Globally Optimizing Research Articles

A hybrid optimization approach for intelligent manufacturing in plastic injection molding by using artificial neural network and genetic algorithm

This study presents a novel hybrid optimization approach for intelligent manufacturing in plastic injection molding (PIM). It focuses on globally optimizing process parameters to ensure high-quality products while reducing cycle time, material waste, and energy consumption. The method combines a backpropagation neural network (BPNN) with a genetic algorithm (GA) and employs a multi-objective optimization model based on design of experiments (DoE). A BP artificial neural network captures the relationship between optimization goals and process parameters. Leveraging the genetic algorithm, it effectively optimizes process parameters for achieving global optimization goals. The case study involves a polypropylene product, considering dimensional deviation, weight, cycle time, and energy consumption during the PIM cycle. Design variables include melt temperature, injection velocity, injection pressure, commutation position, holding pressure, holding time, and cooling time. The results demonstrate that this approach efficiently adjusts process parameters to meet quality standards, significantly reducing raw material consumption (2%), cycle time (12%), and energy consumption (16%). This offers substantial benefits for companies in highly competitive markets demanding swift adoption of smart production methods.

A robust approach to warped Gaussian process-constrained optimization

Optimization problems with uncertain black-box constraints, modeled by warped Gaussian processes, have recently been considered in the Bayesian optimization setting. This work considers optimization problems with aggregated black-box constraints. Each aggregated black-box constraint sums several draws from the same black-box function with different decision variables as arguments in each individual black-box term. Such constraints are important in applications where, e.g., safety-critical measures are aggregated over multiple time periods. Our approach, which uses robust optimization, reformulates these uncertain constraints into deterministic constraints guaranteed to be satisfied with a specified probability, i.e., deterministic approximations to a chance constraint. While robust optimization typically considers parametric uncertainty, our approach considers uncertain functions modeled by warped Gaussian processes. We analyze convexity conditions and propose a custom global optimization strategy for non-convex cases. A case study derived from production planning and an industrially relevant example from oil well drilling show that the approach effectively mitigates uncertainty in the learned curves. For the drill scheduling example, we develop a custom strategy for globally optimizing integer decisions.

Boosting Fronthaul Capacity: Global Optimization of Power Sharing for Centralized Radio Access Network

The limited fronthaul capacity imposes a challenge on the uplink of centralized radio access network (C-RAN). We propose to boost the fronthaul capacity of massive multiple-input multiple-output (MIMO) aided C-RAN by globally optimizing the power sharing between channel estimation and data transmission both for the user devices (UDs) and the remote radio units (RRUs). Intuitively, allocating more power to the channel estimation will result in more accurate channel estimates, which increases the achievable throughput. However, increasing the power allocated to the pilot training will reduce the power assigned to data transmission, which reduces the achievable throughput. In order to optimize the powers allocated to the pilot training and to the data transmission of both the UDs and the RRUs, we assign an individual power sharing factor to each of them and derive an asymptotic closed-form expression of the signal-to-interference-plus-noise for the massive MIMO aided C-RAN consisting of both the UD-to-RRU links and the RRU-to-baseband unit (BBU) links. We then exploit the C-RAN architecture's central computing and control capability for jointly optimizing the UDs' power sharing factors and the RRUs' power sharing factors aiming for maximizing the fronthaul capacity. Our simulation results show that the fronthaul capacity is significantly boosted by the proposed global optimization of the power allocation between channel estimation and data transmission both for the UDs and for their host RRUs. As a specific example of 32 receive antennas (RAs) deployed by RRU and 128 RAs deployed by BBU, the sum-rate of 10 UDs achieved with the optimal power sharing factors improves 33\% compared with the one attained without optimizing power sharing factors.

Abstract 5818: Globally optimizing therapeutic combinations against bortezomib-resistant multiple myeloma using a quantitative parabolic optimization platform

Abstract Multiple myeloma is an incurable hematological malignancy that relies on drug combinations as first and secondary lines of treatment. The inclusion of proteasome inhibitors, such as bortezomib, into these drug combination regimens has improved median survival. Resistance to bortezomib, however, is a common occurrence that ultimately contributes to treatment failure. Thus, there remains a need to identify improved drug combinations that may serve as later lines of treatment for improved treatment against bortezomib-resistant multiple myeloma. We have developed the quantitative parabolic optimization platform (QPOP) to optimize drug combinations against bortezomib-resistant multiple myeloma. By mapping phenotypic output data to parabolic response surfaces, QPOP is able to deterministically optimize drug combinations as well as drug dosages. By continuously optimizing in multiple systems of interest, from in vitro to in vivo, drug combinations can be globally optimized for greater efficacy in increasingly complex biological systems. While QPOP does not rely on molecular mechanism modeling or prediction, identified optimal drug combinations can reverse DNA hypermethylation and silencing of tumor suppressors that occurs following acquired bortezomib-resistance in multiple myeloma. Furthermore, this drug combination is broadly effective across a range of primary multiple myeloma patient samples. Beyond bortezomib-resistant multiple myeloma, global optimization of drug combinations by QPOP can serve to improve drug combination design across a range of other cancers and diseases through a continuous optimization process across the entire drug development pipeline. Citation Format: Masturah Rashid, Tan Boon Toh, Lissa Hooi, Aleidy Silva, Yanzhou Zhang, Neerja Karnani, Sudhakar Jha, Chih-Ming Ho, Wee Joo Chng, Dean Ho, Edward Kai-Hua Chow. Globally optimizing therapeutic combinations against bortezomib-resistant multiple myeloma using a quantitative parabolic optimization platform [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2018; 2018 Apr 14-18; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2018;78(13 Suppl):Abstract nr 5818.

