adjustment with multi-start local optimization. The robustness and efficiency of the proposed approach are confirmed through the resolution of four large-scale problems within one hour, yielding improved results compared to the best-known existing solutions.

Topology and Size Optimized Design and Laser Welding of the U-Frame for Free-Space Laser Communication Telescopes

The success of laser communications heavily relies on the stiffness, dynamic properties, static performance, and manufacturability of the U-frame. The U-frame is a fundamental element in satellite-to-ground laser communication telescopes. However, there is currently a lack of research on the optimal design of U-frames, leading to a significant gap between ideal construction and practical manufacturability. To address these concerns, this study proposes a comprehensive approach that combines multi-objective topology optimization and multi-start size optimization techniques. This approach considers the multidisciplinary constraints imposed by mechanical, control, and optical systems. The objective is to achieve both the conceptual and detailed design of a novel U-frame, while also ensuring thorough consideration of the structure’s manufacturability during the optimization process. The prototype of the optimized U-frame was successfully fabricated using laser welding processes. The tensile test conducted on the prototype supported the idea that laser welding can enhance the micro-grain size of the joint, leading to improved overall mechanical properties. In particular, the joint strength achieved through laser welding was found to be 1.5 times greater than that achieved through TIG (Tungsten Inert Gas) welding. Additionally, the results obtained from the free vibration experiment closely aligned with the simulation, confirming the feasibility of manufacturing the optimized structure. The optimized structure demonstrated an improvement of 7.13% in dynamic performance and 29.61% in static performance compared to the first-generation structure. Additionally, there was a reduction of 29.89% in mass without affecting the remaining performance aspects. The successful fabrication of the prototype validates the feasibility of the proposed welding process and highlights the superiority of the new U-frame.

Design of an ultrasound-emitting drill guide for freehand pedicle screw navigation.

Accurate pedicle screw placement in spinal surgery is critical as inaccuracies can lead to morbidity and suboptimal outcomes. Navigation and robotics have reduced malplacement rates, but their adoption is limited by high costs, learning curves, surgical time, and radiation. The authors propose an ultrasound-emitting and self-localising drill guide for precise screw placement that overcomes the limitations of current techniques. The preliminary configuration analysis involves systematically varying design parameters and assessing localization performance using lumbar spine MRI based simulations. The authors evaluate localization techniques based on accuracy and optimization capture range. Results suggest that feasible designs can accurately estimate position. A promising design features a 5mm radius cannula with ten 35mm-long ultrasound strips, 32 elements per strip, and a fanned-out emission profile. A multi-start active-set optimization algorithm with six initial estimates ensures reliable and efficient localization. The simulation suggests that the proposed design can achieve sufficient localization accuracy for pedicle screw navigation. These findings will guide the fabrication of a novel ultrasound-emitting drill guide for further evaluation and physical testing.

Hierarchical multi-scale parametric optimization of deep neural networks

AbstractTraditionally, sensitivity analysis has been utilized to determine the importance of input variables to a deep neural network (DNN). However, the quantification of sensitivity for each neuron in a network presents a significant challenge. In this article, a selective method for calculating neuron sensitivity in layers of neurons concerning network output is proposed. This approach incorporates scaling factors that facilitate the evaluation and comparison of neuron importance. Additionally, a hierarchical multi-scale optimization framework is proposed, where layers with high-importance neurons are selectively optimized. Unlike the traditional backpropagation method that optimizes the whole network at once, this alternative approach focuses on optimizing the more important layers. This paper provides fundamental theoretical analysis and motivating case study results for the proposed neural network treatment. The framework is shown to be effective in network optimization when applied to simulated and UCI Machine Learning Repository datasets. This alternative training generates local minima close to or even better than those obtained with the backpropagation method, utilizing the same starting points for comparative purposes within a multi-start optimization procedure. Moreover, the proposed approach is observed to be more efficient for large-scale DNNs. These results validate the proposed algorithmic framework as a rigorous and robust new optimization methodology for training (fitting) neural networks to input/output data series of any given system. Graphical Abstract

Likelihood Maximization of Lifetime Distributions With Bathtub-Shaped Failure Rate

