Solving Dynamic Constraint Single Objective Functions using a Nature Inspired Technique

We present in this paper a new algorithm based on Particle Swarm Optimization (PSO) for solving Dynamic Single Objective Constrained Optimization (DCOP) problems. We have modified several different parameters of the original particle swarm optimization algorithm by introducing new types of particles for local search and to detect changes in the search space. The algorithm is tested with a known benchmark set and compare with the results with other contemporary works. We demonstrate the convergence properties by using convergence graphs and also the illustrate the changes in the current benchmark problems for more realistic correspondence to practical real world problems.

Economic, environmental and mixed objective functions in non-linear process optimization using simulated annealing and tabu search

Screening of topologies developed by hierarchical heuristic procedures can be carried out by comparing their optimal performance. In this work we will be exploiting mono-objective process optimization using two algorithms, simulated annealing and tabu search, and four different objective functions: two of the net present value type, one of them including environmental costs and two of the global potential impact type. The hydrodealkylation of toluene to produce benzene was used as case study, considering five topologies with different complexities mainly obtained by including or not liquid recycling and heat integration. The performance of the algorithms together with the objective functions was observed, analyzed and discussed from various perspectives: average deviation of results for each algorithm, capacity for producing high purity product, screening of topologies, objective functions robustness in screening of topologies, trade-offs between economic and environmental type objective functions and variability of optimum solutions.

Particle Swarm algorithm with Fuzzy decision making for a multi-objective economic and environmental optimization of design of a thermal system

Multi-Objective optimization for designing of a benchmark cogeneration system known as CGAM cogeneration system has been performed. In optimization approach, the thermoeconomic and Environmental aspects have been considered, simultaneously. The environmental objective function has been defined and expressed in cost terms. One of the most suitable optimization techniques developed using a particular class of search algorithms known as; Multi-Objective Particle Swarm Optimization (MOPSO) algorithm has been used here. This approach has been applied to find the set of Pareto optimal solutions with respect to the aforementioned objective functions. An example of fuzzy decision-making with the aid of Bellman-Zadeh approach has been presented and a final optimal solution has been introduced.

A new multi-objective model to optimise rail transport scheduler

The sugarcane transport system plays a critical role in the overall performance of Australia’s sugarcane industry. An inefficient sugarcane transport system interrupts the raw sugarcane harvesting process, delays the delivery of sugarcane to the mill, deteriorates the sugar quality, increases the usage of empty bins, and leads to the additional sugarcane production costs. Due to these negative effects, there is an urgent need for an efficient sugarcane transport schedule that should be developed by the rail schedulers. In this study, a multi-objective model using mixed integer programming (MIP) is developed to produce an industry-oriented scheduling optimiser for sugarcane rail transport system. The exact MIP solver (IBM ILOG-CPLEX) is applied to minimise the makespan and the total operating time as multi-objective functions. Moreover, the so-called Siding neighbourhood search (SNS) algorithm is developed and integrated with Sidings Satisfaction Priorities (SSP) and Rail Conflict Elimination (RCE) algorithms to solve the problem in a more efficient way. In implementation, the sugarcane transport system of Kalamia Sugar Mill that is a coastal locality about 1050 km northwest of Brisbane city is investigated as a real case study. Computational experiments indicate that high-quality solutions are obtainable in industry-scale applications.

On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

An investigation of higher-order multi-objective optimisation for 3D aerodynamic shape design