Global optimization of general constrained grey-box models: new method and its application to constrained PDEs for pressure swing adsorption

This paper introduces a novel methodology for the global optimization of general constrained grey-box problems. A grey-box problem may contain a combination of black-box constraints and constraints with a known functional form. The novel features of this work include (i) the selection of initial samples through a subset selection optimization problem from a large number of faster low-fidelity model samples (when a low-fidelity model is available), (ii) the exploration of a diverse set of interpolating and non-interpolating functional forms for representing the objective function and each of the constraints, (iii) the global optimization of the parameter estimation of surrogate functions and the global optimization of the constrained grey-box formulation, and (iv) the updating of variable bounds based on a clustering technique. The performance of the algorithm is presented for a set of case studies representing an expensive non-linear algebraic partial differential equation simulation of a pressure swing adsorption system for $$\hbox {CO}_{2}$$CO2. We address three significant sources of variability and their effects on the consistency and reliability of the algorithm: (i) the initial sampling variability, (ii) the type of surrogate function, and (iii) global versus local optimization of the surrogate function parameter estimation and overall surrogate constrained grey-box problem. It is shown that globally optimizing the parameters in the parameter estimation model, and globally optimizing the constrained grey-box formulation has a significant impact on the performance. The effect of sampling variability is mitigated by a two-stage sampling approach which exploits information from reduced-order models. Finally, the proposed global optimization approach is compared to existing constrained derivative-free optimization algorithms.

An evolutionary multi-objective optimization system for earthworks

Earthworks involve the leveling or shaping of a target area through the moving or processing of the ground surface. Most construction projects require earthworks, which are heavily dependent on mechanical equipment (e.g., excavators, trucks and compactors). Often, earthworks are the most costly and time-consuming component of infrastructure constructions (e.g., road, railway and airports) and current pressure for higher productivity and safety highlights the need to optimize earthworks, which is a nontrivial task. Most previous attempts at tackling this problem focus on single-objective optimization of partial processes or aspects of earthworks, overlooking the advantages of a multi-objective and global optimization. This work describes a novel optimization system based on an evolutionary multi-objective approach, capable of globally optimizing several objectives simultaneously and dynamically. The proposed system views an earthwork construction as a production line, where the goal is to optimize resources under two crucial criteria (costs and duration) and focus the evolutionary search (non-dominated sorting genetic algorithm-II) on compaction allocation, using linear programming to distribute the remaining equipment (e.g., excavators). Several experiments were held using real-world data from a Portuguese construction site, showing that the proposed system is quite competitive when compared with current manual earthwork equipment allocation.

Some observations on exclusion regions in branch and bound algorithms

In branch and bound algorithms for constrained global optimization, an acceleration technique is to construct regions $${\varvec{x}}^{*}$$x? around local optimizing points $$\check{x}$$x?, then delete these regions from further search. The result of the algorithm is then a list of those small regions in which all globally optimizing points must lie. If the constructed regions are too small, the algorithm will not be able to easily reject adjacent regions in the search, while, if the constructed regions are too large, the set of optimizing points is not known accurately. We briefly review previous methods of constructing boxes about approximate optimizing points. We then derive a formula for determining the size of a constructed solution-containing region, depending on a small radius $$\epsilon $$∈, and of constructing a containing box $${\varvec{X}}^{*}\supset {\varvec{x}}^{*}$$X??x? such that all points in $${\varvec{X}}^{*}\setminus {\varvec{x}}^{*}$$X?\x? are proven to be infeasible, without the need to actually process them in the branch and bound algorithm. The construction differs in its motivation and concept from previous methods of constructing such boxes $${\varvec{X}}^{*}$$X?. It may be possible to use this technique to reduce the large amount of processing branch and bound algorithms typically require to fathom regions adjacent to optimizing points, and to obtain more accurate bounds on solution sets.

Fast global stereo matching via energy pyramid minimization

Abstract. We define a global matching framework based on energy pyramid, the Global Matching via Energy Pyramid (GM-EP) algorithm, which estimates the disparity map from a single stereo-pair by solving an energy minimization problem. We efficiently address this minimization by globally optimizing a coarse to fine sequence of sparse Conditional Random Fields (CRF) directly defined on the energy. This global discrete optimization approach guarantees that at each scale we obtain a near optimal solution, and we demonstrate its superiority over state of the art image pyramid approaches through application to real stereo-pairs. We conclude that multiscale approaches should be build on energy pyramids rather than on image pyramids.

