## A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques (1998)

Venue: | Knowledge and Information Systems |

Citations: | 240 - 21 self |

### BibTeX

@ARTICLE{Coello98acomprehensive,

author = {Carlos A. Coello Coello},

title = {A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques},

journal = {Knowledge and Information Systems},

year = {1998},

volume = {1},

pages = {269--308}

}

### Years of Citing Articles

### OpenURL

### Abstract

. This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described mentioning its advantages and disadvantages, their degree of applicability and some of their known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed. Keywords: multiobjective optimization, multicriteria optimization, vector optimization, genetic algorithms, evolutionary algorithms, artificial intelligence. 1 Introduction Since the pioneer work of Rosenberg in the late 60s regarding the possibility of using genetic-based search to deal with multiple objectives, this new area of research (now called evolutionary multiobjective optimization) has grown c...

### Citations

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Citation Context ...one interested in this area who has a previous (at least basic) knowledge of genetic algorithms in general. Those who may need additional information about genetic algorithms should refer to Goldberg =-=[27]-=-, Holland [35], Michalewicz [54], and Mitchell [56] for more information. 2 Statement of the Problem Multiobjective optimization (also called multicriteria optimization, multiperformance or vector opt... |

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Citation Context ...ompressor blade shapes. -- Rodr'iguez V'azquez et al. [78] extended MOGA to use it in genetic programming, introducing the so-called MOGP (Multiple Objective Genetic Programming). Genetic programming =-=[44]-=- replaces the traditional linear chromosomic representation by a hierarchical tree representation that, by definition, is more powerful, but also requires larger population sizes and specialized opera... |

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Citation Context ...has a previous (at least basic) knowledge of genetic algorithms in general. Those who may need additional information about genetic algorithms should refer to Goldberg [27], Holland [35], Michalewicz =-=[54]-=-, and Mitchell [56] for more information. 2 Statement of the Problem Multiobjective optimization (also called multicriteria optimization, multiperformance or vector optimization) can be defined as the... |

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Citation Context ...least basic) knowledge of genetic algorithms in general. Those who may need additional information about genetic algorithms should refer to Goldberg [27], Holland [35], Michalewicz [54], and Mitchell =-=[56]-=- for more information. 2 Statement of the Problem Multiobjective optimization (also called multicriteria optimization, multiperformance or vector optimization) can be defined as the problem of finding... |

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Citation Context ..., known as a Nash equilibrium solution, represents a stable equilibrium condition in the sense that no player can deviate unilaterally from this point for further improvement of his/her own criterion =-=[57]-=-. This point has the characteristic that f 1 (x 1 ; x 2 )sf 1 (x 1 ; x 2 ) (25) and f 2 (x 1 ; x 2 )sf 2 (x 1 ; x 2 ) (26) where x 1 may be to the left or right of x 1 in (25) and x 2 may lie above or... |

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Citation Context ... in this area who has a previous (at least basic) knowledge of genetic algorithms in general. Those who may need additional information about genetic algorithms should refer to Goldberg [27], Holland =-=[35]-=-, Michalewicz [54], and Mitchell [56] for more information. 2 Statement of the Problem Multiobjective optimization (also called multicriteria optimization, multiperformance or vector optimization) can... |

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Citation Context ...the population is suitably ranked. Goldberg also suggested the use of some kind of niching technique to keep the GA from converging to a single point on the front. A niching mechanism such as sharing =-=[29]-=- would allow the GA to maintain individuals all along the non-dominated frontier. Applications -- Hilliard et al. [34] used a Pareto optimality ranking method to handle the objectives of minimizing co... |

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Citation Context ...le to the shape or continuity of the Pareto front, whereas these two issues are a serious concern for mathematical programming techniques. 5.1 Multiple Objective Genetic Algorithm Fonseca and Fleming =-=[17]-=- have proposed a scheme in which the rank of a certain individual corresponds to the number of chromosomes in the current population by which it is dominated. Consider, for example, an individual x i ... |

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Citation Context ...cessfully their approach with the two multiobjective optimization problems provided in the paper by Srinivas and Deb 5 P'eriaux et al. did not succeed at that in the example presented in their paper. =-=[86]-=-, but no further applications of this technique seem to be available at the moment. Strengths and Weaknesses The use of genders is really another way of defining separate subpopulations for each objec... |