Equipment lifetime distributions with bathtub-shaped failure rate can be fitted to data by the maximum likelihood criterion. In the literature, a commonly used method is to find a point in the parameter space where the partial derivatives of the log-likelihood function are zero. As the log-likelihood function is typically nonconvex, this approach may yield a suboptimal fit. In this work, we maximize the log-likelihood function, using a multistart of 100 optimization procedures, by three nonlinear optimization algorithms: 1) Nelder–Mead with adaptive parameters; 2) sequential least squares quadratic programming (SLSQP); 3) limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm with box constraints (L-BFGS-B). We perform a systematic study of refitting ten key lifetime distributions with bathtub-shaped failure rate from the literature to two widely studied datasets. The multistart nonlinear optimization yields better fits than those reported in the literature in 14 out of 19 distribution-dataset pairs, for which reference parameters are available. Based on the results, if gradient information of the log-likelihood function is available, our recommended optimization algorithm for the purpose is SLSQP.

A Multi-Start Gradient Combination Method for High-Performance Global Search

The gradient descent is one of the most common methods to modify the gradient parameters of the neural network, however, it may fall into the local optimum in the training process. As we all know, genetic algorithm can find the global optimal solution through global search, but it may not be efficient, always takes a lot of running time. These two methods are complementary in the running time and the cost, which inspired us to consider the combination of gradient descent and genetic algorithm. In this paper, a multi-start combinatorial optimization method based on the genetic algorithm and the gradient descent is proposed. First, the initial point is selected through the genetic algorithm. Then the combination of multi-start and gradient descent is used, which can quickly achieve the global search and improve the performance with relatively less running time and cost. Compared with the traditional genetic algorithm and gradient descent method, this proposed algorithm has a better performance in computing the global optimum efficiently.

Efficient variational synthesis of quantum circuits with coherent multi-start optimization

We consider the problem of the variational quantum circuit synthesis into a gate set consisting of the CNOT gate and arbitrary single-qubit (1q) gates with the primary target being the minimization of the CNOT count. First we note that along with the discrete architecture search suffering from the combinatorial explosion of complexity, optimization over 1q gates can also be a crucial roadblock due to the omnipresence of local minimums (well known in the context of variational quantum algorithms but apparently underappreciated in the context of the variational compiling). Taking the issue seriously, we make an extensive search over the initial conditions an essential part of our approach. Another key idea we propose is to use parametrized two-qubit (2q) controlled phase gates, which can interpolate between the identity gate and the CNOT gate, and allow a continuous relaxation of the discrete architecture search, which can be executed jointly with the optimization over 1q gates. This coherent optimization of the architecture together with 1q gates appears to work surprisingly well in practice, sometimes even outperforming optimization over 1q gates alone (for fixed optimal architectures). As illustrative examples and applications we derive 8 CNOT and T depth 3 decomposition of the 3q Toffoli gate on the nearest-neighbor topology, rediscover known best decompositions of the 4q Toffoli gate on all 4q topologies including a 1 CNOT gate improvement on the star-shaped topology, and propose decomposition of the 5q Toffoli gate on the nearest-neighbor topology with 48 CNOT gates. We also benchmark the performance of our approach on a number of 5q quantum circuits from the ibm_qx_mapping database showing that it is highly competitive with the existing software. The algorithm developed in this work is available as a Python package CPFlow.

Dynamic modelling predicts lactate and IL-1β as interventional targets in metabolic-inflammation-clock regulatory loop in glioma.

In an attempt to understand the role of dysregulated circadian rhythm in glioma, our recent findings highlighted the existence of a feed-forward loop between tumour metabolite lactate, pro-inflammatory cytokine IL-1β and circadian CLOCK. To further elucidate the implication of this complex interplay, we developed a mathematical model that quantitatively describes this lactate dehydrogenase A (LDHA)-IL-1β-CLOCK/BMAL1 circuit and predicts potential therapeutic targets. The model was calibrated on quantitative western blotting data in two glioma cell lines in response to either lactate inhibition or IL-1β stimulation. The calibrated model described the experimental data well and most of the parameters were identifiable, thus the model was predictive. Sensitivity analysis identified IL-1β and LDHA as potential intervention points. Mathematical models described here can be useful to understand the complex interrelationship between metabolism, inflammation and circadian rhythm, and in designing effective therapeutic strategies. Our findings underscore the importance of including the circadian clock when developing pharmacological approaches that target aberrant tumour metabolism and inflammation. Insight box The complex interplay of metabolism-inflammation-circadian rhythm in tumours is not well understood. Our recent findings provided evidence of a feed-forward loop between tumour metabolite lactate, pro-inflammatory cytokine IL-1β and circadian CLOCK/BMAL1 in glioma. To elucidate the implication of this complex interplay, we developed a mathematical model that quantitatively describes this LDHA-IL-1β-CLOCK/BMAL1 circuit and integrates experimental data to predict potential therapeutic targets. The study employed a multi-start optimization strategy and profile likelihood estimations for parameter estimation and assessing identifiability. The simulations are in reasonable agreement with the experimental data. Sensitivity analysis found LDHA and IL-1β as potential therapeutic points. Mathematical models described here can provide insights to understand the complex interrelationship between metabolism, inflammation and circadian rhythm, and in identifying effective therapeutic targets.