We investigate the performance of different variants of a suitably tailored Tabu Search optimisation algorithm on a higher-order design problem. We consider four objective func- tions to describe the performance of a compressor stator row, subject to a number of equality and inequality constraints. The same design problem has been previously in- vestigated through single-, bi- and three-objective optimisation studies. However, in this study we explore the capabilities of enhanced variants of our Multi-objective Tabu Search (MOTS) optimisation algorithm in the context of detailed 3D aerodynamic shape design. It is shown that with these enhancements to the local search of the MOTS algorithm we can achieve a rapid exploration of complicated design spaces, but there is a trade-off be- tween speed and the quality of the trade-off surface found. Rapidly explored design spaces reveal the extremes of the objective functions, but the compromise optimum areas are not very well explored. However, there are ways to adapt the behaviour of the optimiser and maintain both a very efficient rate of progress towards the global optimum Pareto front and a healthy number of design configurations lying on the trade-off surface and exploring the compromise optimum regions. These compromise solutions almost always represent the best qualitative balance between the objectives under consideration. Such enhancements to the effectiveness of design space exploration make engineering design optimisation with multiple objectives and robustness criteria ever more practicable and attractive for modern advanced engineering design. Finally, new research questions are addressed that highlight the trade-offs between intelligence in optimisation algorithms and acquisition of qualita- tive information through computational engineering design processes that reveal patterns and relations between design parameters and objective functions, but also speed versus optimum quality. © 2012 AIAA.

Multi-objective shape optimisation for horizontal-axis wind turbine blades

We are developing a wind turbine blade optimisation package CoBOLDT (COmputa- tional Blade Optimisation and Load De ation Tool) for the optimisation of large horizontal- axis wind turbines. The core consists of the Multi-Objective Tabu Search (MOTS), which controls a spline parameterisation module, a fast geometry generation and a stationary Blade Element Momentum (BEM) code to optimise an initial wind turbine blade design. The objective functions we investigate are the Annual Energy Production (AEP) and the fl apwise blade root bending moment (MY0) for a stationary wind speed of 50 m/s. For this task we use nine parameters which define the blade chord, the blade twist (4 parameters each) and the blade radius. Throughout the optimisation a number of binary constraints are defined to limit the noise emission, to allow for transportation on land and to control the aerodynamic conditions during all phases of turbine operation. The test case shows that MOTS is capable to find enhanced designs very fast and eficiently and will provide a rich and well explored Pareto front for the designer to chose from. The optimised blade de- sign could improve the AEP of the initial blade by 5% with the same flapwise root bending moment or reduce MY0 by 7.5% with the original energy yield. Due to the fast runtime of order 10 seconds per design, a huge number of optimisation iterations is possible without the need for a large computing cluster. This also allows for increased design flexibility through the introduction of more parameters per blade function or parameterisation of the airfoils in future. © 2012 by Nordex Energy GmbH.

Multi-objective shape optimisation for horizontal-axis wind turbine blades

We are developing a wind turbine blade optimisation package CoBOLDT (COmputa- tional Blade Optimisation and Load Deation Tool) for the optimisation of large horizontal- axis wind turbines. The core consists of the Multi-Objective Tabu Search (MOTS), which controls a spline parameterisation module, a fast geometry generation and a stationary Blade Element Momentum (BEM) code to optimise an initial wind turbine blade design. The objective functions we investigate are the Annual Energy Production (AEP) and the apwise blade root bending moment (MY0) for a stationary wind speed of 50 m/s. For this task we use nine parameters which define the blade chord, the blade twist (4 parameters each) and the blade radius. Throughout the optimisation a number of binary constraints are defined to limit the noise emission, to allow for transportation on land and to control the aerodynamic conditions during all phases of turbine operation. The test case shows that MOTS is capable to find enhanced designs very fast and efficiently and will provide a rich and well explored Pareto front for the designer to chose from. The optimised blade de- sign could improve the AEP of the initial blade by 5% with the same apwise root bending moment or reduce MY0 by 7.5% with the original energy yield. Due to the fast runtime of order 10 seconds per design, a huge number of optimisation iterations is possible without the need for a large computing cluster. This also allows for increased design flexibility through the introduction of more parameters per blade function or parameterisation of the airfoils in future. © 2012 AIAA.

Design of silicone rubber according to requirements based on the multi-objective optimization of chemical reactions

The explicit expression between composition and mechanical properties of silicone rubber was derived from the physics of polymer elasticity, the implicit expression among material composition, reaction conditions and reaction efficiency was obtained from chemical thermodynamics and kinetics, and then an implicit multi-objective optimization model was constructed. Genetic algorithm was applied to optimize material composition and reaction conditions, and the finite element method of cross-linking reaction processes was used to solve multi-objective functions, on the basis of which a new optimization methodology of crosslinking reaction processes was established. Using this methodology, rubber materials can be designed according to pre-specified requirements.

