A novel preference articulation operator for the Evolutionary Multi-Objective Optimisation of classifiers in concealed weapons detection

Abstract The incorporation of decision maker preferences is often neglected in the Evolutionary Multi-Objective Optimisation (EMO) literature. The majority of the research in the field and the development of EMO algorithms is primarily focussed on converging to a Pareto optimal approximation close to or along the true Pareto front of synthetic test problems. However, when EMO is applied to real-world optimisation problems there is often a decision maker who is only interested in a portion of the Pareto front (the Region of Interest) which is defined by their expressed preferences for the problem objectives. In this paper a novel preference articulation operator for EMO algorithms is introduced (named the Weighted Z-score Preference Articulation Operator) with the flexibility of being incorporated a priori, a posteriori or progressively, and as either a primary or auxiliary fitness operator. The Weighted Z-score Preference Articulation Operator is incorporated into an implementation of the Multi-Objective Evolutionary Algorithm Based on Decomposition (named WZ-MOEA/D) and benchmarked against MOEA/D-DRA on a number of bi-objective and five-objective test problems with test cases containing preference information. After promising results are obtained when comparing WZ-MOEA/D to MOEA/D-DRA in the presence of decision maker preferences, WZ-MOEA/D is successfully applied to a real-world optimisation problem to optimise a classifier for concealed weapon detection, producing better results than previously published classifier implementations

The Rolling Tide Evolutionary Algorithm: A Multi-Objective Optimiser for Noisy Optimisation Problems

As the methods for evolutionary multiobjective optimization (EMO) mature and are applied to a greater number of real-world problems, there has been gathering interest in the effect of uncertainty and noise on multiobjective optimization, specifically how algorithms are affected by it, how to mitigate its effects, and whether some optimizers are better suited to dealing with it than others. Here we address the problem of uncertain evaluation, in which the uncertainty can be modeled as an additive noise in objective space. We develop a novel algorithm, the rolling tide evolutionary algorithm (RTEA), which progressively improves the accuracy of its estimated Pareto set, while simultaneously driving the front toward the true Pareto front. It can cope with noise whose characteristics change as a function of location (both design and objective), or which alter during the course of an optimization. Four state-of-the-art noise-tolerant EMO algorithms, as well as four widely used standard EMO algorithms, are compared to RTEA on 70 instances of ten continuous space test problems from the CEC'09 multiobjective optimization test suite. Different instances of these problems are generated by modifying them to exhibit different types and intensities of noise. RTEA seems to provide competitive performance across both the range of test problems used and noise types

Preference focussed many-objective evolutionary computation

Solving complex real-world problems often involves the simultaneous optimisation of multiple con icting performance criteria, these real-world problems occur in the elds of engineering, economics, chemistry, manufacturing, physics and many more. The optimisation process usually involves some design challenges in the form of the optimisation of a number of objectives and constraints. There exist many traditional optimisation methods (calculus based, random search, enumerative, etc...), however, these only o er a single solution in either adequate performance in a narrow problem domain or inadequate performance across a broad problem domain. Evolutionary Multi-objective Optimisation (EMO) algorithms are robust optimisers which are suitable for solving complex real-world multi-objective optimisation problems, as they are able to address each of the con icting objectives simultaneously. Typically, these EMO algorithms are run non-interactively with a Decision Maker (DM) setting the initial parameters of the algorithm and then analysing the results at the end of the optimisation process. When EMO is applied to real-world optimisation problems there is often a DM who is only interested in a portion of the Pareto-optimal front, however, incorporation of DM preferences is often neglected in the EMO literature. In this thesis, the incorporation of DM preferences into EMO search methods has been explored. This has been achieved through the review of EMO literature to identify a powerful method of variation, Covariance Matrix Adaptation (CMA), and its computationally infeasible EMO implementation, MO-CMA-ES. A CMA driven EMO algorithm, CMA-PAES, capable of optimisation in the presence of many objectives has been developed, benchmarked, and statistically veri ed to outperform MO-CMA-ES and MOEA/D-DRA on selected test suites. CMA-PAES and MOEA/D-DRA with the incorporation of the novel Weighted Z-score (WZ) preference articulation operator (supporting a priori, a posteriori or progressive incorporation) are then benchmarked on a range of synthetic and real-world problems. WZ-CMA-PAES is then successfully applied to a real-world problem regarding the optimisation of a classi er for concealed weapon detection, outperforming previously published classi er implementations