Optimization of a multipurpose river basin in anambra state, Nigeria

In this study, the multipurpose objective of development in the Anambra River basin was examined. The study's goals are to determine the net benefits of the various objectives under each purpose currently carried out by the Anambra River Basin, to identify the best way to achieve the goals, and to show, through logical and mathematical reasoning, how money could be allocated to the various goals of a dam project in Anambra State effectively. Economic Efficiency (EE), Regional Economic Redistribution (RER), Social Well-Being (SW), Youth Empowerment (YE), and Environmental Quality Improvement are the objectives taken into account in the study (EQI). The optimization problem in the multi-purpose-objective development of the Anambra State river basin was solved utilizing the multi-start optimization method. The study showed that the basin would achieve enormous financial benefits if it used its N15.0 billion strategic development budget over four years for various purposes as illustrated. The results showed that the following allocation of the five purposes should be optimized simultaneously for an N15.0 billion four-year strategic development fund: EE should receive N0.762 billion, RER should receive N0.594 billion, SW should receive N0.649 billion, YE should receive N0.683 billion, and environmental quality improvement should receive N4.768 billion. It was found that Environmental Quality Improvement was allocated the higher amount while Regional Economic Redistribution was allocated the least amount for the development. The study's findings recommended that the management of the basin stop the practice of allocating funds to various uses at their discretion, which has led to significant oversight and the improper distribution of scarce resources. As a result, every fund distribution must be justified using logic and mathematics. To increase the accuracy of the data, the Anambra State River Basin Development Authorities must intensify record-keeping activities.

Beamforming Optimization for Intelligent Reflecting Surface-Assisted MIMO Systems

To improve the spectral efficiency of symmetry-based intelligent reconfigurable surface (IRS)-assisted MIMO communication systems, this paper investigates the joint precoding and passive beamforming optimization problem for millimeter-wave point-to-point MIMO systems under both ideal and practical IRS phase shifts. For the ideal IRS phase shifts setup, we derive a simplified approximate spectral efficiency expression based on Jensen’s inequality and propose a minimum mean square error (MMSE)-based algorithm to transform the simplified non-convex problem into a solvable convex function. For the practical IRS phase shifts setup, we propose a multi-start stepwise optimization algorithm to obtain the passive beamforming by stepwise iterative search. Finally, with the above-obtained passive beamforming, the optimal precoding is derived by performing the singular value decomposition (SVD) on the effective channel and water-filling power allocation. The simulation results verify our performance analysis and demonstrate that spectral efficiency can be effectively improved compared to various benchmark schemes.

Framework for embedding black-box simulation into mathematical programming via kriging surrogate model applied to natural gas liquefaction process optimization

This paper presents a framework to solve the constrained black-box simulation optimization problem that arises from the optimal energy-efficient design of single-mixed refrigerant natural gas liquefaction process using reliable process simulator. Kriging surrogate model is used to introduce simple, computationally inexpensive, and effective algebraic formulations with reliable derivatives to the black-box objective and constraints functions. The algebraic surrogate optimization problem is embedded into a nonlinear programming (NLP) model in General Algebraic Modeling System (GAMS). The NLP problem is solved using efficient multi-start gradient-based optimization with CONOPT local solver to determine a candidate of decision variables for which the true functions are calculated in the rigorous simulation. The single-mixed refrigerant process is analyzed considering one-to-three-stage expansion and phase separation to assess potential energy savings. The present approach results show that more expansion stages can provide energy savings from 12.02 to 14.70 % comparing two-stage and three-stage expansion system with single-stage. This optimization framework is more effective and consistent than Particle Swarm Optimization and Genetic Algorithm given the same budget of simulation evaluations for the considered simulation optimization problems, resulting in 13.57 to 53.26 % of energy savings.

