A Collection of Challenging Optimization Problems in Science, Engineering and Economics

Function optimization and finding simultaneous solutions of a system of nonlinear equations (SNE) are two closely related and important optimization problems. However, unlike in the case of function optimization in which one is required to find the global minimum and sometimes local minima, a database of challenging SNEs where one is required to find stationary points (extrama and saddle points) is not readily available. In this article, we initiate building such a database of important SNE (which also includes related function optimization problems), arising from Science, Engineering and Economics. After providing a short review of the most commonly used mathematical and computational approaches to find solutions of such systems, we provide a preliminary list of challenging problems by writing the Mathematical formulation down, briefly explaning the origin and importance of the problem and giving a short account on the currently known results, for each of the problems. We anticipate that this database will not only help benchmarking novel numerical methods for solving SNEs and function optimization problems but also will help advancing the corresponding research areas.Comment: Accepted as an invited contribution to the special session on Evolutionary Computation for Nonlinear Equation Systems at the 2015 IEEE Congress on Evolutionary Computation (at Sendai International Center, Sendai, Japan, from 25th to 28th May, 2015.

A Brief Review of Cuckoo Search Algorithm (CSA) Research Progression from 2010 to 2013

Cuckoo Search Algorithm is a new swarm intelligence algorithm which based on breeding behavior of the Cuckoo bird. This paper gives a brief insight of the advancement of the Cuckoo Search Algorithm from 2010 to 2013. The first half of this paper presents the publication trend of Cuckoo Search Algorithm. The remaining of this paper briefly explains the contribution of the individual publication related to Cuckoo Search Algorithm. It is believed that this paper will greatly benefit the reader who needs a bird-eyes view of the Cuckoo Search Algorithm’s publications trend

Evolutionary structural optimisation as a robust and reliable design tool

Evolutionary Structural Optimisation (ESO) is a relatively new design tool used to improve and optimise the design of structures. It is a heuristic method where a few elements of an initial design domain of finite elements are iteratively removed. Such a process is carried out repeatedly until an optimum design is achieved, or until a desired given area or volume is reached. There have been many contributions to the ESO procedure since its conception back in 1992. For example, a provision known as Bi-Directional ESO (BESO) has now been incorporated where elements may not only be removed, but added. Also, rather than deal with elements where they are either present or not, the designer now has the option to change the element's properties in a progressive fashion. This includes the modulus of elasticity, the density of the material and the thickness of plate elements, and is known as Morphing ESO. In addition to the algorithmic aspects of ESO, a large preference exists to optimise a structure based on a selection of criteria for various physical processes. Such examples include stress minimisation, buckling and electromagnetic problems. In a changing world that demands the enhancement of design tools and methods that incorporate optimisation, the development of methods like ESO to accommodate this demand is called for. It is this demand that this thesis seeks to satisfy. This thesis develops and examines the concept of multicriteria optimisation in the ESO process. Taking into account the optimisation of numerous criteria simultaneously, Multicriteria ESO allows a more realistic and accurate approach to optimising a model in any given environment. Two traditional methods � the Weighting method and the Global Criterion (Min-max) method have been used, as has two unconventional methods � the Logical AND method and the Logical OR method. These four methods have been examined for different combinations of Finite Element Analysis (FEA) solver types. This has included linear static FEA solver, the natural frequency FEA solver and a recently developed inertia FE solver. Mean compliance minimisation (stiffness maximisation), frequency maximisation and moment of inertia maximisation are an assortment of the specific objectives incorporated. Such a study has provided a platform to use many other criteria and multiple combinations of criteria. In extending the features of ESO, and hence its practical capabilities as a design tool, the creation of another optimisation method based on ESO has been ushered in. This method concerns the betterment of the bending and rotational performance of cross-sectional areas and is known as Evolutionary Moment of Inertia Optimisation (EMIO). Again founded upon a domain of finite elements, the EMIO method seeks to either minimise or maximise the rectangular, product and polar moments of inertia. This dissertation then goes one step further to include the EMIO method as one of the objectives considered in Multicriteria ESO as mentioned above. Most structures, (if not all) in reality are not homogenous as assumed by many structural optimisation methods. In fact, many structures (particularly biological ones) are composed of different materials or the same material with continually varying properties. In this thesis, a new feature called Constant Width Layer (CWL) ESO is developed, in which a distinct layer of material evolves with the developing boundary. During the optimisation process, the width of the outer surrounding material remains constant and is defined by the user. Finally, in verifying its usefulness to the practical aspect of design, the work presented herein applies the CWL ESO and the ESO methods to two dental case studies. They concern the optimisation of an anterior (front of the mouth) ceramic dental bridge and the optimisation of a posterior (back of the mouth) ceramic dental bridge. Comparisons of these optimised models are then made to those developed by other methods