A Tutorial on Evolutionary Multi-Objective Optimization (EMO)

Many real-world search and optimization problems are naturally posed as non-linear programming problems having multiple objectives. Due to lack of suitable solution techniques, such problems are artificially converted into a single-objective problem and solved. The difficulty arises because such problems give rise to a set of Pareto-optimal solutions, instead of a single optimum solution. It then becomes important to find not just one Pareto-optimal solution but as many of them as possible. Classical methods are not quite efficient in solving these problems because they require repetitive applications to find multiple Pareto-optimal solutions and in some occasions repetitive applications do not guarantee finding distinct Pareto-optimal solutions. The population approach of evolutionary algorithms (EAs) allows an efficient way to find multiple Pareto-optimal solutions simultaneously in a single simulation run. In this tutorial, we discussed the following aspects related to EMO: 1. The basic differences in principle of EMO with classical methods. 2. A gentle introduction to evolutionary algorithms with simple examples. A simple method of handling constraints was also discussed. 3. The concept of domination and methods of finding non-dominated solutions in a population of solutions were discussed. 4. A brief history of the development of EMO is highlighted. 5. A number of main EMO methods (NSGA-II, SPEA and PAES) were discussed. 6. The advantage of EMO methodologies was discussed by presenting a number of case studies. They clearly showed the advantage of finding a number of Pareto-optimal solutions simultaneously. 7. Three advantages of using an EMO methodology were stressed: (i) For a better decision making (in terms of choosing a compromised solution) in the presence of multiple solutions (ii) For finding important relationships among decision variables (useful in design optimization). Some case studies from engineering demonstrated the importance of such studies. (iii) For solving other optimization problems efficiently. For example, in solving genetic programming problems, the so-called `bloating problem of increased program size can be solved by using a second objective of minimizing the size of the programs. 8. A number of salient research topics were highlighted. Some of them are as follows: (i) Development of scalable test problems (ii) Development of computationally fast EMO methods (iii) Performance metrics for evaluating EMO methods (iv) Interactive EMO methodologies (v) Robust multi-objective optimization procedures (vi) Finding knee or other important solutions including partial Pareto-optimal set (vii) Multi-objective scheduling and other optimization problems. It was clear from the discussions that evolutionary search methods offers an alternate means of solving multi-objective optimization problems compared to classical approaches. This is why multi-objective optimization using EAs is getting a growing attention in the recent years. The motivated readers may explore current research issues and other important studies from various texts (Coello et al, 2003; Deb, 2001), conference proceedings (EMO-01 and EMO-03 Proceedings) and numerous research papers (http://www.lania.mx/~ccoello/EMOO/). References: ---------- C. A. C. Coello, D. A. VanVeldhuizen, and G. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems. Boston, MA: Kluwer Academic Publishers, 2002. K.Deb. Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley, 2001. C. Fonseca, P. Fleming, E. Zitzler, K. Deb, and L. Thiele, editors. Proceedings of the Second Evolutionary Multi-Criterion Optimization (EMO-03) Conference (Lecture Notes in Computer Science (LNCS) 2632). Heidelberg: Springer, 2003. E. Zitzler, K. Deb, L. Thiele, C. A. C. Coello, and D. Corne, editors. Proceedings of the First Evolutionary Multi-Criterion Optimization (EMO-01) Conference (Lecture Notes in Computer Science (LNCS) 1993). Heidelberg: Springer, 2001

On the evolutionary optimisation of many conflicting objectives

This inquiry explores the effectiveness of a class of modern evolutionary algorithms, represented by Non-dominated Sorting Genetic Algorithm (NSGA) components, for solving optimisation tasks with many conflicting objectives. Optimiser behaviour is assessed for a grid of mutation and recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal trade-off surface. Performance sweet-spots for both variation operators are observed to contract as the number of objectives is increased. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance for higher numbers of objectives, even when large population sizes are used. Explanations for this behaviour are offered via the concepts of dominance resistance and active diversity promotion

Towards efficient multiobjective optimization: multiobjective statistical criterions