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Citation Context ...etic operators Generation (t+1) Start all over again Fig. 2. Schematic of VEGA selection. It is assumed that the population size is N and that there are M objective functions. 4.1 VEGA David Schaffer =-=[83]-=- extended Grefenstette's GENESIS program [31] to include multiple objective functions. Schaffer's approach was to use an extension of the Simple Genetic Algorithm (SGA) that he called the Vector Evalu... |

340 | Evolutionary algorithms for multiobjective optimization: Methods and Applications
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Citation Context ...s is that it is more inefficient (both computationally and in terms of quality of the Pareto fronts produced) than MOGA, and more sentitive to the value of the sharing factor oe share . Other authors =-=[106, 105] report th-=-at the NSGA performed quite well in terms of "coverage" of the Pareto front (i.e., it spreads in a more uniform way the population over the Pareto front) when applied to the 0/1 knapsack pro... |

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Citation Context ...will satisfy the m inequality constraints: g i (��x)s0 i = 1; 2; : : : ; m (1) 2 Right after the submission of this paper, David A. Van Veldhuizen and Gary B. Lamont made available a technical rep=-=ort [99] tha-=-t contains another remarkable survey of the area that complements the material contained in this paper. the p equality constraints h i (��x) = 0 i = 1; 2; : : : ; p (2) and optimizes the vector fu... |

301 | Nonlinear programming
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Citation Context ...generation of non-inferior solutions for multiobjective optimization. This is an obvious consequence of the fact that it was implied by Kuhn and Tucker in their seminal work on numerical optimization =-=[45]-=-. The main strength of this method is its efficiency (computationally speaking), and can be applied to generate a strongly non-dominated solution that can be used as an initial solution for other tech... |

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Citation Context ... of oe share becomes another parameter with which the user has to experiment until a reasonable setting is found. Even when important work has been done in this area (see for example Deb and Goldberg =-=[15]-=- and Fonseca & Fleming [17]), most of that research is focused on single-objective optimization, or multimodal optimization. -- Some researchers have also found alternative applications of multiobject... |

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Citation Context ... to total weight, asymptotical stability and eigenvalues constraints. -- Yang and Gen [104] used a weighted sum approach to solve a bicriteria linear transportation problem. More recently, Gen et al. =-=[25, 26]-=- extended this approach to allow more than two objectives, and added fuzzy logic to handle the uncertainty involved in the decision making process. A weighted sum is still used in this approach, but i... |

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Citation Context ... into an unconstrained multiobjective optimization problem, which is solved using Fonseca's MOGA [17]. This approach was used by Surry et al. to optimize gas supply networks [89]. Fonseca and Fleming =-=[19]-=- also proposed to handle constraints as objectives, and applied their approach to the design of a gas turbine [20]. Parmee and Purchase [67] implemented a version of VEGA [83] to handle constraints re... |

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Citation Context ...heuristic mutation that basically defined rules to exchange bit positions had to be used to avoid premature convergence of the population. Strenghts and Weaknesses It has been cited in the literature =-=[87, 14]-=- that the main weakness of MOGA is that it performs sharing on the objective value space, which implies that two different vectors with the same objective function values can not exist simultaneously ... |

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Citation Context ...s is that it is more inefficient (both computationally and in terms of quality of the Pareto fronts produced) than MOGA, and more sentitive to the value of the sharing factor oe share . Other authors =-=[106, 105] report th-=-at the NSGA performed quite well in terms of "coverage" of the Pareto front (i.e., it spreads in a more uniform way the population over the Pareto front) when applied to the 0/1 knapsack pro... |

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Citation Context ...ated individuals to maintain diversity in the population. Strengths and Weaknesses Although Schaffer reported some success, and the main strength of this approach is its simplicity, Richardson et al. =-=[76]-=- noted that the shuffling and merging of all the sub-populations corresponds to averaging the fitness components associated with each of the objectives. Since Schaffer used proportional fitness assign... |

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Citation Context ...nsformed into a single objective optimization problem by taking a linear combination of these 2 objectives. Applications -- Valenzuela-Rend'on and Uresti-Charre [96] obtained better results than NPGA =-=[36]-=- (see below) in 3 biobjective optimization problems, both in terms of the number of points in the Pareto front at the final iteration, and in terms of the total number of function evaluations. However... |