PID control system analysis, design, and technology

Designing and tuning a proportional-integral-derivative (PID) controller appears to be conceptually intuitive, but can be hard in practice, if multiple (and often conflicting) objectives such as short transient and high stability are to be achieved. Usually, initial designs obtained by all means need to be adjusted repeatedly through computer simulations until the closed-loop system performs or compromises as desired. This stimulates the development of "intelligent" tools that can assist engineers to achieve the best overall PID control for the entire operating envelope. This development has further led to the incorporation of some advanced tuning algorithms into PID hardware modules. Corresponding to these developments, this paper presents a modern overview of functionalities and tuning methods in patents, software packages and commercial hardware modules. It is seen that many PID variants have been developed in order to improve transient performance, but standardising and modularising PID control are desired, although challenging. The inclusion of system identification and "intelligent" techniques in software based PID systems helps automate the entire design and tuning process to a useful degree. This should also assist future development of "plug-and-play" PID controllers that are widely applicable and can be set up easily and operate optimally for enhanced productivity, improved quality and reduced maintenance requirements

Optimization of assembly line balancing with energy efficiency by using tiki-taka algorithm

Assembly line balancing (ALB) could be translated as the activity that is applied to optimize the layout of an assembly line by distributing a balance workload assembly among workstations. Based on the previous research conducted by researchers, most of the assembly line model studies focused extensively on the problem models that related to time, space, workers, and a few resources. However, there is a shortage of studies that considers the utilization of electrical energy in assembly line design. This situation stimulates this research to further investigate the Assembly Line Balancing with Energy Efficiency (ALB-EE). This research aimed to establish a computational model that represents the ALB-EE, propose a new Tiki-Taka Algorithm (TTA) to solve and optimize the ALB-EE and validate the developed model through a real-life case study. In the modeling phase, all the ALB-EE optimization objectives are presented in a mathematical form to earn line efficiency and energy utilization. Then, the TTA is developed before undergoing functionality tests by benchmarking with Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), Genetic Algorithm (GA), and Whale Optimization Algorithm (WOA). Lastly, a study of the industrial case was performed as a validation of the developed model and algorithm. An automotive company is selected, and the collected actual data is used for validation purposes. As a result, the Optimized TTA performs best compared to PSO, GWO, GA, and WOA in most of the test problems. Meanwhile, the case study validation activity resulting an increase in line efficiency from 92.7% to 95.1% by task arrangement with the utilization of TTA. Through the improved line efficiency, the total energy consumed is also reduced to 3,305,478.46 J from the initial figure of 3,374,329.46 J. This is a clear indication that the developed TTA algorithm is reliable and could be used in optimizing a real-life problem by the resequence of the assembly task, thus reducing the cycle time and could reduce the total energy consumption by machiner

Optimisation of Product Recovery Options in End-of-Life Product Disassembly by Robots

In a circular economy, strategies for product recovery, such as reuse, recycling, and remanufacturing, play an important role at the end of a product’s life. A sustainability model was developed to solve the problem of sequence-dependent robotic disassembly line balancing. This research aimed to assess the viability of the model, which was optimised using the Multi-Objective Bees Algorithm in a robotic disassembly setting. Two industrial gear pumps were used as case studies. Four objectives (maximising profit, energy savings, emissions reductions and minimising line imbalance) were set. Several product recovery scenarios were developed to find the best recovery plans for each component. An efficient metaheuristic, the Bees Algorithm, was used to find the best solution. The robotic disassembly plans were generated and assigned to robotic workstations simultaneously. Using the proposed sustainability model on end-of-life industrial gear pumps shows the applicability of the model to real-world problems. The Multi-Objective Bees Algorithm was able to find the best scenario for product recovery by assigning each component to recycling, reuse, remanufacturing, or disposal. The performance of the algorithm is consistent, producing a similar performance for all sustainable strategies. This study addresses issues that arise with product recovery options for end-of-life products and provides optimal solutions through case studies