The use of Surrogate Based Optimization (SBO) is widely spread in engineering design to reduce the number of computational expensive simulations. However, "real-world" problems often consist of multiple, conflicting objectives leading to a set of equivalent solutions (the Pareto front). The objectives are often aggregated into a single cost function to reduce the computational cost, though a better approach is to use multiobjective optimization methods to directly identify a set of Pareto-optimal solutions, which can be used by the designer to make more efficient design decisions (instead of making those decisions upfront). Most of the work in multiobjective optimization is focused on MultiObjective Evolutionary Algorithms (MOEAs). While MOEAs are well-suited to handle large, intractable design spaces, they typically require thousands of expensive simulations, which is prohibitively expensive for the problems under study. Therefore, the use of surrogate models in multiobjective optimization, denoted as MultiObjective Surrogate-Based Optimization (MOSBO), may prove to be even more worthwhile than SBO methods to expedite the optimization process. In this paper, the authors propose the Efficient Multiobjective Optimization (EMO) algorithm which uses Kriging models and multiobjective versions of the expected improvement and probability of improvement criterions to identify the Pareto front with a minimal number of expensive simulations. The EMO algorithm is applied on multiple standard benchmark problems and compared against the well-known NSGA-II and SPEA2 multiobjective optimization methods with promising results

Dynamic Multi-Objective Optimization With jMetal and Spark: a Case Study

Technologies for Big Data and Data Science are receiving increasing research interest nowadays. This paper introduces the prototyping architecture of a tool aimed to solve Big Data Optimization problems. Our tool combines the jMetal framework for multi-objective optimization with Apache Spark, a technology that is gaining momentum. In particular, we make use of the streaming facilities of Spark to feed an optimization problem with data from different sources. We demonstrate the use of our tool by solving a dynamic bi-objective instance of the Traveling Salesman Problem (TSP) based on near real-time traffic data from New York City, which is updated several times per minute. Our experiment shows that both jMetal and Spark can be integrated providing a software platform to deal with dynamic multi-optimization problems.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Fast calculation of multiobjective probability of improvement and expected improvement criteria for Pareto optimization

The use of surrogate based optimization (SBO) is widely spread in engineering design to reduce the number of computational expensive simulations. However, "real-world" problems often consist of multiple, conflicting objectives leading to a set of competitive solutions (the Pareto front). The objectives are often aggregated into a single cost function to reduce the computational cost, though a better approach is to use multiobjective optimization methods to directly identify a set of Pareto-optimal solutions, which can be used by the designer to make more efficient design decisions (instead of weighting and aggregating the costs upfront). Most of the work in multiobjective optimization is focused on multiobjective evolutionary algorithms (MOEAs). While MOEAs are well-suited to handle large, intractable design spaces, they typically require thousands of expensive simulations, which is prohibitively expensive for the problems under study. Therefore, the use of surrogate models in multiobjective optimization, denoted as multiobjective surrogate-based optimization, may prove to be even more worthwhile than SBO methods to expedite the optimization of computational expensive systems. In this paper, the authors propose the efficient multiobjective optimization (EMO) algorithm which uses Kriging models and multiobjective versions of the probability of improvement and expected improvement criteria to identify the Pareto front with a minimal number of expensive simulations. The EMO algorithm is applied on multiple standard benchmark problems and compared against the well-known NSGA-II, SPEA2 and SMS-EMOA multiobjective optimization methods

Ergonomic Chair Design by Fusing Qualitative and Quantitative Criteria using Interactive Genetic Algorithms

This paper emphasizes the necessity of formally bringing qualitative and quantitative criteria of ergonomic design together, and provides a novel complementary design framework with this aim. Within this framework, different design criteria are viewed as optimization objectives; and design solutions are iteratively improved through the cooperative efforts of computer and user. The framework is rooted in multi-objective optimization, genetic algorithms and interactive user evaluation. Three different algorithms based on the framework are developed, and tested with an ergonomic chair design problem. The parallel and multi-objective approaches show promising results in fitness convergence, design diversity and user satisfaction metrics

A convergence acceleration operator for multiobjective optimisation

A novel multiobjective optimisation accelerator is introduced that uses direct manipulation in objective space together with neural network mappings from objective space to decision space. This operator is a portable component that can be hybridized with any multiobjective optimisation algorithm. The purpose of this Convergence Acceleration Operator (CAO) is to enhance the search capability and the speed of convergence of the host algorithm. The operator acts directly in objective space to suggest improvements to solutions obtained by a multiobjective evolutionary algorithm (MOEA). These suggested improved objective vectors are then mapped into decision variable space and tested. The CAO is incorporated with two leading MOEAs, the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and the Strength Pareto Evolutionary Algorithm (SPEA2) and tested. Results show that the hybridized algorithms consistently improve the speed of convergence of the original algorithm whilst maintaining the desired distribution of solutions