CMA-PAES: Pareto archived evolution strategy using covariance matrix adaptation for multi-objective optimisation

The quality of Evolutionary Multi-Objective Optimisation (EMO) approximation sets can be measured by their proximity, diversity and pertinence. In this paper we introduce a modular and extensible Multi-Objective Evolutionary Algorithm (MOEA) capable of converging to the Pareto-optimal front in a minimal number of function evaluations and producing a diverse approximation set. This algorithm, called the Covariance Matrix Adaptation Pareto Archived Evolution Strategy (CMA-PAES), is a form of (μ + λ) Evolution Strategy which uses an online archive of previously found Pareto-optimal solutions (maintained by a bounded Pareto-archiving scheme) as well as a population of solutions which are subjected to variation using Covariance Matrix Adaptation. The performance of CMA-PAES is compared to NSGA-II (currently considered the benchmark MOEA in the literature) on the ZDT test suite of bi-objective optimisation problems and the significance of the results are analysed using randomisation testing. © 2012 IEEE

Hybrid behavioural-based multi-objective space trajectory optimization

In this chapter we present a hybridization of a stochastic based search approach for multi-objective optimization with a deterministic domain decomposition of the solution space. Prior to the presentation of the algorithm we introduce a general formulation of the optimization problem that is suitable to describe both single and multi-objective problems. The stochastic approach, based on behaviorism, combinedwith the decomposition of the solutions pace was tested on a set of standard multi-objective optimization problems and on a simple but representative case of space trajectory design

Multiobjective Simulation Optimization Using Enhanced Evolutionary Algorithm Approaches

In today\u27s competitive business environment, a firm\u27s ability to make the correct, critical decisions can be translated into a great competitive advantage. Most of these critical real-world decisions involve the optimization not only of multiple objectives simultaneously, but also conflicting objectives, where improving one objective may degrade the performance of one or more of the other objectives. Traditional approaches for solving multiobjective optimization problems typically try to scalarize the multiple objectives into a single objective. This transforms the original multiple optimization problem formulation into a single objective optimization problem with a single solution. However, the drawbacks to these traditional approaches have motivated researchers and practitioners to seek alternative techniques that yield a set of Pareto optimal solutions rather than only a single solution. The problem becomes much more complicated in stochastic environments when the objectives take on uncertain (or noisy ) values due to random influences within the system being optimized, which is the case in real-world environments. Moreover, in stochastic environments, a solution approach should be sufficiently robust and/or capable of handling the uncertainty of the objective values. This makes the development of effective solution techniques that generate Pareto optimal solutions within these problem environments even more challenging than in their deterministic counterparts. Furthermore, many real-world problems involve complicated, black-box objective functions making a large number of solution evaluations computationally- and/or financially-prohibitive. This is often the case when complex computer simulation models are used to repeatedly evaluate possible solutions in search of the best solution (or set of solutions). Therefore, multiobjective optimization approaches capable of rapidly finding a diverse set of Pareto optimal solutions would be greatly beneficial. This research proposes two new multiobjective evolutionary algorithms (MOEAs), called fast Pareto genetic algorithm (FPGA) and stochastic Pareto genetic algorithm (SPGA), for optimization problems with multiple deterministic objectives and stochastic objectives, respectively. New search operators are introduced and employed to enhance the algorithms\u27 performance in terms of converging fast to the true Pareto optimal frontier while maintaining a diverse set of nondominated solutions along the Pareto optimal front. New concepts of solution dominance are defined for better discrimination among competing solutions in stochastic environments. SPGA uses a solution ranking strategy based on these new concepts. Computational results for a suite of published test problems indicate that both FPGA and SPGA are promising approaches. The results show that both FPGA and SPGA outperform the improved nondominated sorting genetic algorithm (NSGA-II), widely-considered benchmark in the MOEA research community, in terms of fast convergence to the true Pareto optimal frontier and diversity among the solutions along the front. The results also show that FPGA and SPGA require far fewer solution evaluations than NSGA-II, which is crucial in computationally-expensive simulation modeling applications

The influence of mutation on population dynamics in multiobjective genetic programming

Using multiobjective genetic programming with a complexity objective to overcome tree bloat is usually very successful but can sometimes lead to undesirable collapse of the population to all single-node trees. In this paper we report a detailed examination of why and when collapse occurs. We have used different types of crossover and mutation operators (depth-fair and sub-tree), different evolutionary approaches (generational and steady-state), and different datasets (6-parity Boolean and a range of benchmark machine learning problems) to strengthen our conclusion. We conclude that mutation has a vital role in preventing population collapse by counterbalancing parsimony pressure and preserving population diversity. Also, mutation controls the size of the generated individuals which tends to dominate the time needed for fitness evaluation and therefore the whole evolutionary process. Further, the average size of the individuals in a GP population depends on the evolutionary approach employed. We also demonstrate that mutation has a wider role than merely culling single-node individuals from the population; even within a diversity-preserving algorithm such as SPEA2 mutation has a role in preserving diversity

