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Software testing, test case generation, constraints, search-based testing

Software testing, test case generation, constraints, search-based testing

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    Cpaior13.ppt Cpaior13.ppt Presentation Transcript

    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Constraint-based Fitness Function for Search-based Software Testing Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions Abdelilah Sakti Yann-Ga¨l Gu´h´neuc e e e Gilles Pesant Department of Computer and Software Engineering ´ Ecole Polytechnique de Montr´al, Qu´bec, Canada e e May 21, 2013 CPAIOR, Yorktown Heights Pattern Trace Identification, Detection, and Enhancement in Java SOftware Cost-effective Change and Evolution Research Lab
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions 2 / 14 What is the cost of a programming error ?
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions 2 / 14 What is the cost of a programming error ? Every year inadequate infrastructure software costs the U.S. economy around 60 billion $.
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions 2 / 14 What is the cost of a programming error ? Every year inadequate infrastructure software costs the U.S. economy around 60 billion $. Between 1985 and 1987 : the radiotherapy machine Therac-25 sent to patients a X-ray dose 100 times greater than expected. At least five deaths ; Several other patients were severely affected by radiation.
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions What is the cost of a programming error ? Every year inadequate infrastructure software costs the U.S. economy around 60 billion $. Between 1985 and 1987 : the radiotherapy machine Therac-25 sent to patients a X-ray dose 100 times greater than expected. At least five deaths ; Several other patients were severely affected by radiation. Only a high quality software can reduce errors cost. Testing is an important technique for validating and checking the correctness of software. Despite that the testing may cost more than 50% of the budget of critical software, it remains an inevitable phase in the life cycle of software. 2 / 14
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions 3 / 14 Software testing Formal Methods Is a way of modelling and verifying a software by using mathematics or logic techniques ; Aims to prove and argue that a software respect some properties (e.g., an undesired behaviour will never occur). Some complex programmes are difficult or impossible to model.
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions Software testing Formal Methods Is a way of modelling and verifying a software by using mathematics or logic techniques ; Aims to prove and argue that a software respect some properties (e.g., an undesired behaviour will never occur). Some complex programmes are difficult or impossible to model. Informal or Pragmatic Techniques Performed by executing a real implementation on a small subset of all possible inputs data that satisfies some criteria (e.g., all statements, all branches...) ; Aims to show the presence of errors. 3 / 14
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions Software testing Formal Methods Is a way of modelling and verifying a software by using mathematics or logic techniques ; Aims to prove and argue that a software respect some properties (e.g., an undesired behaviour will never occur). Some complex programmes are difficult or impossible to model. Informal or Pragmatic Techniques Performed by executing a real implementation on a small subset of all possible inputs data that satisfies some criteria (e.g., all statements, all branches...) ; Aims to show the presence of errors. One main challenge is automating inputs data generation. 3 / 14
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions 4 / 14 Search Based Software Testing (SBST)
    • Constraint-based Fitness Function for Search-based Software Testing Search Based Software Testing (SBST) Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Fitness Evaluation Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions The Fitness Evaluation is the core of SBST. 4 / 14
    • Constraint-based Fitness Function for Search-based Software Testing Search Based Software Testing (SBST) Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction What is the cost of a programming error ? Software testing Search Based Software Testing (SBST) Fitness Evaluation Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions The Fitness Evaluation is the core of SBST. An evolution in the fitness evaluation may bring a significant enhancement to SBST 4 / 14
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness Evaluation Conclusions 5 / 14 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target }
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } tinyy == z tinyy > 0 tinyx == 10 Evaluation Conclusions 5 / 14 tinyTarget tinyEND
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } i1 : (10,−30,60) i2 : (30, −20, −20) tinyy == z tinyy > 0 tinyx == 10 Evaluation Conclusions 5 / 14 tinyTarget tinyEND
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } i1 : (10,−30,60) i2 : (30, −20, −20) tinyy == z i1 tinyy > 0 Critical Branch of i1 tinyx == 10 Evaluation Conclusions 5 / 14 tinyTarget tinyEND