Constrained Multi-Objective Aerofoil Design Using a Multi-Level Optimisation Strategy

A novel approach for the multi-objective design optimisation of aerofoil profiles is presented. The proposed method aims to exploit the relative strengths of global and local optimisation algorithms, whilst using surrogate models to limit the number of computationally expensive CFD simulations required. The local search stage utilises a re-parameterisation scheme that increases the flexibility of the geometry description by iteratively increasing the number of design variables, enabling superior designs to be generated with minimal user intervention. Capability of the algorithm is demonstrated via the conceptual design of aerofoil sections for use on a lightweight laminar flow business jet. The design case is formulated to account for take-off performance while reducing sensitivity to leading edge contamination. The algorithm successfully manipulates boundary layer transition location to provide a potential set of aerofoils that represent the trade-offs between drag at cruise and climb conditions in the presence of a challenging constraint set. Variations in the underlying flow physics between Pareto-optimal aerofoils are examined to aid understanding of the mechanisms that drive the trade-offs in objective functions.

Multi-objective clustering ensemble for gene expression data analysis

In this paper, we present an algorithm for cluster analysis that integrates aspects from cluster ensemble and multi-objective clustering. The algorithm is based on a Pareto-based multi-objective genetic algorithm, with a special crossover operator, which uses clustering validation measures as objective functions. The algorithm proposed can deal with data sets presenting different types of clusters, without the need of expertise in cluster analysis. its result is a concise set of partitions representing alternative trade-offs among the objective functions. We compare the results obtained with our algorithm, in the context of gene expression data sets, to those achieved with multi-objective Clustering with automatic K-determination (MOCK). the algorithm most closely related to ours. (C) 2009 Elsevier B.V. All rights reserved.

A multi-objective adaptive immune algorithm for multi-application NoC mapping

Current SoC design trends are characterized by the integration of larger amount of IPs targeting a wide range of application fields. Such multi-application systems are constrained by a set of requirements. In such scenario network-on-chips (NoC) are becoming more important as the on-chip communication structure. Designing an optimal NoC for satisfying the requirements of each individual application requires the specification of a large set of configuration parameters leading to a wide solution space. It has been shown that IP mapping is one of the most critical parameters in NoC design, strongly influencing the SoC performance. IP mapping has been solved for single application systems using single and multi-objective optimization algorithms. In this paper we propose the use of a multi-objective adaptive immune algorithm (M(2)AIA), an evolutionary approach to solve the multi-application NoC mapping problem. Latency and power consumption were adopted as the target multi-objective functions. To compare the efficiency of our approach, our results are compared with those of the genetic and branch and bound multi-objective mapping algorithms. We tested 11 well-known benchmarks, including random and real applications, and combines up to 8 applications at the same SoC. The experimental results showed that the M(2)AIA decreases in average the power consumption and the latency 27.3 and 42.1 % compared to the branch and bound approach and 29.3 and 36.1 % over the genetic approach.

A new method for decision making in multi-objective optimization problems

Many engineering sectors are challenged by multi-objective optimization problems. Even if the idea behind these problems is simple and well established, the implementation of any procedure to solve them is not a trivial task. The use of evolutionary algorithms to find candidate solutions is widespread. Usually they supply a discrete picture of the non-dominated solutions, a Pareto set. Although it is very interesting to know the non-dominated solutions, an additional criterion is needed to select one solution to be deployed. To better support the design process, this paper presents a new method of solving non-linear multi-objective optimization problems by adding a control function that will guide the optimization process over the Pareto set that does not need to be found explicitly. The proposed methodology differs from the classical methods that combine the objective functions in a single scale, and is based on a unique run of non-linear single-objective optimizers.

SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.