Gideon Avigad

Interactive Evolutionary Multiobjective Search and Optimization of Set-Based Concepts

This paper deals with interactive concept-based multiobjective problems (IC-MOPs) and their solution by an evolutionary computation approach. The presented methodology is motivated by the need to support engineers during the conceptual design stage. IC-MOPs are based on a nontraditional concept-based approach to search and optimization. It involves conceptual solutions, which are represented by sets of particular solutions, with each concept having a one-to-many relation with the objective space. Such a set-based concept representation is most suitable for human-computer interaction. Here, a fundamental type of IC-MOPs, namely, the Pareto-directed one, is formally defined, and its solution is presented. Next, a new interactive concept-based multiobjective evolutionary algorithm is introduced, and measures to assess its resulting fronts are devised. Finally, the proposed approach and the suggested search algorithm are studied using both academic test functions and an engineering problem.

Set-based concept selection in multi-objective problems: optimality versus variability approach

This paper presents a novel approach to support the selection of conceptual solutions to multi-objective problems. The proposed method involves a comparison between concepts, based on the performances of sets of solutions that represent them. The set-based comparison of concepts is consistent with the so-called Toyota set-based concurrent engineering process. Such an approach discourages early exploitation of solutions and promotes extended exploration of the design space by means of sets of solutions. Both optimality and variability of concepts are considered, and their measures are devised to pose the selection problem as an auxiliary multi-objective problem. The auxiliary objectives are to maximise optimality and to maximise the variability. This highlights the inherent multi-objectivity of concept selection and supports decision-making under the possible contradictory nature of optimality and variability of concepts. Both academic and engineering problems are used to demonstrate the approach and to expose the inherent subjectivity of the measures, which are dependent on the selection of a window of interest by the decision-makers.

The Gradient Free Directed Search Method as Local Search within Multi-Objective Evolutionary Algorithms

Recently, the Directed Search Method has been proposed as a point-wise iterative search procedure that allows to steer the search, in any direction given in objective space, of a multi-objective optimization problem. While the original version requires the objectives’ gradients, we consider here a possible modification that allows to realize the method without gradient information. This makes the novel algorithm in particular interesting for hybridization with set oriented search procedures, such as multi-objective evolutionary algorithms.

PSA – A New Scalable Space Partition Based Selection Algorithm for MOEAs

It has generally been acknowledged that both proximity to the Pareto front and a certain diversity along the front should be targeted when using evolutionary algorithms to evolve solutions to multi-objective optimization problems. Although many evolutionary algorithms are equipped with mechanisms to achieve both targets, most give priority to proximity over diversity. This priority is embedded within the algorithms through the selection of solutions to the elite population based on the concept of dominance. Although the current study does not change this embedded preference, it does utilize an improved diversity preservation mechanism that is based on a recently introduced partitioning algorithm for function selection. It is shown that this partitioning allows for the selection of a well-diversified set out of an arbitrary given set. Further, when embedded into an evolutionary search, this procedure significantly enhances the exploitation of diversity. The procedure is demonstrated on commonly used test cases for up to five objectives. The potential for further improving evolutionary algorithms through the use of the partitioning algorithm is highlighted.

Set-based concept selection in multi-objective problems involving delayed decisions

This paper introduces a computational approach to support concept selection in multi-objective design. It is motivated by: (1) a common need to delay some decisions during conceptual design due to the presence of uncertainties; and (2) intentional delay of decisions for the purpose of maintaining several optional concepts, as suggested by the concurrent engineering procedure of Toyota. Here, for the first time, a multi-objective set-based concept (SBC) selection problem with delayed decisions is formulated and solved. SBCs are conceptual solutions, which are represented by sets of particular solutions, with each concept having a one-to-many relation with the objective space. Several novel notions, such as higher-level concepts, multi-model concepts and robust concepts to delayed decisions, are defined and used. These lead to an auxiliary multi-objective decision problem. The auxiliary objectives are concept optimality and variability, both paramount to concept selection, with concept variability strongly supporting the idea of intentionally keeping several useful alternatives as long as possible. Academic and engineering examples are provided to demonstrate the proposed approach and its applicability to real-life problems. The results demonstrate that the suggested technique may well support the process of delayed decision either when needed or when deliberately done.