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Multiobjective strategies for New Product Development in the pharmaceutical industry

New Product Development (NPD) constitutes a challenging problem in the pharmaceutical industry, due to the characteristics of the development pipeline. Formally, the NPD problem can be stated as follows: select a set of R&D projects from a pool of candidate projects in order to satisfy several criteria (economic profitability, time to market) while coping with the uncertain nature of the projects. More precisely, the recurrent key issues are to determine the projects to develop once target molecules have been identified, their order and the level of resources to assign. In this context, the proposed approach combines discrete event stochastic simulation (Monte Carlo approach) with multiobjective genetic algorithms (NSGAII type, Non-Sorted Genetic Algorithm II) to optimize the highly combinatorial portfolio management problem. In that context, Genetic Algorithms (GAs) are particularly attractive for treating this kind of problem, due to their ability to directly lead to the so-called Pareto front and to account for the combinatorial aspect. This work is illustrated with a study case involving nine interdependent new product candidates targeting three diseases. An analysis is performed for this test bench on the different pairs of criteria both for the bi- and tricriteria optimization: large portfolios cause resource queues and delays time to launch and are eliminated by the bi- and tricriteria optimization strategy. The optimization strategy is thus interesting to detect the sequence candidates. Time is an important criterion to consider simultaneously with NPV and risk criteria. The order in which drugs are released in the pipeline is of great importance as with scheduling problems

Approximate solutions in space mission design

In this paper, we address multi-objective space mission design problems. From a practical point of view, it is often the case that,during the preliminary phase of the design of a space mission, the solutions that are actually considered are not 'optimal' (in the Pareto sense)but belong to the basin of attraction of optimal ones (i.e. they are nearly optimal). This choice is motivated either by additional requirements that the decision maker has to take into account or, more often, by robustness considerations. For this, we suggest a novel MOEA which is a modification of the well-known NSGA-II algorithm equipped with a recently proposed archiving strategy which aims at storing the set of approximate solutions of a given MOP. Using this algorithm we will examine some space trajectory design problems and demonstrate the benefit of the novel approach

Multi-agent collaborative search : an agent-based memetic multi-objective optimization algorithm applied to space trajectory design

This article presents an algorithm for multi-objective optimization that blends together a number of heuristics. A population of agents combines heuristics that aim at exploring the search space both globally and in a neighbourhood of each agent. These heuristics are complemented with a combination of a local and global archive. The novel agent-based algorithm is tested at first on a set of standard problems and then on three specific problems in space trajectory design. Its performance is compared against a number of state-of-the-art multi-objective optimization algorithms that use the Pareto dominance as selection criterion: non-dominated sorting genetic algorithm (NSGA-II), Pareto archived evolution strategy (PAES), multiple objective particle swarm optimization (MOPSO), and multiple trajectory search (MTS). The results demonstrate that the agent-based search can identify parts of the Pareto set that the other algorithms were not able to capture. Furthermore, convergence is statistically better although the variance of the results is in some cases higher

Computing the set of Epsilon-efficient solutions in multiobjective space mission design

In this work, we consider multiobjective space mission design problems. We will start from the need, from a practical point of view, to consider in addition to the (Pareto) optimal solutions also nearly optimal ones. In fact, extending the set of solutions for a given mission to those nearly optimal significantly increases the number of options for the decision maker and gives a measure of the size of the launch windows corresponding to each optimal solution, i.e., a measure of its robustness. Whereas the possible loss of such approximate solutions compared to optimal—and possibly even ‘better’—ones is dispensable. For this, we will examine several typical problems in space trajectory design—a biimpulsive transfer from the Earth to the asteroid Apophis and two low-thrust multigravity assist transfers—and demonstrate the possible benefit of the novel approach. Further, we will present a multiobjective evolutionary algorithm which is designed for this purpose

Optimization. An attempt at describing the State of the Art

This paper is an attempt at describing the State of the Art of the vast field of continuous optimization. We will survey deterministic and stochastic methods as well as hybrid approaches in their application to single objective and multiobjective optimization. We study the parameters of optimization algorithms and possibilities for tuning them. Finally, we discuss several methods for using approximate models for computationally expensive problems