Using Optimality Theory and Reference Points to Improve the Diversity and Convergence of a Fuzzy-Adaptive Multi-Objective Particle Swarm Optimizer

Particle Swarm Optimization (PSO) has received increasing attention from the evolutionary optimization research community in the last twenty years. PSO is a metaheuristic approach based on collective intelligence obtained by emulating the swarming behavior of bees. A number of multi-objective variants of the original PSO algorithm that extend its applicability to optimization problems with conflicting objectives have also been developed; these multi-objective PSO (MOPSO) algorithms demonstrate comparable performance to other state-of-the-art metaheuristics. The existence of multiple optimal solutions (Pareto-optimal set) in optimization problems with conflicting objectives is not the only challenge posed to an optimizer, as the latter needs to be able to identify and preserve a well-distributed set of solutions during the search of the decision variable space. Recent attempts by evolutionary optimization researchers to incorporate mathematical convergence conditions into genetic algorithm optimizers have led to the derivation of a point-wise proximity measure, which is based on the solution of the achievement scalarizing function (ASF) optimization problem with a complementary slackness condition that quantifies the violation of the Karush-Kuhn-Tucker necessary conditions of optimality. In this work, the aforementioned KKT proximity measure is incorporated into the original Adaptive Coevolutionary Multi-Objective Swarm Optimizer (ACMOPSO) in order to monitor the convergence of the sub-swarms towards the Pareto-optimal front and provide feedback to Mamdani-type fuzzy logic controllers (FLCs) that are utilized for online adaptation of the algorithmic parameters. The proposed Fuzzy-Adaptive Multi-Objective Optimization Algorithm with the KKT proximity measure (FAMOPSOkkt) utilizes a set of reference points to cluster the computed nondominated solutions. These clusters interact with their corresponding sub-swarms to provide the swarm leaders and are also utilized to manage the external archive of nondominated solutions. The performance of the proposed algorithm is evaluated on benchmark problems chosen from the multi-objective optimization literature and compared to the performance of state-of-the-art multi-objective optimization algorithms with similar features

Multi-objective routing optimization using evolutionary algorithms

Wireless ad hoc networks suffer from several limitations, such as routing failures, potentially excessive bandwidth requirements, computational constraints and limited storage capability. Their routing strategy plays a significant role in determining the overall performance of the multi-hop network. However, in conventional network design only one of the desired routing-related objectives is optimized, while other objectives are typically assumed to be the constraints imposed on the problem. In this paper, we invoke the Non-dominated Sorting based Genetic Algorithm-II (NSGA-II) and the MultiObjective Differential Evolution (MODE) algorithm for finding optimal routes from a given source to a given destination in the face of conflicting design objectives, such as the dissipated energy and the end-to-end delay in a fully-connected arbitrary multi-hop network. Our simulation results show that both the NSGA-II and MODE algorithms are efficient in solving these routing problems and are capable of finding the Pareto-optimal solutions at lower complexity than the ’brute-force’ exhaustive search, when the number of nodes is higher than or equal to 10. Additionally, we demonstrate that at the same complexity, the MODE algorithm is capable of finding solutions closer to the Pareto front and typically, converges faster than the NSGA-II algorithm

Proximity measures based on KKT points for constrained multi-objective optimization

An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush-Kuhn-Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the violation of the KKT conditions. It can be computed easily and is continuous in every efficient solution. Hence, it can be used as an indicator for the proximity of a certain point to the set of efficient (Edgeworth-Pareto-minimal) solutions and is well suited for algorithmic use due to its continuity properties. This is especially useful within evolutionary algorithms for candidate selection and termination, which we also illustrate numerically for some test problems

A Hierachical Evolutionary Algorithm for Multiobjective Optimization in IMRT

Purpose: Current inverse planning methods for IMRT are limited because they are not designed to explore the trade-offs between the competing objectives between the tumor and normal tissues. Our goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans. Methods: We developed a hierarchical evolutionary multiobjective algorithm designed to quickly generate a diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the trade-offs in the plans. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. Results: Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for optimizations. The MOEA improvements were evaluated for example prostate cases with one target and two OARs. The modified MOEA dominated 11.3% of plans using a standard genetic algorithm package. By implementing domination advantage and protocol objectives, small diverse populations of clinically acceptable plans that were only dominated 0.2% by the Pareto front could be generated in a fraction of an hour. Conclusions: Our MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. It optimizes not only beamlet intensities but also objective function parameters on a patient-specific basis

Multi-objective evolutionary design of robust controllers on the grid

Coupling conventional controller design methods, model based controller synthesis and simulation, and multi-objective evolutionary optimisation methods frequently results in an extremely computationally expensive design process. However, the emerging paradigm of grid computing provides a powerful platform for the solution of such problems by providing transparent access to large-scale distributed high-performance compute resources. As well as substantially speeding up the time taken to find a single controller design satisfying a set of performance requirements this grid-enabled design process allows a designer to effectively explore the solution space of potential candidate solutions. An example of this is in the multi-objective evolutionary design of robust controllers, where each candidate controller design has to be synthesised and the resulting performance of the compensated system evaluated by computer simulation. This paper introduces a grid-enabled framework for the multi-objective optimisation of computationally expensive problems which will then be demonstrated using and example of the multi-objective evolutionary design of a robust lateral stability controller for a real-world aircraft using H ∞ loop shaping

Multi-objective optimisation of safety related systems: An application to Short Term Conflict Alert.

Copyright © 2006 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Notes: In this paper multi-objective optimisation is used for the first time to adjust the 1500 parameters of Short-Term Conflict Alert systems to optimise the Receiver Operating Characteristic (ROC) by simultaneously reducing the false positive rate and increasing the true positive alert rate, something that previous work by other researchers had not succeeded in doing. Importantly for such safety-critical systems, the method also yields an assessment of the confidence that may be placed in the optimised ROC curves. The paper results from a collaboration with NATS and a current KTP project, also with NATS, is deploying the methods in air-traffic control centres nationwide.Many safety related and critical systems warn of potentially dangerous events; for example, the short term conflict alert (STCA) system warns of airspace infractions between aircraft. Although installed with current technology, such critical systems may become out of date due to changes in the circumstances in which they function, operational procedures, and the regulatory environment. Current practice is to "tune," by hand, the many parameters governing the system in order to optimize the operating point in terms of the true positive and false positive rates, which are frequently associated with highly imbalanced costs. We cast the tuning of critical systems as a multiobjective optimization problem. We show how a region of the optimal receiver operating characteristic (ROC) curve may be obtained, permitting the system operators to select the operating point. We apply this methodology to the STCA system, using a multiobjective (1+1) evolution strategy, showing that we can improve upon the current hand-tuned operating point, as well as providing the salient ROC curve describing the true positive versus false positive tradeoff. We also provide results for three-objective optimization of the alert response time in addition to the true and false positive rates. Additionally, we illustrate the use of bootstrapping for representing evaluation uncertainty on estimated Pareto fronts, where the evaluation of a system is based upon a finite set of representative data