MinCentre: using clustering in global optimisation

A common problem that arises in many scientific fields is locating the global minimum of a multi-modal function. A novel clustering technique that tackles this problem is introduced here. The proposed method creates clusters from uniform samples of the objective function with the usage of the K-means clustering technique. For every cluster a centre is created. Finally, a simple rejection procedure is applied to the created clusters in order to remove clusters that are close to others. The proposed method is tested on a series of well-known optimisation problems from the relevant literature and the results are reported and compared against the simple multi-start global optimisation method.

Influence of water content on the mechanical behavior of gelatin based hydrogels: Synthesis, characterization, and modeling

Gelatin hydrogels are a promising candidate in biomedical fields due to their mechanical and chemical characteristics. In the present work, the effect of variation of water content on the mechanical properties of gelatin-based hydrogels is investigated through mechanical characterization and mathematical modeling. The pure gelatin hydrogels and gelatin/polyvinyl alcohol-based composite hydrogels having 90%, 70%, and 50% water content are prepared using the solvent casting method. To characterize the mechanical behavior, these hydrogels are subjected to monotonic stretch, constant stretch, constant stress, multistep stretch, and cyclic stretch loading. On the basis of experimental observations, a phenomenological and micromechanics approach-based mathematical model is proposed to capture the hyperelastic and viscous behavior of the hydrogels. Further, the simulations based on the multistart optimization are performed to obtain the material parameters using the proposed model. The mechanical characterization and the modeling results indicate that the gelatin-based hydrogels show the significant viscoelastic behavior at lower water content (70% and 50%), and it reduced at higher water content (90%).

Multistart global optimization with tunnelling and an evolutionary strategy supervised by a martingale

ABSTRACT Global optimization is one of the most difficult research topics in the optimization area. In the past few decades, many stochastic methods have been proposed that proved to be effective. In this article, a new multistart global optimization method, using tunnelling and an evolutionary strategy and supervised by a martingale (MGO-TEM) is proposed, which also belongs to the stochastic family. MGO-TEM is under a multistart framework such that a local search method will be called when a new sample point is generated. A sampling technique that is a hybrid of tunnelling and an evolutionary strategy is proposed in MGO-TEM with a set of stopping criteria whose derivation is based on martingale theory. Through experiments, MGO-TEM is compared with 10 other well-known algorithms on 55 single-objective test functions, and the results show that MGO-TEM is superior to all of them. Moreover, MGO-TEM is user-friendly since there are only two parameters to be tuned.

Discrete optimization design for a cabin-skeleton coupling structure of blended-wing-body underwater glider

Objectives The blended-wing-body underwater glider cabin-skeleton coupling structure is optimized by using a data-driven discrete optimization idea. Methods Firstly, a Kriging-assisted discrete global optimization algorithm (KDGO) is proposed for computationally intensive black-box problems. The KDGO uses a novel infill-sampling strategy to capture discrete sample points with better performance. In the infill-sampling strategy, a multi-start method with data mining strategy is introduced, including multi-start optimization, projection, sampling, and selection. Secondly, the parametric skeleton-cabin coupling structure model was established and was analyzed by finite element in the lifting deformation and deep-water pressure conditions. Then, take the float-to-weight ratio and the strength and stability of the skeleton-cabin structure as the as the goal and constraints, respectively. Meanwhile, considering the interference between shape and cabin and the coupling relationship between skeleton and cabin, then establish a discrete optimization mathematical model of the overall coupling structure. Finally, the discrete optimization algorithm and coupling structure simulation are combined to build an overall optimization framework. Results By using KDGO to conduct 200 function evaluations and comparing the optimal feasible point in DoE with the global optimal feasible point after optimization, it was found that the optimized float-to-weight ratio of the coupling structure increased by nearly 40%, and satisfactory results were obtained. Conclusion The research results can provide a reference for the cabin-skeleton coupling structure design of blended-wing-body underwater glider.

Penetration Depth Between Two Convex Polyhedra: An Efficient Stochastic Global Optimization Approach.

During the detailed design phase of an aerospace program, one of the most important consistency checks is to ensure that no two distinct objects occupy the same physical space. Since exact geometrical modeling is usually intractable, geometry models are discretized, which often introduces small interferences not present in the fully detailed model. In this paper, we focus on computing the depth of the interference, so that these false positive interferences can be removed, and attention can be properly focused on the actual design. Specifically, we focus on efficiently computing the penetration depth between two polyhedra, which is a well-studied problem in the computer graphics community. We formulate the problem as a constrained five-variable global optimization problem, and then derive an equivalent unconstrained, two-variable nonsmooth problem. To solve the optimization problem, we apply a popular stochastic multistart optimization algorithm in a novel way, which exploits the advantages of each problem formulation simultaneously. Numerical results for the algorithm, applied to 14 randomly generated pairs of penetrating polytopes, illustrate both the effectiveness and efficiency of the method.