109 |
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Citation Context ... superior to a VEGA by Liepins et al. [48] when applied to a variety of set covering problems. -- Ritzel et al. [77] also used non-dominated ranking and selection combined with deterministic crowding =-=[53]-=- as the niching mechanism. They applied the GA to a groundwater pollution containment problem in which cost and reliability were the objectives. Though the actual Pareto front was unknown, Ritzel et a... |

105 | A Variant of Evolution Strategies for Vector Optimization
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Citation Context ...n another version of this algorithm (that apparently worked quite well), an objective was randomly selected at each run. Fourman used this approach to design compact symbolic layouts [24]. -- Kursawe =-=[47]-=- formulated a multiobjective version of evolution strategies [84] (ESs) based on lexicographic ordering. Selection consisted of as many steps as objective functions had the problem. At each step, one ... |

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Citation Context ... which satisfies the equations of Steps 1 and 2 may be called the best compromise solution considering all the criteria simultaneously and on equal terms of importance. Applications -- Hajela and Lin =-=[33]-=- included the weights of each objective in the chromosome, and promoted their diversity in the population through fitness sharing. Their goal was to be able to simultaneously generate a family of Pare... |

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Citation Context ...ome the difficulties involved in the aggregating approaches, much work has been devoted to the development of alternative techniques based on population policies or special handling of the objectives =-=[70]-=-. Some of the most popular approaches that fall into this category will be examined in this section. Individual 1 Individual 2 Individual N Individual 3 Sub-population 1 lation 2 Sub-popuSub -populati... |

87 | On the performance assessment and comparison of stochastic multiobjective optimizers
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Citation Context ...e used, unless there is some previous knowledge of the points which lie in the Pareto front (in which case there is obviously no need for a multiobjective optimization technique). Fonseca and Fleming =-=[23]-=- proposed the definition of certain (arbitrary) goals that we wish the GA to attain; then we can perform multiple runs and apply standard non-parametric statistical procedures to evaluate the quality ... |

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Compaction of symbolic layout using genetic algorithms
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Citation Context ...s0; j = 1; 2; : : : ; m (23) f l (��x) = f l ; l = 1; 2; : : : ; i \Gamma 1 (24) The solution obtained at the end, i.e., x k is taken as the desired solution x of the problem. Applications -- Four=-=man [24]-=- suggested a selection scheme based on lexicographic ordering. In a first version of his algorithm, objectives were assigned different priorities by the user and each pair of individuals were compared... |

61 |
Using genetic algorithms to solve a multiple objective groundwater pollution containment problem
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Citation Context ...it has the disadvantage of missing concave portions of the trade-off curve (in other words, the approach does not generate proper Pareto optimal solutions in the presence of non-convex search spaces) =-=[77]-=-, which is a serious drawback in most real-world applications. 3.2 Goal Programming Charnes and Cooper [5] and Ijiri [39] are credited with the development of the goal programming method for a linear ... |

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Simulation of genetic populations with biochemical properties. Doctoral dissertation
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Citation Context ...ions. The Pareto front is marked with a bold line. 3 Approaches That Use Aggregating Functions The notion of genetic search in a multicriteria problem dates back to the late 60s, in which Rosenberg's =-=[80]-=- study contained a suggestion that would have led to multicriteria optimization if he had carried it out as presented. His suggestion was to use multiple properties (nearness to some specified chemica... |

57 | On a Multi-Objective Evolutionary Algorithm and Its Convergence to the Pareto Set
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Citation Context ...opulation size, crossover and mutation rates, niche sizes, and elitism) and the way in which the selection technique adopted affects the performance of an algorithm. In this direction, Gunter Rudolph =-=[81]-=- has recently showed that theoretical results of convergence derived from single-objective evolutionary optimization cannot be used in the presence of multiple objectives. In his study, Rudolph propos... |

52 |
The Application of Genetic Algorithms to Resource Scheduling
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Citation Context ...is case, the vector function is normalized to the form �� f(��x) = [ �� f 1 (��x); �� f 2 (��x); : : : ; �� f k (��x)] T , where �� f i (��x) = f i (��x)=f =-=0 i . Applications -- Syswerda and Palmucci [90]-=- used weights in their fitness function to add or subtract values during the schedule evaluation of a resource scheduler, depending on the existence or absence of penalties (constraints violated). -- ... |