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } i1 : (10,−30,60) i2 : (30, −20, −20) tinyy == z i1 tinyy > 0 Critical Branch of i1 tinyx == 10 Evaluation tinyTarget Conclusions tinyEND Test candidate i1 i2 5 / 14 fAL 3 fSE
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } i1 : (10,−30,60) i2 : (30, −20, −20) tinyy == z i1 tinyy > 0 Critical Branch of i1 tinyx == 10 Evaluation tinyTarget Conclusions tinyEND Test candidate i1 i2 5 / 14 fAL 3+ 90 91 fSE
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } i1 : (10,−30,60) i2 : (30, −20, −20) tinyy == z i1 tinyy > 0 Critical Branch of i1 tinyx == 10 Evaluation tinyTarget Conclusions tinyEND Test candidate i1 i2 5 / 14 fAL 3+ 90 91 fSE 90 91
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } i1 : (10,−30,60) i2 : (30, −20, −20) tinyy == z i1 tinyy > 0 Critical Branch of i1 tinyx == 10 Evaluation tinyTarget Conclusions tinyEND Test candidate i1 i2 5 / 14 fAL 3+ 90 91 fSE 90 91 + 31 32
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } i1 : (10,−30,60) i2 : (30, −20, −20) tinyy == z i1 tinyy > 0 Critical Branch of i1 tinyx == 10 Evaluation tinyTarget Conclusions tinyEND Test candidate i1 i2 5 / 14 fAL 3+ 90 91 90 91 + 31 32 fSE +0
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } i1 : (10,−30,60) i2 : (30, −20, −20) tinyy == z i1 tinyy > 0 i2 Critical Branch of i1 tinyx == 10 Evaluation tinyTarget Conclusions tinyEND Test candidate i1 i2 5 / 14 fAL 90 3+ 91 = 3.9890 2 + 21 =2.9545 22 fSE 31 + 32 +0= 1.9577 + 21 + 20 =1.9068 22 21 90 91 0
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Motivating Example tinyx, y, z 1 2 Introduction 3 Motivating Example 5 Fitness Function Based on Branch Hardness 4 6 int sample(int x,int y,int z){ if(y==z) if(y>0) if(x==10) ...//Target } i1 : (10,−30,60) i2 : (30, −20, −20) tinyy == z i1 tinyy > 0 i2 Critical Branch of i1 tinyx == 10 Evaluation tinyTarget Conclusions tinyEND Test candidate i1 i2 5 / 14 fAL 90 3+ 91 = 3.9890 2 + 21 =2.9545 22 fSE 31 + 32 +0= 1.9577 + 21 + 20 =1.9068 22 21 90 91 0 Both fitness functions favour i2 over i1 because either they do not consider non-executed branches or they ignore some branches’ future.
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions 6 / 14 Fitness Function Based on Branch Hardness Combines SBST with static analysis of the non-executed branches. Prioritizes branches according to how hard it is to satisfy them.
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions 6 / 14 Fitness Function Based on Branch Hardness Combines SBST with static analysis of the non-executed branches. Prioritizes branches according to how hard it is to satisfy them. Defines the difficulty to satisfy a constraint in terms of its arity and its projection tightness (the ratio of the approximate number of solutions to the size of its search space).
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions 6 / 14 Fitness Function Based on Branch Hardness Combines SBST with static analysis of the non-executed branches. Prioritizes branches according to how hard it is to satisfy them. Defines the difficulty to satisfy a constraint in terms of its arity and its projection tightness (the ratio of the approximate number of solutions to the size of its search space). 1. The lower the arity of the constraint, the less freedom we have to choose some of its variables in order to evolve the test candidate.
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions 6 / 14 Fitness Function Based on Branch Hardness Combines SBST with static analysis of the non-executed branches. Prioritizes branches according to how hard it is to satisfy them. Defines the difficulty to satisfy a constraint in terms of its arity and its projection tightness (the ratio of the approximate number of solutions to the size of its search space). 1. The lower the arity of the constraint, the less freedom we have to choose some of its variables in order to evolve the test candidate. 2. A projection tightness close to 0 will indicate high constrainedness and hardness to satisfy a constraint.
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions 7 / 14 Branch-Hardness Metrics Difficulty Coefficient (DC) DC is a possible representation of the hardness of a branch ; Each constraint has its own DC that is determined according to its arity and tightness ; DC(c) = B 2 · 1 arityc + B · (1 − tightness) + 1 .
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Branch-Hardness Metrics Difficulty Coefficient (DC) DC is a possible representation of the hardness of a branch ; Each constraint has its own DC that is determined according to its arity and tightness ; DC(c) = B 2 · 1 arityc + B · (1 − tightness) + 1 . Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions Difficulty Level (DL) DL is based on DC ranking (r) ; DL is a representation of a relative hardness level of a constraint in a set of constraints ; DL(c, C) = 7 / 14 |C|, 2r−1 · (|C| + 1), if r = 0 . if r > 0
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions 8 / 14 Branch-Hardness Fitness Functions DC Fitness Function (fDC ) DC is used as a penalty coefficient for breaking a constraint ; The target of this fitness function is determining a standard-branch-distance. fDC (i, C) = c∈C DC(c) · η(i, c) .
