Erella Eisenstadt

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.

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.

Supporting the selection of robust engineering concepts under suppliers related uncertainties

In this paper, a computational tool to support designers in choosing an engineering concept is proposed. It takes into account aspects of supply chains (with a focus on suppliers’ related uncertainties) already at the conceptual design stage. It is suggested that a decision on an engineering concept would take into account its robustness to such uncertainties. The introduction and examination of such robustness considerations within the conceptual design stage are undertaken by finding a set of variants for each concept under consideration. The robustness of a concept is gained by allowing the selected concept-related solution to the problem to be later changed to another concept-related variant in response to changes associated with supply chains. In the paper, we propose a procedure that allows a search for such variants that may serve as solutions that promote robustness to suppliers’ related uncertainties. Utilising the suggested procedure may support designers in making decisions when considering these uncertainties. We argue that considering elements of supply chains already during the conceptual design space may affect the choice of a concept. An engineering problem is utilised in order to demonstrate the methodology and its applicability to real-life engineering problems.

Solution of Multi-objective Min-Max and Max-Min Games by Evolution

In this paper, a multi-objective optimal interception problem is proposed and solved using a Multi-Objective Evolutionary Algorithm. The traditional setting of an interception engagement between pursuer and evader is targeted either at minimizing a miss distance for a given interception duration or at minimizing an interception time for a given miss distance. Such a setting overlooks an important aspect — the purpose of launching the evader in the first place. Naturally, the evader seeks to evade the pursuer (by keeping away from it), but what about hitting its target? In contrast with the traditional setting, in this paper a multi-objective game is played between a pursuer and an evader. The pursuer aims at keeping a minimum final distance between itself and the evader, which it attempts to keep away from its target. The evader, on the other hand, aims at coming as close as possible to a predefined target while keeping as far away as possible from the pursuer. Both players (pursuer and evader) utilize neural net controllers that evolve during the proposed evolutionary optimization. The game is shown to involve very interesting issues related to the decision-making process while the dilemmas of both opponents are taken into consideration.

Evolving a Pareto Front for an Optimal Bi-objective Robust Interception Problem with Imperfect Information

In this paper, a multi-objective optimal interception problem with imperfect information is solved by using a Multi-Objective Evolutionary Algorithm (MOEA). The traditional setting of the interception problem is aimed either at minimizing a miss distance for a given interception duration or at minimizing an interception time for a given miss distance. In contrast with such a setting, here the problem is posed as a simultaneous search for both objectives. Moreover, it is assumed that the interceptor has imperfect information on the target. This problem can be considered as a game between the interceptor, who is aiming at a minimum final distance between himself and the target at a minimal final time, and an artificial opponent aiming at maximizing these values. The artificial opponent represents the effect of the interceptor’s imperfect information (measurement inaccuracies) on the success of the interception. Both players utilize neural net controllers that evolve during the evolutionary optimization. This study is the first attempt to utilize evolutionary multi-objective optimization for solving multi-objective differential games, and as far as our review went, the first attempt to solve multi-objective differential games in general.

Evolution of Contours for Topology Optimization

Topology optimization is used to find a preliminary structural configuration that meets a predefined criterion. It involves optimizing both the external boundary and the distribution of the internal material within a structure. Usually, counters are used a posteriori to the topology optimization to further adapt the shape of the topology according to manufacturing needs. Here we suggest optimizing topologies by evolving counters. We consider both outer and inner counters to allow for holes in the structure. Due to the difficulty of defining a reliable measure for the differences among shapes, little research attention has been focused on simultaneously finding diverse sets of optimal topologies. Here, niching is implemented within a suggested evolutionary algorithm in order to find diverse topologies. The niching is then embedded within the algorithm through the use of our recently introduced partitioning algorithm. For this algorithm to be used, the topologies are represented as functions. Two examples are given to demonstrate the approach. These examples show that the algorithm evolves a set of diverse optimal topologies.

Transient responses’ optimization by means of set-based multi-objective evolution

In this article, a novel solution to multi-objective problems involving the optimization of transient responses is suggested. It is claimed that the common approach of treating such problems by introducing auxiliary objectives overlooks tradeoffs that should be presented to the decision makers. This means that, if at some time during the responses, one of the responses is optimal, it should not be overlooked. An evolutionary multi-objective algorithm is suggested in order to search for these optimal solutions. For this purpose, state-wise domination is utilized with a new crowding measure for ordered sets being suggested. The approach is tested on both artificial as well as on real life problems in order to explain the methodology and demonstrate its applicability and importance. The results indicate that, from an engineering point of view, the approach possesses several advantages over existing approaches. Moreover, the applications highlight the importance of set-based evolution.

Trajectory planning for multiple unmanned vehicles under reciprocal constraints

In this article, a special class of trajectory optimization problems is formalized and solved. It involves the optimization of different unmanned vehicle (UMV) trajectories that are coupled through reciprocal constraints. It is shown in the article that searching for a solution to the problem at hand may stipulate not just planning a longer than the shortest possible path for each UMV, but also choosing slower travel speeds in order to co-ordinate between the UMVs. Although it seems that solving the problem possesses merits, it has been only partially treated before. Here it is solved by utilizing an evolutionary approach which involves a new algorithmic feature that allows striving towards the desired optimality. The approach is demonstrated and studied through solving and simulating several trajectory planning problems. It is shown that a wide range of problems might be related to that class of problems.