Branching and bounding improvements for global optimization algorithms with Lipschitz continuity properties

We present improvements to branch and bound techniques for globally optimizing functions with Lipschitz continuity properties by developing novel bounding procedures and parallelisation strategies. The bounding procedures involve nonconvex quadratic or cubic lower bounds on the objective and use estimates of the spectrum of the Hessian or derivative tensor, respectively. As the nonconvex lower bounds are only tractable if solved over Euclidean balls, we implement them in the context of a recent branch and bound algorithm (Fowkes et al. in J Glob Optim 56:1791---1815, 2013) that uses overlapping balls. Compared to the rectangular tessellations of traditional branch and bound, overlapping ball coverings result in an increased number of subproblems that need to be solved and hence makes the need for their parallelization even more stringent and challenging. We develop parallel variants based on both data- and task-parallel paradigms, which we test on an HPC cluster on standard test problems with promising results.

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi: 10.1007/s10898-012-9874-7 ), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers.

Integration of scheduling and control with online closed-loop implementation: Fast computational strategy and large-scale global optimization algorithm

In this paper, we propose a novel integration method to solve the scheduling problem and the control problem simultaneously. The integrated problem is formulated as a mixed-integer dynamic optimization (MIDO) problem which contains discrete variables in the scheduling problem and constraints of differential equations from the control problem. Because online implementation is crucial to deal with uncertainties and disturbances in operation and control of the production system, we develop a fast computational strategy to solve the integration problem efficiently and allow its online applications. In the proposed integration framework, we first generate a set of controller candidates offline for each possible transition, and then reformulate the integration problem as a simultaneous scheduling and controller selection problem. This is a mixed-integer nonlinear fractional programming problem with a non-convex nonlinear objective function and linear constraints. To solve the resulting large-scale problem within sufficiently short computational time for online implementation, we propose a global optimization method based on the model properties and the Dinkelbach's algorithm. The advantage of the proposed method is demonstrated through four case studies on an MMA polymer manufacturing process. The results show that the proposed integration framework achieves a lower cost rate than the conventional sequential method, because the proposed framework provides a better tradeoff between the conflicting factors in scheduling and control problems. Compared with the simultaneous approach based on the full discretization and reformulation of the MIDO problem, the proposed integration framework is computationally much more efficient, especially for large-scale cases. The proposed method addresses the challenges in the online implementation of the integrated scheduling and control decisions by globally optimizing the integrated problem in an efficient way. The results also show that the online solution is crucial to deal with the various uncertainties and disturbances in the production system.

Outer approximation-based algorithm for biotechnology studies in systems biology

Optimization methods play a central role in systems biology studies as they can help in identifying key processes that can be experimentally changed so that specific biological goals can be attained. Standard optimization methods used in this field rely on simplified linear models that may fail in capturing the underlying complexity of the target metabolic network. Within this general context, we present a novel approach to globally optimize metabolic networks. The approach presented relies on (1) adopting a general modeling framework for metabolic networks: the Generalized Mass Action (GMA) representation; (2) posing the optimization task as a non-convex nonlinear programming (NLP) problem; and (3) devising an efficient solution method for globally optimizing the resulting NLP that embeds a GMA model of the metabolic network. The capabilities of our method are illustrated through two case studies: the anaerobic fermentation pathway in Saccharomyces cerevisiae and the citric acid production using Aspergillus niger. Numerical results show that the method presented provides near optimal solutions in low CPU times even in cases where the commercial global optimization package BARON fails to close the optimality gap.

A Method for allowing Local Editing of Globally Optimized Splines

AbstractThe present work describes an algorithm for modifying spline curves in the neighborhood of an editing point while preserving global smoothness properties. Current spline algorithms have either a graphical editing mode in which the user edits local properties of the spline, or a globally optimizing mode, in which the spline coefficients are determined such that overall properties e. g. smoothness, distance to support points, or physical behavior are optimized. With globally optimized splines, editing parameters at one point causes their transmission through the whole spline. Hence, the user has the impression that it is not possible to change the shape of the spline without disturbing the overall behavior. This can be circumvented by forcing the trajectory of the globally optimized curve to lie in the close vicinity of the original curve far away from the edited point. The present work describes an algorithm for local editing of spline curves that are produced by a global optimizer. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Deterministic Global Design Optimization Method for Nonconvex Generalized Polynomial Problems

A new design optimization method is described for finding global solutions of models with a nonconvex objective function and nonlinear constraints. All functions are assumed to be generalized polynomials. By introducing new variables, the original model is transformed into one with a linear objective function, one convex and one reversed convex constraint. A two-phase algorithm that includes global feasible search and local optimal search is used for globally optimizing the transformed model. Several examples illustrate the method.