IEEE Consumer Electronics Magazine - March/April 2021 - 22

Smart Vehicles

The three algorithms implemented as part of
VESPA are discussed next.
Simulated Annealing þ Greedy Random Adaptive Search Procedure (SA þ GRASP): Simulated
annealing (SA) is a search algorithm that is useful
in finding the global optima when the design space
has multiple local optima.17 The process is analogous to the way metals cool and anneal.18 Typically, SA picks the best solution at each iteration,
but can also pick the worst solution based on a
temperature-dependent probability, which can
allow it to climb out of local minima to arrive at
global minima.19 But SA suffers from the drawback
of behaving like a greedy algorithm at lower temperatures as it tends to accepts only those solution configurations very close in cost function
value to the previous solution, so it can get
stuck in local minima in more complex design
spaces.20 The Greedy Randomized Adaptive
Search Procedure (GRASP) algorithm is another
search algorithm that is used in many exploration
problems,21 but it does not always generate
optimal solutions during the greedy construction
phase and can get stuck in local optima easily.
The SAþGRASP algorithm eliminates the inherent drawbacks of each algorithm. Specifically,
the greedy randomized construction phase of the
algorithm is used to create disturbances in the
existing list of best sensor configurations in our
problem, to generate better solutions. A new solution is generated in each iteration by selecting the
better solution between the greedy solution from
the greedy randomized construction phase and
the configuration found from the local search. We
decreased the SA temperature variable from Tmax
¼ 10 000 to Tmin ¼ 0 at the rate of 4 per iteration.
The search repeats by decreasing SA temperature
till an optimal solution is found or a stopping criterion is achieved.
Genetic Algorithm: The GA is an evolutionary
algorithm that can solve optimization problems
by mimicking the process of natural selection.22 It
repeatedly selects a population of candidate solutions, and then improves the solutions by modifying them. GA has the ability to optimize problems
where the design space is discontinuous and also
if the cost function is nondifferentiable.23 The GA
is adapted for our design space such that a chromosome is defined by the combined location and
orientation of each sensor's configuration

22

(consisting of six parameters: x, y, z, roll, pitch,
and yaw). For a given set of N sensors, the number
of parameters stored in each chromosome is thus
" 6N. " Next, in the selection stage, the cost function
values are computed for 100 configurations at a
time, and a roulette wheel selection method is
used to select which set of chromosomes will be
involved in the crossover step based on their cost
function probability value, computed as a fraction
of the cumulative cost function sum of all chromosomes considered in the selection. In the crossover stage, the crossover parameter is set to 0.5,
which allows 50 out of the 100 chromosomes to
produce offspring. The mutation parameter is set
to 0.2 such that in the mutation stage, the mutation rate is set to 10, which is the number of new
genes allowed for mutation in each iteration.
Particle Swarm Optimization: PSO considers a
group of particles where each particle has a position and velocity and is a solution to the optimization problem.24 In our problem each sensor
configuration in the design space is represented
as a particle having a defined position and velocity. With a random start, the cost function in (5)
evaluates the quality of the solution of a particle.
The particle's velocity and position values are
updated recursively using a linear update.24
Each particle stores a trace of its best position
within the group and globally as well. The history of the cost function values for this trace can
explain the effectiveness of changing the position of a particular sensor from the set of heterogeneous sensors.25 Unlike GA, PSO does not
have any evolution operators like crossovers or
mutation.26 PSO also does not require any binary
encoding of solution configurations as in GA.27
The total number of particles considered were
50, and the importance of personal best and
importance of neighborhood best parameters
were both empirically selected to be 2.

EXPERIMENTS
Experimental Setup
To evaluate our VESPA framework, we consider a scenario with a maximum of eight sensors:
four radars and four camera vision sensors. Many
recent contributions, such as the work presented
in,28 and 29 combine radar and camera modalities
for ADAS applications. We did not include LiDARs

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