51 |
Goal Programming and Extensions
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Citation Context ...ormulation of the goal programming objective function is a weighted sum of the pth power of the deviation jf i (��x) \Gamma T i j [32]. Such a formulation has been called generalized goal programm=-=ing [37, 38]. This tec-=-hnique has also been called "target vector optimization" by other authors [12]. Applications -- Wienke et al. [102] used this approach in combination with a genetic algorithm to optimize sim... |

48 | A multi-objective approach to constrained optimization of gas supply networks: The COMOGAmethod
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Citation Context ...election ratio was defined as the ratio of the fraction of strings selected on the basis of the first objective (reliability) to the fraction selected via the second objective (cost). -- Surry et al. =-=[89]-=- proposed an interesting application of VEGA to model constraints in a single-objective optimization problem to avoid the need of a penalty function. Surry et al., however, modified the standard proce... |

46 |
Finding Acceptable Solutions in the Pareto-Optimal Range using Multiobjective Genetic Algorithms
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Citation Context ...eakness is its dependence on the value of oe share , but the idea of using a utility function that is dynamically modified, as in this case, has also been exploited more recently by other researchers =-=[96, 4, 30]-=-. 4.7 Use of the Contact Theorem to Detect Pareto Optimal Solutions Osyczka and Kundu [62] proposed the use of an algorithm based on the contact theorem (one of the main theorems in multiobjective opt... |

46 | Genesis: a system for using genetic search procedures - Grefenstette - 1984 |

43 |
Multi-objective optimization by genetic algorithms: a review. Evol. Comput
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- 1996
(Show Context)
Citation Context ...considerable volume of research in evolutionary multiobjective optimization in the last 15 years, there have been only two surveys of this area published in the technical literature 2 : Tamaki et al. =-=[91]-=-, which is a very short and quick review of some of the main approaches, and Fonseca and Fleming [18, 21] which is a remarkable account of the issues that make this problem interesting from the evolut... |

40 |
An Empirical Study of Evolutionary Techniques for Multiobjective Optimization in Engineering Design
- Coello, A
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(Show Context)
Citation Context ...the deviation jf i (��x) \Gamma T i j [32]. Such a formulation has been called generalized goal programming [37, 38]. This technique has also been called "target vector optimization" by =-=other authors [12]-=-. Applications -- Wienke et al. [102] used this approach in combination with a genetic algorithm to optimize simultaneously the intensities of six atomic emission lines of trace elements in alumina po... |

31 |
A New Method to Solve Generalized Multicriteria Optimization Problems Using the Simple Genetic Algorithm
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(Show Context)
Citation Context ...t is dynamically modified, as in this case, has also been exploited more recently by other researchers [96, 4, 30]. 4.7 Use of the Contact Theorem to Detect Pareto Optimal Solutions Osyczka and Kundu =-=[62]-=- proposed the use of an algorithm based on the contact theorem (one of the main theorems in multiobjective optimization [49]) to determine relative distances of a solution vector with respect to the P... |

30 |
The development of a directed genetic search technique for heavily constrained design spaces
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- 1994
(Show Context)
Citation Context .... to optimize gas supply networks [89]. Fonseca and Fleming [19] also proposed to handle constraints as objectives, and applied their approach to the design of a gas turbine [20]. Parmee and Purchase =-=[67]-=- implemented a version of VEGA [83] to handle constraints relating to a gas turbine design problem as objectives to allow the GA to locate a feasible region within the highly constrained search space ... |

30 |
A model of multiattribute decisionmaking and trade-off weight determination under uncertainty
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Citation Context ...proach (i.e., the use of weights) and ranking techniques in which the level of preference may be defined. Greenwood et al. [30] used an approach called specified multi-attribute value theory (ISMAUT) =-=[101]-=- which, combined with a GA, allows the definition of preferences by the GA itself, rather than asking the intervention of the decision maker. However, the decision maker still gets to decide what part... |