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Branch-Hardness Fitness Functions DC Fitness Function (fDC ) DC is used as a penalty coefficient for breaking a constraint ; The target of this fitness function is determining a standard-branch-distance. fDC (i, C) = c∈C DC(c) · η(i, c) . Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions DL Fitness Function (fDL ) DL is used as a constant penalty for breaking a constraint in a set of constraints to satisfy ; fDL (i, C) = where (i, c) = 8 / 14 c∈C (i, c) + η(i, c), 0, if η(i, c) = 0 . DL(c, C), if η(i, c) = 0
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions 9 / 14 Applying fDC on our motivating example Assume that all domains are equal to [−99, 100]. DC for each branch 1. DC(”y == z”) = 102 · 0.5 + 10 · 0.995 + 1 = 60.95 ; 2. DC(”y > 0”) = 102 · 1 + 10 · 0.5 + 1 = 106 ; 3. DC(”x == 10”) = 102 · 1 + 10 · 0.995 + 1 = 110.95.
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Applying fDC on our motivating example Assume that all domains are equal to [−99, 100]. DC for each branch 1. DC(”y == z”) = 102 · 0.5 + 10 · 0.995 + 1 = 60.95 ; 2. DC(”y > 0”) = 102 · 1 + 10 · 0.5 + 1 = 106 ; 3. DC(”x == 10”) = 102 · 1 + 10 · 0.995 + 1 = 110.95. Overview Branch-Hardness Metrics Branch-Hardness Fitness Functions Applying fDC on our motivating example Evaluation Conclusions (fDC ) for each test candidate 90 fDC (i1 , C) = 60.95· 91 +106· 31 +110.95· 0 = 162.9677 ; 32 1 fDC (i2 , C) = 60.95· 0 +106· 21 +110.95· 20 = 206.8485. 1 22 21 Contrary to fAL and fSE this fitness function makes the adequate choice by choosing the test candidate i1 instead of i2 . 9 / 14
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Evaluation Subjects and configuration EA Results SA Results Conclusions 10 / 14 Evaluation Subjects and configuration analysed meta-heuristics and fitness functions Two widely used meta-heuristic algorithms are analysed : Simulated Annealing (SA) and Evolutionary Algorithm (EA). fAL and fSE from the literature ; fSEL a natural combination of fAL and fSE ; Our fitness functions fDC and fDL .
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Evaluation Subjects and configuration EA Results SA Results Conclusions Evaluation Subjects and configuration analysed meta-heuristics and fitness functions Two widely used meta-heuristic algorithms are analysed : Simulated Annealing (SA) and Evolutionary Algorithm (EA). fAL and fSE from the literature ; fSEL a natural combination of fAL and fSE ; Our fitness functions fDC and fDL . Subjects 440 synthetic test targets that were randomly generated. 20 executions for every combination of fitness function and meta-heuristic algorithm. If test data was not found after 25000 (respectively 100000) fitness evaluations for EA (respectively SA), the search was terminated. 10 / 14
    • Constraint-based Fitness Function for Search-based Software Testing Evaluation EA Results Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant EA: Comparing all fitnesses on 440 test targets Approach Level Symbolic Enhanced Symbolic Enhanced with levels Difficulty Coefficient Difficulty Level Introduction Motivating Example Fitness Function Based on Branch Hardness 80 60 Evaluation Subjects and configuration EA Results 40 SA Results Conclusions 20 0 0 5000 10000 15000 Evaluations 11 / 14 20000 25000
    • Constraint-based Fitness Function for Search-based Software Testing Evaluation SA Results Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant SA: Comparing all fitnesses on 440 test targets Approach Level Symbolic Enhanced Symbolic Enhanced with levels Difficulty Coefficient Difficulty Level Introduction 80 Fitness Function Based on Branch Hardness Evaluation Subjects and configuration EA Results SA Results Conclusions Branch Coverage % Motivating Example 60 40 20 0 0e+00 2e+04 4e+04 6e+04 Evaluations 12 / 14 8e+04 1e+05
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions 13 / 14 Conclusions Two new metrics to measure the difficulty to satisfy a constraint in the context of test case generation for software testing are defined ; Two new fitness functions for SBST are defined ; Our new fitness functions are significantly more effective and efficient than with the largely used fitness functions from the literature. The obtained results are promising but more experiments must be performed.
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions Conclusions Two new metrics to measure the difficulty to satisfy a constraint in the context of test case generation for software testing are defined ; Two new fitness functions for SBST are defined ; Our new fitness functions are significantly more effective and efficient than with the largely used fitness functions from the literature. The obtained results are promising but more experiments must be performed. Future work Performing more experiments on real world programs ; Extending our approach by defining new ways to compute projection tightness for constraints involving other data types than integer. 13 / 14
    • Constraint-based Fitness Function for Search-based Software Testing Abdelilah Sakti, Yann-Ga¨l e Gu´h´neuc, Gilles e e Pesant Introduction Motivating Example Fitness Function Based on Branch Hardness Evaluation Conclusions 14 / 14 Thank you Questions ?