Handling changes of performance requirements in multi-objective problems

In this paper, the need for rapid, low-cost changes in a design, in response to changes in performance requirements (PRs), within multi-objective problems, is considered. In the current study, the rapid response is attained through a priori design of a set of satisfying solutions, such that any PR may be satisfied by at least one member of the set. The purpose is to design such a set so that once the PRs change, the changes needed in order to adapt to the existing product (one member of the set) to the new requirements are minimal, while maintaining the aspiration for optimal performances. It is assumed here that minimal changes are related to small changes in the design parameters. In order to find the optimal set, sets of candidate solutions are evolved using an evolutionary multi-objective optimisation algorithm. The algorithm enhances a search pressure towards sets with minimal distances between their members (in design space) and with optimal performances, which are assessed by utilising the hyper-volume measure. An artificial and a real life example are utilised in order to explain the approach and to show its applicability to engineering problems.

Pareto layer: Its formulation and search by way of evolutionary multi-objective optimization

This article examines multi-objective problems where a solution (product) is related to a cluster of performance vectors within a multi-objective space. Here the origin of such a cluster is not uncertainty, as is typical, but rather the range of performances attainable by the product. It is shown that, in such cases, comparison of a solution to other solutions should be based on its best performance vectors, which are extracted from the cluster. The result of solving the introduced problem is a set of Pareto optimal solutions and their representation in the objective space, which is referred to here as the Pareto layer. The authors claim that the introduced Pareto layer is a previously unattended novel representation. In order to search for these optimal solutions, an evolutionary multi-objective algorithm is suggested. The article also treats the selection of a solution from the obtained optimal set.

Optimal strategies for multi objective games and their search by evolutionary multi objective optimization

While both games and Multi-Objective Optimization (MOO) have been studied extensively in the literature, Multi-Objective Games (MOGs) have received less research attention. Existing studies deal mainly with mathematical formulations of the optimum. However, a definition and search for the representation of the optimal set, in the multi objective space, has not been attended. More specifically, a Pareto front for MOGs has not been defined or searched for in a concise way. In this paper we define such a front and propose a set-based multi-objective evolutionary algorithm to search for it. The resulting front, which is shown to be a layer rather than a clear-cut front, may support players in making strategic decisions during MOGs. Two examples are used to demonstrate the applicability of the algorithm. The results show that artificial intelligence may help solve complicated MOGs, thus highlighting a new and exciting research direction.

Simultaneous concept-based evolutionary multi-objective optimization

In contrast to traditional multi-objective problems the concept-based version of such problems involves sets of particular solutions, which represent predefined conceptual solutions. This paper addresses the concept-based multi-objective problem by proposing two novel multi objective evolutionary algorithms. It also compares two major search approaches.The suggested algorithms deal with resource sharing among concepts, and within each concept, while simultaneously evolving concepts towards a Pareto front by way of their representing sets. The introduced algorithms, which use a simultaneous search approach, are compared with a sequential one. For this purpose concept-based performance indicators are suggested and used. The comparison study includes both the computational time and the quality of the concept-based front representation. Finally, the effect on the computational time of both the concept fitness evaluation time and concept optimality, for both the sequential and simultaneous approaches, is highlighted.

Co-evolution of strategies for multi-objective games under postponed objective preferences

The vast majority of studies that are related to game theory are on Single Objective Games (SOG), also known as single payoff games. Multi-Objective Games (MOGs), which are also termed as multi payoff, multi criteria or vector payoff games, have received lesser attention. Yet, in many practical problems, generally each player cope with multiple objectives that might be contradicting. In such problems, a vector of objective functions must be considered. The common approach to deal with MOGs is to assume that the preferences of the players are known. In such a case a utility function is used, which transforms the MOG into a surrogate SOG., This paper deals with non-cooperative MOGs in a non-traditional way. The zero-sum MOG, which is considered here, involves two players that postponed their objective preferences, allowing them to decide on their preferences after tradeoffs are revealed. To solve such problems we propose a co-evolutionary algorithm based on a worst-case domination relation among sets. The suggested algorithm is tested on a simple differential game (tug-of-war). The obtained results serve to illustrate the approach and demonstrate the applicability of the proposed co-evolutionary algorithm.