27 |
Multicriterion optimization in engineering with Fortran programs
- Osyczka
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(Show Context)
Citation Context ..., was taken from game theory, which deals with solving conflicting situations. The min-max approach to a linear model was proposed by Jutler [43] and Solich [85], and was further developed by Osyczka =-=[59, 60, 64]-=-, Rao [73] and Tseng and Lu [95]. The min-max optimum compares relative deviations from the separately attainable minima. Consider the ith objective function for which the relative deviation can be ca... |

26 | A Multi-Sexual Genetic Algorithm for Multiobjective Optimization
- Lis, Eiben
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(Show Context)
Citation Context ...ould modify the way in which mating was performed. The idea was to model the sexual attraction that some individuals have over others in nature, which determines a not so random mating. Lis and Eiben =-=[50]-=- also incorporated gender in their GA, but in a more general sense. In this case, the number of genders (or sexes), was not limited to two, but it could be as many as objectives we had. Another distin... |

25 |
Multicriteria Optimization for Engineering Design
- Osyczka
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(Show Context)
Citation Context ...for more information. 2 Statement of the Problem Multiobjective optimization (also called multicriteria optimization, multiperformance or vector optimization) can be defined as the problem of finding =-=[65]-=-: a vector of decision variables which satisfies constraints and optimizes a vector function whose elements represent the objective functions. These functions form a mathematical description of perfor... |

23 |
Cours d’Economie Politique, volume I
- Pareto
(Show Context)
Citation Context ...cular set x 1 ; x 2 ; : : : ; x k which yields the optimum values of all the objective functions. 2.1 Pareto Optimum The concept of Pareto optimum was formulated by Vilfredo Pareto in the XIX century =-=[66], and constitute-=-s by itself the origin of research in multiobjective optimization. We say that a point �� x 2 F is Pareto optimal if for every �� x 2 F either, i 2 I (f i (��x) = f i (��x )) (4) or, t... |

22 | A Non-Generational Genetic Algorithm for Multiobjective Optimisation
- Valenzuela-Rendón, Uresti-Charre
- 1997
(Show Context)
Citation Context ...eakness is its dependence on the value of oe share , but the idea of using a utility function that is dynamically modified, as in this case, has also been exploited more recently by other researchers =-=[96, 4, 30]-=-. 4.7 Use of the Contact Theorem to Detect Pareto Optimal Solutions Osyczka and Kundu [62] proposed the use of an algorithm based on the contact theorem (one of the main theorems in multiobjective opt... |

21 |
Low implementation cost IIR digital filter design using genetic algorithms
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- 1993
(Show Context)
Citation Context ...s et al. [42] used weights for their genetic operators in order to reflect their effectiveness when a GA was applied to generate hyperstructures from a set of chemical structures. -- Wilson & Macleod =-=[103]-=- used this approach as one of the methods incorporated into a GA to design multiplierless IIR filters in which the two conflicting objectives were to minimize the response error and the implementation... |

20 |
Coupling genetic algorithms and gradient based optimization techniques
- Quagliarella, Vicini
- 1997
(Show Context)
Citation Context ...for the GA. Thus, through a process of running the GA numerous times with different values of the constrained objectives, a trade-off surface can be developed. Applications -- Quagliarella and Vicini =-=[71]-=- suggested the use of this technique coupled with a hybrid GA (a genetic algorithm that used gradient based optimization techniques to speed up the search in order to reduce the computational cost req... |

20 | Evolutionary computation and convergence to a Pareto front
- Veldhuizen, Lamont
- 1998
(Show Context)
Citation Context ...it against other similar techniques. However, these arbitrary goals are not easy to define either. Other (similar) metrics have been proposed in the literature. For example, Van Veldhuizen and Lamont =-=[98]-=- proposed the so-called generational distance, which is a measure of how close is our current Pareto front from the real Pareto front (assuming we know where it lies). Zitzler and Thiele [105] propose... |

19 |
Application of Genetic Algorithms to Task Planning and Learning
- Jakob, Gorges-Schleuter, et al.
- 1992
(Show Context)
Citation Context ... in their fitness function to add or subtract values during the schedule evaluation of a resource scheduler, depending on the existence or absence of penalties (constraints violated). -- Jakob et al. =-=[41]-=- used a weighted sum of the several objectives involved in a task planning problem : to move the tool center point of an industrial robot to a given location as precisely and quickly as possible, avoi... |