Global and local surrogate-assisted differential evolution for expensive constrained optimization

The file attached to this record is the author's final peer reviewed version.For expensive constrained optimization problems, the computation of objective function and constraints is very time-consuming. This paper proposes a novel global and local surrogate-assisted differential evolution for solving expensive constrained optimization problems with inequality constraints. The proposed method consists of two main phases: global surrogate-assisted phase and local surrogate-assisted phase. In the global surrogate-assisted phase, differential evolution serves as the search engine to produce multiple trial vectors. Afterward, the generalized regression neural network is used to evaluate these trial vectors. In order to select the best candidate from these trial vectors, two rules are combined. The first is the feasibility rule, which at first guides the population toward the feasible region, and then toward the optimal solution. In addition, the second rule puts more emphasis on the solution with the highest predicted uncertainty, and thus alleviates the inaccuracy of the surrogates. In the local surrogate-assisted phase, the interior point method coupled with radial basis function is utilized to refine each individual in the population. During the evolution, the global surrogate-assisted phase has the capability to promptly locate the promising region and the local surrogate-assisted phase is able to speed up the convergence. Therefore, by combining these two important elements, the number of fitness evaluations can be reduced remarkably. The proposed method has been tested on numerous benchmark test functions from three test suites and two real-world cases. The experimental results demonstrate that the performance of the proposed method is better than that of other state-of-the-art methods

Optimized task scheduling based on hybrid symbiotic organisms search algorithms for cloud computing environment

In Cloud Computing model, users are charged according to the usage of resources and desired Quality of Service (QoS). Task scheduling algorithms are responsible for specifying adequate set of resources to execute user applications in the form of tasks, and schedule decisions of task scheduling algorithms are based on QoS requirements defined by the user. Task scheduling problem is an NP-Complete problem, due to the NP-Complete nature of task scheduling problems and huge search space presented by large scale problem instances, many of the existing solution algorithms incur high computational complexity and cannot effectively obtain global optimum solutions. Recently, Symbiotic Organisms Search (SOS) has been applied to various optimization problems and results obtained were found to be competitive with state-of-the-art metaheuristic algorithms. However, similar to the case other metaheuristic optimization algorithms, the efficiency of SOS algorithm deteriorates as the size of the search space increases. Moreover, SOS suffers from local optima entrapment and its static control parameters cannot maintain a balance between local and global search. In this study, Cooperative Coevolutionary Constrained Multiobjective Symbiotic Organisms Search (CC-CMSOS), Cooperative Coevolutionary Constrained Multi-objective Memetic Symbiotic Organisms Search (CC-CMMSOS), and Cooperative Coevolutionary Constrained Multi-objective Adaptive Benefit Factor Symbiotic Organisms Search (CC-CMABFSOS) algorithms are proposed to solve constrained multi-objective large scale task scheduling optimization problem on IaaS cloud computing environment. To address the issue of scalability, the concept of Cooperative Coevolutionary for enhancing SOS named CC-CMSOS make SOS more efficient for solving large scale task scheduling problems. CC-CMMSOS algorithm further improves the performance of SOS algorithm by hybridizing with Simulated Annealing (SA) to avoid entrapment in local optima for global convergence. Finally, CC-CMABFSOS algorithm adaptively turn SOS control parameters to balance the local and global search procedure for faster convergence speed. The performance of the proposed CC-CMSOS, CC-CMMSOS, and CC-CMABFSOS algorithms are evaluated on CloudSim simulator, using both standard workload traces and synthesized workloads for larger problem instances of up to 5000. Moreover, CC-CMSOS, CC-CMMSOS, and CC-CMABFSOS algorithms are compared with multi-objective optimization algorithms, namely, EMS-C, ECMSMOO, and BOGA. The CC-CMSOS, CC-CMMSOS, and CC-CMABFSOS algorithms obtained significant improved optimal trade-offs between execution time (makespan) and financial cost (cost) while meeting deadline constraints with no computational overhead. The performance improvements obtained by the proposed algorithms in terms of hypervolume ranges from 8.72% to 37.95% across the workloads. Therefore, the proposed algorithms have potentials to improve the performance of QoS delivery