An Algorithm Framework for Facility Service Districting Problem

Objectives Facility service districting problem(FSDP) refers to the design of facility service areas according to the facility locations and service capacities in a geographical region. The design criteria for service areas include the balance of service demand and supply, the highest service accessibility, and the spatial contiguity. The spatial contiguity is a necessity for satisfying some policies on public services, such as school districting and medical districting. However, solving the FSDP with contiguity constraints is challenging. We present a hybrid algorithm framework for solving the FSDP. Methods The algorithm is proposed based on the general local search algorithm and furtherly enhanced by multi-start, ruin-recreate, set-partitioning and other optimization strategies. The basic modules such as initial solution generation method, local search operators, solution perturbation, model building and solving, and search strategies, are provided in the framework. Using these building blocks, some exact, metaheuristic and hybrid algorithms could be implemented effectively. Five algorithms are implemented for the FSDP: Exact method by solving a mixed integer linear programming model, simulated annealing (SA) algorithm, iterative local search (ILS) algorithm, SA with set-partitioning, and ILS with set-partitioning. In addition, four instances are designed to test the algorithms. The instance size, supply-demand ratio, and geographic environment are considered in the instance design. Results There are several findings from computing experimentation: Optimal or near-optimal solutions of the instances could be obtained by CPLEX optimizer; high-quality solutions could be found by SA and ILS algorithms much more efficiently; the set-partitioning procedure is capable of improving the solution quality. Conclusions Based on the proposed algorithm framework, it is easy and flexible to design local-search based matheuristics and hybrid algorithms for the FSDP. High quality solutions could be obtained by coupling the local search with ruin-recreate perturbation and set-partitioning.

Finding diverse ways to improve algebraic connectivity through multi-start optimization

AbstractThe algebraic connectivity, also known as the Fiedler value, is a spectral measure of network connectivity that can be increased through edge addition. We present an algorithm for producing many diverse ways to add a fixed number of edges to a network to achieve a near optimal Fiedler value. Previous Fielder value optimization algorithms (i.e. the greedy algorithm) output only one solution. Obtaining a single solution is rarely good enough for real-world network redesign problems, as practical constraints (political, physical or financial) may prevent implementation. Our algorithm takes a multi-start optimization approach, adding a random initial edge and then applies a greedy heuristic to improve the Fiedler value. The random choice moves us to a new region of the search space, enabling discovery of diverse solutions. Additionally, we present a Determinantal Point Process framework for quantifying diversity. We then apply a Markov chain Monte Carlo technique to sift through the large number of output solutions and locate a smaller, more manageable collection of highly diverse solutions that can be presented to network redesign engineers. We demonstrate the effectiveness of our algorithm on real-world graphs with varied structures.

Identifiability of tissue material parameters from uniaxial tests using multi-start optimization

Determining tissue biomechanical material properties from mechanical test data is frequently required in a variety of applications. However, the validity of the resulting constitutive model parameters is the subject of debate in the field. Parameter optimization in tissue mechanics often comes down to the “identifiability” or “uniqueness” of constitutive model parameters; however, despite advances in formulating complex constitutive relations and many classic and creative curve-fitting approaches, there is currently no accessible framework to study the identifiability of tissue material parameters. Our objective was to assess the identifiability of material parameters for established constitutive models of fiber-reinforced soft tissues, biomaterials, and tissue-engineered constructs and establish a generalizable procedure for other applications. To do so, we generated synthetic experimental data by simulating uniaxial tension and compression tests, commonly used in biomechanics. We then fit this data using a multi-start optimization technique based on the nonlinear least-squares method with multiple initial parameter guesses. We considered tendon and sclera as example tissues, using constitutive models that describe these fiber-reinforced tissues. We demonstrated that not all the model parameters of these constitutive models were identifiable from uniaxial mechanical tests, despite achieving virtually identical fits to the stress-stretch response. We further show that when the lateral strain was considered as an additional fitting criterion, more parameters are identifiable, but some remain unidentified. This work provides a practical approach for addressing parameter identifiability in tissue mechanics.